U.S. patent application number 09/748189 was filed with the patent office on 2002-03-14 for method of evaluating deteriorated state of catalytic converter for purifying exhaust gas.
This patent application is currently assigned to HONDA GIKEN KOGYO KABUSHIKI KAISHA. Invention is credited to Akazaki, Shusuke, Iwaki, Yoshihisa, Ueno, Masaki.
Application Number | 20020029561 09/748189 |
Document ID | / |
Family ID | 18500383 |
Filed Date | 2002-03-14 |
United States Patent
Application |
20020029561 |
Kind Code |
A1 |
Ueno, Masaki ; et
al. |
March 14, 2002 |
Method of evaluating deteriorated state of catalytic converter for
purifying exhaust gas
Abstract
The values of parameters of a model of an object exhaust system
including a catalytic converter are identified from the data of
outputs from an air-fuel ratio sensor and an O.sub.2 sensor which
are disposed respectively upstream and downstream of the catalytic
converter while an internal combustion engine associated with the
catalytic converter is in operation. A deterioration evaluating
parameter representing the degree of variation of time-series data
of the identified parameters is determined from the time-series
data of the identified parameters. The deteriorated state of the
catalytic converter is evaluated based on the deterioration
evaluating parameter.
Inventors: |
Ueno, Masaki; (Wako-shi,
JP) ; Iwaki, Yoshihisa; (Wako-shi, JP) ;
Akazaki, Shusuke; (Wako-shi, JP) |
Correspondence
Address: |
ARENT FOX KINTNER PLOTKIN & KAHN, PLLC
Suite 600
1050 Connecticut Avenue, N.W.
Washington
DC
20036-5339
US
|
Assignee: |
HONDA GIKEN KOGYO KABUSHIKI
KAISHA
|
Family ID: |
18500383 |
Appl. No.: |
09/748189 |
Filed: |
December 27, 2000 |
Current U.S.
Class: |
60/277 ; 60/274;
60/285 |
Current CPC
Class: |
F01N 11/007 20130101;
F01N 2550/02 20130101; F01N 2900/0422 20130101; Y02T 10/40
20130101; Y02T 10/47 20130101 |
Class at
Publication: |
60/277 ; 60/274;
60/285 |
International
Class: |
F01N 003/00; F01N
007/00 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 28, 1999 |
JP |
372400/11 HEISEI |
Claims
What is claimed is:
1. A method of evaluating a deteriorated state of a catalytic
converter for purifying an exhaust gas produced when an air-fuel
mixture is combusted, comprising the steps of: supplying the
exhaust gas downstream to an exhaust passage which has a first
exhaust gas sensor and a second exhaust gas sensor that are
disposed respectively upstream and downstream of the catalytic
converter, for generating respective outputs depending on
components of the exhaust gas; detecting data of the outputs of
said first exhaust gas sensor and said second exhaust gas sensor
when the exhaust gas is supplied to said exhaust passage;
sequentially identifying the value of at least one parameter to be
set of a model that is constructed as representing a behavior of an
object exhaust system which ranges from said first exhaust gas
sensor to said second exhaust gas sensor and includes said
catalytic converter in said exhaust passage, based on the detected
data of the outputs of said first exhaust gas sensor and said
second exhaust gas sensor; and determining data representing a
degree of variation of time-series data of the identified value of
the parameter of said model, as a deterioration evaluating
parameter, from the time-series data of said identified value, and
evaluating a deteriorated state of said catalytic converter based
on the determined deterioration evaluating parameter.
2. A method according to claim 1, wherein said first exhaust gas
sensor comprises a sensor for producing an output representing the
air-fuel ratio of said air-fuel mixture from which the exhaust gas
entering said catalytic converter is produced, and said second
exhaust gas sensor comprises a sensor for producing an output
representing the content of a particular component of the exhaust
gas that has passed through said catalytic converter.
3. A method according to claim 1, wherein said catalytic converter
comprises a catalytic converter disposed in the exhaust passage of
an internal combustion engine which combusts said air-fuel mixture
therein.
4. A method according to claim 2, wherein said catalytic converter
comprises a catalytic converter disposed in the exhaust passage of
an internal combustion engine which combusts said air-fuel mixture
therein.
5. A method according to claim 4, further comprising the step of:
controlling the air-fuel ratio of said internal combustion engine
in order to converge the output of said second exhaust gas sensor
to a predetermined target value when the exhaust gas is supplied to
said exhaust passage upon operation of said internal combustion
engine; wherein said value of the parameter is identified and said
deteriorated state of said catalytic converter is evaluated
concurrent with said step of controlling the air-fuel ratio of said
internal combustion engine.
6. A method according to claim 5, wherein said step of controlling
the air-fuel ratio of said internal combustion engine comprises the
steps of: calculating a target air-fuel ratio of said internal
combustion engine in order to converge the output of said second
exhaust gas sensor to said target value; and controlling the
air-fuel ratio of said internal combustion engine according to a
feedback control process in order to converge the air-fuel ratio
represented by the output of said first exhaust gas sensor to said
target air-fuel ratio.
7. A method according to claim 6, wherein said target air-fuel
ratio is calculated by a sliding mode controller.
8. A method according to claim 6, wherein said target air-fuel
ratio is calculated by an algorithm determined in advance using the
identified data of said parameter.
9. A method according to claim 6, wherein the air-fuel ratio of
said internal combustion engine is controlled according to the
feedback control process by a recursive-type controller.
10. A method according to claim 1, wherein said model comprises a
model expressing said object exhaust system as a discrete-time
system for generating the output of said second exhaust gas sensor
from the output of said first exhaust gas sensor via a response
delay element and/or a dead time element, and includes, as said
parameter, at least one of a coefficient relative to the output of
said first exhaust gas sensor and a coefficient relative to the
output of said second exhaust gas sensor.
11. A method according to claim 10, wherein said parameter includes
the coefficient relative to the output of said first exhaust gas
sensor, and said step of evaluating the deteriorated state of said
catalytic converter comprises the step of: evaluating the
deteriorated state of said catalytic converter based on said
deterioration evaluating parameter determined from time-series data
of the identified value of the coefficient relative to the output
of said first exhaust gas sensor.
12. A method according to claim 10 or 11, wherein said step of
sequentially identifying the value of said parameter comprises the
steps of: sequentially identifying the value of said parameter
according to an algorithm for sequentially updating and identifying
the value bf said parameter in order to minimize an error between
the output of said second exhaust gas sensor in said model and an
actual output of said second exhaust gas sensor; and filtering the
output of said second exhaust gas sensor in said model and the
actual output of said second exhaust gas sensor with the same
frequency passing characteristics in calculating said error.
13. A method according to claim 10 or 11, wherein said step of
sequentially identifying the value of said parameter comprises the
step of: sequentially identifying the value of said parameter
depending on a particular behavior of said object exhaust
system.
14. A method according to claim 13, wherein said step of
sequentially identifying the value of said parameter comprises the
step of: recognizing the particular behavior of said object exhaust
system based on the value of a function that is determined by a
predetermined number of time-series data prior to the present of
the output of said second exhaust gas sensor.
15. A method according to claim 1 or 11, wherein said step of
sequentially identifying the value of said parameter comprises the
step of: limiting the identified value of said parameter.
16. A method according to claim 1 or 11, wherein said step of
sequentially identifying the value of said parameter comprises the
step of: calculating the identified value of said parameter based
on the difference between an actual output of said first exhaust
gas sensor and a predetermined reference value and the difference
between an actual output of said second exhaust gas sensor and a
predetermined reference value, which differences are used as the
data of the outputs of said first and second exhaust gas
sensors.
17. A method according to claim 1 or 11, wherein said step of
evaluating the deteriorated state of said catalytic converter
comprises the steps of: determining a central value of the
identified value of said parameter by effecting a low-pass
filtering process on the time-series data of the identified value
of said parameter; and determining said deterioration evaluating
parameter from the difference between said central value and each
of the time-series data of the identified value of said
parameter.
18. A method according to claim 17, wherein said low-pass filtering
process comprises a filtering process according to a sequential
statistical algorithm.
19. A method according to claim 17, wherein said step of evaluating
the deteriorated state of said catalytic converter comprises the
step of: determining said deterioration evaluating parameter by
effecting a low-pass filtering process on the square or absolute
value of the difference between said central value and each of the
time-series data of the identified value of said parameter.
20. A method according to claim 19, wherein said low-pass filtering
process comprises a filtering process according to a sequential
statistical algorithm.
21. A method according to claim 1 or 11, further comprising the
step of: determining whether the exhaust gas is supplied to said
exhaust passage at a substantially constant rate or not; wherein
said step of evaluating the deteriorated state of said catalytic
converter comprises the step of: preventing said deterioration
evaluating parameter from being determined using data of the
identified value if it is determined that the exhaust gas is
supplied to said exhaust passage at the substantially constant
rate.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a method of evaluating a
deteriorated state of a catalytic converter for purifying an
exhaust gas, such as a catalytic converter for use on an automobile
or a hybrid vehicle.
[0003] 2. Description of the Related Art
[0004] Conventional processes of determining the deteriorated state
of a catalytic converter for purifying exhaust gases produced when
an air-fuel mixture is combusted, e.g., a catalytic converter
disposed in the exhaust passage of an internal combustion engine,
are known from Japanese patent publication No. 2,526,640 and
Japanese laid-open patent publication No. 7-19033, for example.
[0005] The disclosed techniques are based on the fact that when the
air-fuel ratio of an air-fuel mixture to be combusted by an
internal combustion engine is changed from a leaner value to a
richer value or from a richer value to a leaner value, the outputs
from oxygen concentration sensors that are positioned respectively
upstream and downstream of a catalytic converter combined with the
internal combustion engine are inverted. More specifically, under
certain operating conditions of the internal combustion engine,
i.e., when the power output of the internal combustion engine is
increased or the fuel supplied to the internal combustion engine is
cut off as disclosed in Japanese patent publication No. 2,526,640
or when certain conditions are satisfied, e.g., the load and
rotational speed of the internal combustion engine are in
predetermined ranges as disclosed in Japanese laid-open patent
publication No. 7-19033, the air-fuel ratio is positively changed
from a leaner value to a richer value or from a richer value to a
leaner value. At this time, the time consumed after the output of
the upstream oxygen concentration sensor is inverted until the
output of the downstream oxygen concentration sensor is inverted,
and the period at which the output of the downstream oxygen
concentration sensor is inverted are measured, and the deteriorated
state of the catalytic converter is evaluated based on the measured
values.
[0006] According to these techniques, when the internal combustion
engine is operating under ordinary conditions, i.e., conditions
without determining the deteriorated state of the catalytic
converter, the air-fuel ratio is feedback-controlled depending on
the inversion of the outputs from the oxygen concentration sensors
in order to keep the air-fuel ratio of the internal combustion
engine in the vicinity of a stoichiometric air-fuel ratio, for
thereby allowing the catalytic converter to keep an appropriate
purifying capability.
[0007] However, the above processes of evaluating the deteriorated
state of the catalytic converter have suffered the following
difficulties:
[0008] In order to determine the deteriorated state of the
catalytic converter, the air-fuel ratio of the internal combustion
engine needs to be positively changed to a leaner value or a richer
value. Therefore, while the air-fuel ratio of the internal
combustion engine is being feedback-controlled in order to allow
the catalytic converter to keep an appropriate purifying
capability, it is not possible to determine the deteriorated state
of the catalytic converter. When the deteriorated state of the
catalytic converter is determined, it is difficult to keep an
appropriate purifying capability of the catalytic converter.
[0009] According to the conventional processes, the operating state
of the internal combustion engine which is capable of determining
the deteriorated state of the catalytic converter or the state in
which exhaust gases are generated by the internal combustion engine
in that operating state is limited to a certain special state.
Specifically, according to the process disclosed in Japanese patent
publication No. 2,526,640, the deteriorated state of the catalytic
converter can be determined only if the output of the downstream
O.sub.2 sensor is produced in a leaner air-fuel ratio range when
the output power of the internal combustion engine is to be
increased and at the time of starting to increase the output power
of the internal combustion engine, and only if the output of the
downstream O.sub.2 sensor is produced in a richer air-fuel ratio
range when the supply of fuel to the internal combustion engine is
to be cut off and at the time of cutting off the supply of fuel to
the internal combustion engine.
[0010] According to the process disclosed in Japanese laid-open
patent publication No. 7-19033, the deteriorated state of the
catalytic converter can be determined only if the load (represented
by the intake air rate, the throttle valve opening, the fuel
injection quantity, and the intake air pressure) and the rotational
speed of the internal combustion engine fall in a predetermined
range, the intake air temperature is equal to or higher than a
preset value, and the load of the internal combustion engine varies
by an amount equal to or greater than a preset value. Therefore, if
the internal combustion engine which generates exhaust gases to be
supplied to the catalytic converter, which may be disposed in the
exhaust passage of the internal combustion engine, operates in
various operating states or the exhaust gases are generated in
various states, then there are not many opportunities to be able to
determine the deteriorated state of the catalytic converter, and
the reliability of the determined deteriorated state of the
catalytic converter under such conditions is low.
[0011] The applicant of the present application has proposed a
system having a first exhaust gas sensor disposed upstream of a
catalytic converter for generating an output representing the
air-fuel ratio of an air-fuel mixture combusted by an internal
combustion engine, and a second exhaust gas sensor disposed
downstream of the catalytic converter for generating an output
representing the concentration of a certain component of exhaust
gases, e.g., the concentration of oxygen, the system being arranged
to control the air-fuel ratio of the internal combustion engine
according to a feedback control process to achieve an optimum
purifying capability of the catalytic converter based on outputs
from the sensors (see Japanese laid-open patent publication No.
9-324681 and U.S. Pat. No. 5,852,930 and Japanese laid-open patent
publication No. 11-93740 and U.S. Pat. No. 6,079,205).
[0012] The proposed system determines a target air-fuel ratio for
the internal combustion engine to cause the output (the detected
value of the oxygen concentration) of the second exhaust gas sensor
to have a given constant value, and feedback-controls the air-fuel
ratio of the internal combustion engine to converge the output (the
detected value of the air-fuel ratio) of the first exhaust gas
sensor to the target air-fuel ratio, for thereby achieving the
optimum purifying capability of the catalytic converter.
[0013] Since the system can stably achieve the optimum purifying
capability of the catalytic converter according to the above
air-fuel ratio control process, it is desirable to be able to
evaluate the deteriorated state of the catalytic converter while
performing the air-fuel ratio control process.
SUMMARY OF THE INVENTION
[0014] It is therefore an object of the present invention to
provide a method capable of appropriately evaluating a deteriorated
state of a catalytic converter for purifying an exhaust gas in
various states in which an exhaust gas to be purified by the
catalytic converter is generated or in various states in which an
internal combustion engine that generates the exhaust gas is
operated.
[0015] Another object of the present invention is to provide a
method capable of appropriately evaluating a deteriorated state of
a catalytic converter for purifying an exhaust gas while
maintaining a desired purifying capability of the catalytic
converter which is disposed in the exhaust passage of an internal
combustion engine.
[0016] To achieve the above objects, there is provided in
accordance with the present invention a method of evaluating a
deteriorated state of a catalytic converter for purifying an
exhaust gas produced when an air-fuel mixture is combusted,
comprising the steps of supplying the exhaust gas downstream to an
exhaust passage which has a first exhaust gas sensor and a second
exhaust gas sensor that are disposed respectively upstream and
downstream of the catalytic converter, for generating respective
outputs depending on components of the exhaust gas, detecting data
of the outputs of the first exhaust gas sensor and the second
exhaust gas sensor when the exhaust gas is supplied to the exhaust
passage, sequentially identifying the value of at least one
parameter to be set of a model that is constructed as representing
a behavior of an object exhaust system which ranges from the first
exhaust gas sensor to the second exhaust gas sensor and includes
the catalytic converter in the exhaust passage, based on the
detected data of the outputs of the first exhaust gas sensor and
the second exhaust gas sensor, and determining data representing a
degree of variation of time-series data of the identified value of
the parameter of the model, as a deterioration evaluating
parameter, from the time-series data of the identified value, and
evaluating a deteriorated state of the catalytic converter based on
the determined deterioration evaluating parameter.
[0017] Studies made by the inventors indicate that a model
expressing the behavior of the object exhaust system including the
catalytic converter and ranging from the first exhaust gas sensor
to the second exhaust gas sensor is constructed, and when the value
of the parameter to be set, i.e., the parameter to be set to a
certain value in defining the behavior of the model, is
sequentially identified based on the data of the output of the
exhaust gas sensors that are acquired while the exhaust gas is
being supplied to the exhaust passage, the time-series data of the
identified value of the parameter exhibits a certain characteristic
tendency against the deteriorated state of the catalytic converter.
Specifically, if the deterioration of the catalytic converter is
small, the time-series data of the identified value of the
parameter varies to a small extent, and if the deterioration of the
catalytic converter becomes larger, the time-series data of the
identified value of the parameter varies to a relatively large
extent. Therefore, as the deterioration of the catalytic converter
progresses, the variation of the identified value of the parameter
of the model tends to become larger. This is considered to be due
to the fact that the matching between the model of the object
exhaust system and the actual behavior of the object exhaust system
is lowered as the deterioration of the catalytic converter
progresses.
[0018] According to the present invention, in evaluating the
deterioration of the catalytic converter, the data representing the
degree of variation of time-series data of the identified value of
the parameter of the model is determined as the deterioration
evaluating parameter from the time-series data of the identified
value, and the deteriorated state of the catalytic converter is
determined based on the determined deterioration evaluating
parameter.
[0019] Preferably, the first exhaust gas sensor comprises a sensor
for producing an output representing the air-fuel ratio of the
air-fuel mixture from which the exhaust gas entering the catalytic
converter is produced, and the second exhaust gas sensor comprises
a sensor for producing an output representing the content of a
particular component of the exhaust gas that has passed through the
catalytic converter.
[0020] When the value of the parameter of the model of the object
exhaust system which employs the above sensors as the first and
second exhaust gas sensors are identified based on the data of the
outputs of the first and second exhaust gas sensors at the time the
exhaust gas is supplied to the exhaust passage, the above tendency
of the identified value against the deteriorated state of the
catalytic converter tends to appear relatively easily. Therefore,
it is easy to evaluate the deteriorated state of the catalytic
converter based on the deterioration evaluating parameter which
represents the degree of variation of time-series data of the
identified value of the parameter.
[0021] Since it is possible to evaluate the deteriorated state of
the catalytic converter when the exhaust gas to be supplied to the
catalytic converter is generated in various states or the internal
combustion engine operates in various operating states, the
catalytic converter is preferably disposed in the exhaust passage
of the internal combustion engine which combusts the air-fuel
mixture therein.
[0022] If the first exhaust gas sensor comprises a sensor for
producing an output representing the air-fuel ratio of the air-fuel
mixture, and the second exhaust gas sensor comprises a sensor for
producing an output representing the content of a particular
component of the exhaust gas that has passed through the catalytic
converter, then the method preferably further comprising the step
of controlling the air-fuel ratio of the internal combustion engine
in order to converge the output of the second exhaust gas sensor to
a predetermined target value when the exhaust gas is supplied to
the exhaust passage upon operation of the internal combustion
engine, wherein the value of the parameter is identified and the
deteriorated state of the catalytic converter is evaluated
concurrent with the step of controlling the air-fuel ratio of the
internal combustion engine.
[0023] By controlling the air-fuel ratio of the internal combustion
engine, or more specifically the air-fuel ratio of the air-fuel
mixture combusted in the internal combustion engine, to converge
the output of the second exhaust gas sensor which represents the
content of the particular component of the exhaust gas having pass
through the catalytic converter, it is possible to achieve a
desired purifying capability of the catalytic converter for
purifying the exhaust gas emitted from the internal combustion
engine. When the value of the parameter is identified and the
deteriorated state of the catalytic converter is evaluated
concurrent with the step of controlling the air-fuel ratio of the
internal combustion engine, the deteriorated state of the catalytic
converter can be evaluated while maintaining the desired purifying
capability of the catalytic converter during operation of the
internal combustion engine.
[0024] If an oxygen concentration sensor (O.sub.2 sensor) is used
as the second exhaust gas sensor, then an optimum purifying
capability of the catalytic converter is achieved by controlling
the air-fuel ratio of the internal combustion engine to keep the
output of the sensor at a given constant level.
[0025] The step of controlling the air-fuel ratio of the internal
combustion engine preferably comprises the steps of calculating a
target air-fuel ratio of the internal combustion engine in order to
converge the output of the second exhaust gas sensor to the target
value, and controlling the air-fuel ratio of the internal
combustion engine according to a feedback control process in order
to converge the air-fuel ratio represented by the output of the
first exhaust gas sensor to the target air-fuel ratio.
[0026] By thus controlling the air-fuel ratio of the internal
combustion engine, the air-fuel ratio detected by the first exhaust
gas sensor can stably be controlled at an air-fuel ratio suitable
to achieve the desired purifying capability of the catalytic
converter, i.e., the target air-fuel ratio. Since the air-fuel
ratio of the internal combustion engine is stably controlled, the
behavior of the data of the outputs of the first and second exhaust
gas sensors which are used to identify the value of the parameter
is made smooth. As a result, the effect of disturbances other than
the deteriorated state of the catalytic converter on the identified
value of the parameter is reduced. Consequently, the deteriorated
state of the catalytic converter can appropriately be evaluated
based on the deterioration evaluating parameter which represents
the degree of variation of time-series data of the identified value
of the parameter.
[0027] While the target air-fuel ratio can be calculated using a
PID controller, it is preferably calculated by a sliding mode
controller.
[0028] Specifically, the sliding mode controller is advantageous in
that it is more resistant to disturbances than the PID controller.
The target air-fuel ratio calculated by the sliding mode controller
makes stable the process of controlling the air-fuel ratio. As a
result, the desired purifying capability of the catalytic converter
can be achieved more reliably. At the same time, because the effect
of disturbances other than the deteriorated state of the catalytic
converter on the identified value of the parameter is minimized,
the deterioration evaluating parameter which represents the degree
of variation of time-series data of the identified value of the
parameter is made reliable as being highly correlated to the
deteriorated state of the catalytic converter. Thus, the
deteriorated state of the catalytic converter can be evaluated more
adequately based on the deterioration evaluating parameter.
[0029] In controlling the air-fuel ratio of the internal combustion
engine concurrent with evaluating the deteriorated state of the
catalytic converter, the target air-fuel ratio is preferably
calculated by an algorithm determined in advance using the
identified data of the parameter.
[0030] Specifically, since the identified value of the parameter
reflects the actual behavioral characteristics of the object
exhaust system, when the target air-fuel ratio for converging the
output of the second exhaust gas sensor to the target value is
calculated using the identified value, the accuracy of the target
air-fuel ratio is increased. As a consequence, the desired
purifying capability of the catalytic converter can be achieved
more reliably.
[0031] While the air-fuel ratio of the internal combustion engine
can be feedback-controlled by a PID controller, it is preferably
controlled by a recursive-type controller.
[0032] When the air-fuel ratio of the internal combustion engine is
feedback-controlled by a recursive-type controller, or specifically
an adaptive controller, it is possible to feedback-control the
air-fuel ratio detected by the first exhaust gas sensor more
accurately at the target air-fuel ratio while suppressing the
effect of characteristic changes of the internal combustion engine
than if a PID controller is used. The desired purifying capability
of the catalytic converter can be achieved more reliably, and the
reliability of the deterioration evaluating parameter which
represents the degree of variation of time-series data of the
identified value of the parameter is increased, so that the
deteriorated state of the catalytic converter can be evaluated more
adequately based on the deterioration evaluating parameter.
[0033] The recursive-type controller determines a new manipulated
variable according to a given recursive formula including
time-series data in the past prior to the present of a manipulated
variable for the air-fuel ratio of the internal combustion engine,
or more specifically a manipulated variable for the fuel supply
quantity of the internal combustion engine, for example, in order
to converge the air-fuel ratio represented by the output of the
first exhaust gas sensor to the target air-fuel ratio, and controls
the air-fuel ratio of the internal combustion engine with the
manipulated variable.
[0034] The model comprises a model expressing the object exhaust
system as a discrete-time system for generating the output of the
second exhaust gas sensor from the output of the first exhaust gas
sensor via a response delay element and/or a dead time element, and
includes, as the parameter, at least one of a coefficient relative
to the output of the first exhaust gas sensor and a coefficient
relative to the output of the second exhaust gas sensor.
[0035] The model mathematically expresses the output of the second
exhaust gas sensor in each control cycle with the outputs of the
second exhaust gas sensor and the first exhaust gas sensor in a
past control cycle and coefficients of the outputs of the sensors.
The output of the second exhaust gas sensor in the past control
cycle corresponds to the response delay element. When the output of
the first exhaust gas sensor in a control cycle prior to the dead
time of the object exhaust system is used as the output of the
first exhaust gas sensor in the above model, it corresponds to the
dead time element.
[0036] By thus constructing the model of the object exhaust system
and the values of the coefficients used in the model as the
parameter are identified based on the data of the outputs of the
first and second exhaust gas sensors, the identified value of the
parameter (coefficients) of the model accurately reflects the
actual behavioral characteristics of the catalytic converter
included in the exhaust system. As a result, the reliability of the
deterioration evaluating parameter which represents the degree of
variation of time-series data of the identified value of the
parameter is achieved as the deterioration evaluating parameter is
correlated to the deteriorated state of the catalytic converter.
Therefore, the deteriorated state of the catalytic converter can be
evaluated adequately based on the deterioration evaluating
parameter. By modeling the object exhaust system as a discrete time
system, the value of the parameter (coefficients) can be identified
on a real-time basis.
[0037] With the object exhaust system being thus modeled, the
parameter preferably includes the coefficient relative to the
output of the first exhaust gas sensor, and the step of evaluating
the deteriorated state of the catalytic converter preferably
comprises the step of evaluating the deteriorated state of the
catalytic converter based on the deterioration evaluating parameter
determined from time-series data of the identified value of the
coefficient relative to the output of the first exhaust gas
sensor.
[0038] Specifically, when the identified value of the coefficients
relative to the output of the first exhaust gas sensor and the
identified value of the coefficients relative to the output of the
second exhaust gas sensor are compared with each other, the
time-series data of the former identified value exhibits the above
tendency against the deteriorated state of the catalytic converter
more than the time-series data of the latter identified value.
Therefore, the deteriorated state of the catalytic converter can be
evaluated more adequately based on the deterioration evaluating
parameter that is determined from the time-series data of the
identified value of the coefficients relative to the output of the
first exhaust gas sensor.
[0039] With the object exhaust system being thus modeled, the step
of sequentially identifying the value of the parameter comprises
the steps of sequentially identifying the value of the parameter
according to an algorithm for sequentially updating and identifying
the value of the parameter in order to minimize an error between
the output of the second exhaust gas sensor in the model and an
actual output of the second exhaust gas sensor, and filtering the
output of the second exhaust gas sensor in the model and the actual
output of the second exhaust gas sensor with the same frequency
passing characteristics in calculating the error.
[0040] It is thus possible to identify the value of the parameter
(coefficients) in a manner to cause the frequency characteristics
of the actual object exhaust system including the catalytic
converter and the model, or more specifically the frequency
characteristics of changes of the output of the second exhaust gas
sensor (corresponding to the output of the model) with respect to
changes of the output of the first exhaust gas sensor
(corresponding to the input of the model), to match each other.
Thus, the identified value of the parameter is highly reliable as
reflecting the behavioral characteristics of the object exhaust
system including the catalytic converter. Therefore, the
deteriorated state of the catalytic converter can be evaluated more
adequately based on the deterioration evaluating parameter which
represents the degree of variation of the timeseries data of the
identified value.
[0041] The step of sequentially identifying the value of the
parameter preferably comprises the step of sequentially identifying
the value of the parameter depending on a particular behavior of
the object exhaust system.
[0042] Depending on the behavior of the object exhaust system, the
identified value of the parameter may lack reliability. By
identifying the value of the parameter in a certain behavior of the
object exhaust system, i.e., a behavior in which air-fuel ratio of
the air-fuel mixture recognized by the oxygen concentration in the
exhaust gas changes from a leaner value to a richer value, the
identified value of the parameter is made highly reliable as
reflecting the behavioral characteristics of the object exhaust
system. Thus, the reliability of the evaluation of the deteriorated
state of the catalytic converter based on the deterioration
evaluating parameter which represents the degree of variation of
the time-series data of the identified value is increased.
[0043] The step of sequentially identifying the value of the
parameter preferably comprises the step of recognizing the
particular behavior of the object exhaust system based on the value
of a function that is determined by a predetermined number of
time-series data prior to the present of the output of the second
exhaust gas sensor.
[0044] The step of sequentially identifying the value of the
parameter preferably comprises the step of limiting the identified
value of the parameter.
[0045] The above process makes it possible to prevent the value of
the parameter from being unduly identified due to a disturbance
other than the deteriorated state of the catalytic converter. As a
result, the reliability of the evaluation of the deteriorated state
of the catalytic converter based on the deterioration evaluating
parameter is increased. As the identified value is prevented from
being determined as a noisy value, the stability of the process of
controlling the air-fuel ratio of the internal combustion engine
using the identified value is increased.
[0046] The step of sequentially identifying the value of the
parameter preferably comprises the step of calculating the
identified value of the parameter based on the difference between
an actual output of the first exhaust gas sensor and a
predetermined reference value and the difference between an actual
output of the second exhaust gas sensor and a predetermined
reference value, which differences are used as the data of the
outputs of the first and second exhaust gas sensors.
[0047] In calculating the identified value of the parameter, the
difference between the actual output of the first exhaust gas
sensor and the predetermined reference value and the difference
between the actual output of the second exhaust gas sensor and the
predetermined reference value are used as the data of the outputs
of the first and second exhaust gas sensors. In this manner, an
algorithm for calculating the identified value can be constructed
relatively easily, and the accuracy of the identified value is
increased.
[0048] As described above, for controlling the air-fuel ratio of
the internal combustion engine in order to converge the output of
the first exhaust gas sensor to a given target value, the reference
value relative to the first exhaust gas sensor is preferably set to
the above target value.
[0049] The step of evaluating the deteriorated state of the
catalytic converter comprises the steps of determining a central
value of the identified value of the parameter by effecting a
low-pass filtering process on the time-series data of the
identified value of the parameter, and determining the
deterioration evaluating parameter from the difference between the
central value and each of the timeseries data of the identified
value of the parameter.
[0050] Specifically, by effecting the low-pass filtering process on
the time-series data of the identified value of the parameter of
the model, the central value of the identified value can be
determined. Inasmuch as the degree of variation of the time-series
data of the identified value is closely related to the magnitude of
the difference between the central value and each of the
time-series data of the identified value, the deterioration
evaluating parameter which represents the degree of variation can
be obtained by determining the deterioration evaluating parameter
from the difference.
[0051] The low-pass filtering process preferably comprises a
filtering process according to a sequential statistical
algorithm.
[0052] When the central value is determined by the filtering
process according to the sequential statistical algorithm, the
central value of the identified value can be determined with a
small memory capacity without the need for a memory for storing
many time-series data of the identified value.
[0053] The sequential statistical algorithm may comprise a method
of least squares, a method of weighted least squares, a degressive
gain method, a fixed gain method, etc.
[0054] While the absolute value of the difference between the data
of the individual identified value and the central value or the
square of the difference may be used as the deterioration
evaluating parameter, it is preferable to determine the
deterioration evaluating parameter by effecting a low-pass
filtering process on the square or absolute value of the difference
between the data of the individual identified value and the central
value.
[0055] The value of the deterioration evaluating parameter thus
determined is highly correlated to the deteriorated state of the
catalytic converter, and monotonously increases as the
deterioration of the catalytic converter progresses. The variation
of values of the deterioration evaluating parameter at respective
deteriorated states of the catalytic converter is small, i.e., the
extent of deterioration of the catalytic converter and the value of
the deterioration evaluating parameter have a clear 1:1
correspondence. Therefore, the deteriorated state of the catalytic
converter can be evaluated highly reliably and accurately based on
the deterioration evaluating parameter.
[0056] The filtering process for determining the deterioration
evaluating parameter should preferably a filtering process
according to a sequential statistical algorithm as with the process
of determining the central value of the identified value.
[0057] When the deterioration evaluating parameter is determined by
the filtering process according to the sequential statistical
algorithm, which preferably comprises a method of least squares, a
method of weighted least squares, a degressive gain method, a fixed
gain method, etc., the deterioration evaluating parameter as the
central value of the square or absolute value of the difference can
be determined with a small memory capacity without the need for a
memory for storing many time-series data of the square or absolute
value of the difference.
[0058] The method further comprises the step of determining whether
the exhaust gas is supplied to the exhaust passage at a
substantially constant rate or not, and the step of evaluating the
deteriorated state of the catalytic converter comprises the step of
preventing the deterioration evaluating parameter from being
determined using data of the identified value if it is determined
that the exhaust gas is supplied to the exhaust passage at the
substantially constant rate.
[0059] Specifically if the exhaust gas is supplied to the exhaust
passage at the substantially constant rate, since the output of the
first or second exhaust gas sensor varies to a small extent, even
when the deterioration of the catalytic converter progresses
relatively largely, the variation of identified values of the
parameter may possibly be relatively small. In such a situation,
since the time-series data of the identified value does not
properly reflect the deteriorated state of the catalytic converter,
even if the deterioration evaluating parameter is determined from
the time-series data, it is not suitable in evaluating the
deteriorated state of the catalytic converter. According to the
present invention, therefore, if it is determined that the exhaust
gas is supplied to the exhaust passage at the substantially
constant rate, the deterioration evaluating parameter is prevented
from being determined using data of the identified value.
Accordingly, the reliability of the deterioration evaluating
parameter is achieved.
[0060] The above and other objects, features, and advantages of the
present invention will become apparent from the following
description when taken in conjunction with the accompanying
drawings which illustrate a preferred embodiment of the present
invention by way of example.
BRIEF DESCRIPTION OF THE DRAWINGS
[0061] FIG. 1 is a block diagram of an overall system arrangement
of an apparatus for carrying out a method of evaluating a
deteriorated state of a catalytic converter for purifying an
exhaust gas, according to the present invention;
[0062] FIG. 2 is a diagram showing output characteristics of an
O.sub.2 sensor and an air-fuel ratio sensor used in the apparatus
shown in FIG. 1;
[0063] FIG. 3 is a block diagram showing a basic arrangement of an
exhaust-side main processor of the apparatus shown in FIG. 1;
[0064] FIG. 4 is a diagram illustrative of a sliding mode control
process employed by the apparatus shown in FIG. 1;
[0065] FIG. 5 is a diagram illustrative of a process of evaluating
the deteriorated state of a catalytic converter employed by the
apparatus shown in FIG. 1;
[0066] FIG. 6 is a diagram illustrative of the process of
evaluating the deteriorated state of the catalytic converter
employed by the apparatus shown in FIG. 1;
[0067] FIG. 7 is a block diagram of an adaptive controller employed
in the apparatus shown in FIG. 1;
[0068] FIG. 8 is a flowchart of a process of controlling fuel in an
internal combustion engine with the apparatus shown in FIG. 1;
[0069] FIG. 9 is a flowchart of a main routine of the exhaust-side
main processor of the apparatus shown in FIG. 1;
[0070] FIG. 10 is a flowchart of a subroutine of the main routine
shown in FIG. 9;
[0071] FIG. 11 is a flowchart of a subroutine of the main routine
shown in FIG. 9;
[0072] FIG. 12 is a flowchart of a subroutine of the main routine
shown in FIG. 9;
[0073] FIG. 13 is a diagram illustrating a partial process of the
subroutine shown in FIG. 12;
[0074] FIG. 14 is a diagram illustrating a partial process of the
subroutine shown in FIG. 12;
[0075] FIG. 15 is a diagram illustrating a partial process of the
subroutine shown in FIG. 12;
[0076] FIG. 16 is a diagram illustrating a partial process of the
subroutine shown in FIG. 12;
[0077] FIG. 17 is a diagram illustrating a subroutine of the
subroutine shown in FIG. 12;
[0078] FIG. 18 is a flowchart of a subroutine of the main routine
shown in FIG. 9;
[0079] FIG. 19 is a flowchart of a subroutine of the subroutine
shown in FIG. 18;
[0080] FIG. 20 is a flowchart of a subroutine of the subroutine
shown in FIG. 18;
[0081] FIG. 21 is a flowchart of a subroutine of the subroutine
shown in FIG. 18;
[0082] FIG. 22 is a flowchart of a subroutine of the subroutine
shown in FIG. 18; and
[0083] FIG. 23 is a flowchart of a subroutine of the main routine
shown in FIG. 9.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0084] An apparatus for carrying out a method of evaluating a
deteriorated state of a catalytic converter for purifying an
exhaust gas according to the present invention will first be
described below with reference to FIGS. 1 through 23.
[0085] FIG. 1 shows in block form the apparatus for carrying out
the method according to the present invention. As shown in FIG. 1,
an internal combustion engine 1 such as a four-cylinder internal
combustion engine is mounted as a propulsion source on an
automobile or a hybrid vehicle, for example. When a mixture of fuel
and air is combusted in each cylinder of the internal combustion
engine 1, an exhaust gas is generated and emitted from each
cylinder into a common discharge pipe 2 positioned near the
internal combustion engine 1, from which the exhaust gas is
discharged into the atmosphere. Two three-way catalytic converters
3, 4 are mounted in the common exhaust pipe 2 at successively
downstream locations thereon.
[0086] The upstream catalytic converter 3 is evaluated for its
deteriorated state according to the present invention. The
downstream catalytic converter 4 may be dispensed with.
[0087] The apparatus serves to control the air-fuel ratio of the
internal combustion engine 1, i.e., the air-fuel ratio of an
air-fuel mixture combusted by the internal combustion engine 1, in
order to achieve an optimum purifying capability of the catalytic
converter 3. While controlling the air-fuel ratio, the apparatus
also evaluates the deteriorated state of the catalytic converter
3.
[0088] In order to perform the above processing, the apparatus has
an air-fuel ratio sensor 5 mounted as a first exhaust gas sensor on
the exhaust pipe 2 upstream of the catalytic converter 3, or more
precisely at a position where exhaust gases from the cylinders of
the internal combustion engine 1 are put together, an O.sub.2
sensor (oxygen concentration sensor) 6 mounted as a second exhaust
gas sensor on the exhaust pipe 2 downstream of the catalytic
converter 3 and upstream of the catalytic converter 4, and a
control unit 7 for carrying out a control process (described later
on) and evaluating the deteriorated state of the catalytic
converter 3 based on detected outputs from the sensors 5, 6.
[0089] The control unit 7 is supplied with detected outputs from
the sensors 5, 6 and also detected outputs from various other
sensors (not shown) for detecting operating conditions of the
internal combustion engine 1, including a engine speed sensor, an
intake pressure sensor, a coolant temperature sensor, etc.
[0090] The O.sub.2 sensor 6 comprises an ordinary O.sub.2 sensor
for generating an output VO2/OUT having a level depending on the
oxygen concentration in the exhaust gas that has passed through the
catalytic converter 3, i.e., an output VO2/OUT representing a
detected value of the oxygen concentration of the exhaust gas. The
oxygen concentration in the exhaust gas is commensurate with the
air-fuel ratio of an air-fuel mixture which, when combusted,
produces the exhaust gas. The output VO2/OUT from the O.sub.2
sensor 6 will change with high sensitivity in proportion to the
oxygen concentration in the exhaust gas, with the air-fuel ratio
corresponding to the oxygen concentration in the exhaust gas being
in a range A close to a stoichiometric air-fuel ratio, as indicated
by the solid-line curve a in FIG. 2. At oxygen concentrations
corresponding to air-fuel ratios outside of the range A, the output
VO2/OUT from the O.sub.2 sensor 6 is saturated and is of a
substantially constant level.
[0091] The air-fuel ratio sensor 5 generates an output KACT
representing a detected value of the air-fuel ratio which is
recognized from the concentration of oxygen in the exhaust gas that
enters the catalytic converter 3. The air-fuel ratio sensor 5
comprises a wide-range air-fuel ration sensor disclosed in detail
in Japanese laid-open patent publication No. 4-369471, which
corresponds to U.S. Pat. No. 5,391,282. As indicated by the
solid-line curve b in FIG. 2, the air-fuel ratio sensor 5 generates
an output whose level is proportional to the concentration of
oxygen in the exhaust gas in a wider range than the O.sub.2 sensor
6. Stated otherwise, the air-fuel ratio sensor 5 (hereinafter
referred to as "LAF sensor 5") generates an output whose level
corresponds to the concentration of oxygen in the exhaust gas in a
wide range of air-fuel ratios.
[0092] The control unit 7 comprises a control unit 7a (hereinafter
referred to as an "exhaust-side control unit 7a") for performing a
process of calculating a target air-fuel ratio KCMD for the
internal combustion engine 1, or specifically a target value for
the air-fuel ratio detected by the LAF sensor 5, and a process of
evaluating the deteriorated state of the catalytic converter 3, and
a control unit 7b (hereinafter referred to as an "engine-side
control unit 7b") for carryout out a process of controlling the
air-fuel ratio of the internal combustion engine 1 based on the
target air-fuel ratio KCMD. As described in detail later on, the
control units 7a, 7b perform their processes in respective given
control cycles.
[0093] The engine-side control unit 7b will further be described
below with reference to FIG. 1. The engine-side control unit 7b
has, as its functions, a basic fuel injection quantity calculator 8
for determining a basic fuel injection quantity Tim to be injected
into the internal combustion engine 1, a first correction
coefficient calculator 9 for determining a first correction
coefficient KTOTAL to correct the basic fuel injection quantity
Tim, and a second correction coefficient calculator 10 for
determining a secand correction coefficient KCMDM to correct the
basic fuel injection quantity Tim.
[0094] The basic fuel injection quantity calculator 8 determines a
reference fuel injection quantity (fuel supply quantity) from the
rotational speed NE and intake pressure PB of the internal
combustion engine 1 using a predetermined map, and corrects the
determined reference fuel injection quantity depending on the
effective opening area of a throttle valve (not shown) of the
internal combustion engine 1, thereby calculating a basic fuel
injection quantity Tim.
[0095] The first correction coefficient KTOTAL determined by the
first correction coefficient calculator 9 serves to correct the
basic fuel injection quantity Tim in view of an exhaust gas
recirculation ratio of the internal combustion engine 1, i.e., the
proportion of an exhaust gas contained in an air-fuel mixture
introduced into the internal combustion engine 1, an amount of
purged fuel supplied to the internal combustion engine 1 when a
canister (not shown) is purged, a coolant temperature, an intake
temperature, etc.
[0096] The second correction coefficient KCMDM determined by the
second correction coefficient calculator 10 serves to correct the
basic fuel injection quantity Tim in view of the charging
efficiency of an air-fuel mixture due to the cooling effect of fuel
flowing into the internal combustion engine 1 depending on a target
air-fuel ratio KCMD determined by the exhaust-side control unit 7a,
as described later on.
[0097] The engine-side control unit 7b corrects the basic fuel
injection quantity Tim with the first correction coefficient KTOTAL
and the second correction coefficient KCMDM by multiplying the
basic fuel injection quantity Tim by the first correction
coefficient KTOTAL and the second correction coefficient KCMDM,
thus producing a demand fuel injection quantity Tcyl for the
internal combustion engine 1.
[0098] Specific details of processes for calculating the basic fuel
injection quantity Tim, the first correction coefficient KTOTAL,
and the second correction coefficient KCMDM are disclosed in detail
in Japanese laid-open patent publication No. 5-79374 and U.S. Pat.
No. 5,253,630, and will not be described below.
[0099] The engine-side control unit 7b also has, in addition to the
above functions, a feedback controller 14 for feedback-controlling
the air-fuel ratio of the air-fuel mixture to be combusted in the
internal combustion engine 1 by adjusting a fuel injection quantity
of the internal combustion engine 1 so as to converge the output
KACT of the LAF sensor 5 (the detected air-fuel ratio of the
internal combustion engine 1) toward the target air-fuel ratio KCMD
which is calculated by the exhaust-side control unit 7a.
[0100] The feedback controller 14 comprises a general feedback
controller 15 for feedback-controlling a total fuel injection
quantity for all the cylinders of the internal combustion engine 1
and a local feedback controller 16 for feedback-controlling a fuel
injection quantity for each of the cylinders of the internal
combustion engine 1.
[0101] The general feedback controller 15 sequentially determines a
feedback correction coefficient KFB to correct the demand fuel
injection quantity Tcyl (by multiplying the demand fuel injection
quantity Tcyl) so as to converge the output KACT from the LAF
sensor 5 toward the target air-fuel ratio KCMD.
[0102] The general feedback controller 15 comprises a PID
controller 17 for generating a feedback manipulated variable KLAF
as the feedback correction coefficient KFB depending on the
difference between the output KACT from the LAF sensor 5 and the
target air-fuel ratio KCMD according to a known PID control
process, and an adaptive controller 18 (indicated by "STR" in FIG.
1) for adaptively determining a feedback manipulated variable KSTR
for determining the feedback correction coefficient KFB in view of
changes in operating conditions of the internal combustion engine 1
or characteristic changes thereof from the output KACT from the LAF
sensor 5 and the target air-fuel ratio KCMD.
[0103] In the present embodiment, the feedback manipulated variable
KLAF generated by the PID controller 17 is of "1" and can be used
directly as the feedback correction coefficient KFB when the output
KACT (the detected air-fuel ratio) from the LAF sensor 5 is equal
to the target air-fuel ratio KCMD. The feedback manipulated
variable KSTR generated by the adaptive controller 18 becomes the
target air-fuel ratio KCMD when the output KACT from the LAF sensor
5 is equal to the target air-fuel ratio KCMD. A feedback
manipulated variable kstr (=KSTR/KCMD) which is produced by
dividing the feedback manipulated variable KSTR by the target
air-fuel ratio KCMD with a divider 19 can be used as the feedback
correction coefficient KFB.
[0104] The feedback manipulated variable KLAF generated by the PID
controller 17 and the feedback manipulated variable kstr which is
produced by dividing the feedback manipulated variable KSTR from
the adaptive controller 18 by the target air-fuel ratio KCMD are
selected one at a time by a switcher 20. A selected one of the
feedback manipulated variable KLAF and the feedback manipulated
variable KSTR is used as the feedback correction coefficient KFB.
The demand fuel injection quantity Tcyl is corrected by being
multiplied by the feedback correction coefficient KFB. Details of
the general feedback controller 15 (particularly, the adaptive
controller 18) will be described later on.
[0105] The local feedback controller 16 comprises an observer 21
for estimating real air-fuel ratios #nA/F (n=1, 2, 3, 4) of the
respective cylinders from the output KACT from the LAF sensor 5,
and a plurality of PID controllers 22 (as many as the number of the
cylinders) for determining respective feedback correction
coefficients #nKLAF for fuel injection quantities for the cylinders
from the respective real air-fuel ratios #nA/F estimated by the
observer 21 according to a PID control process so as to eliminate
variations of the air-fuel ratios of the cylinders.
[0106] Briefly stated, the observer 21 estimates a real air-fuel
ratio #nA/F of each of the cylinders as follows: A system from the
internal combustion engine 1 to the LAF sensor 5 (where the exhaust
gases from the cylinders are combined) is considered to be a system
for generating an air-fuel ratio detected by the LAF sensor 5 from
a real air-fuel ratio #nA/F of each of the cylinders, and is
modeled in view of a detection response delay (e.g., a time lag of
first order) of the LAF sensor 5 and a chronological contribution
of the air-fuel ratio of each of the cylinders to the air-fuel
ratio detected by the LAF sensor 5. Based on the modeled system, a
real air-fuel ratio #nA/F of each of the cylinders is estimated
from the output KACT from the LAF sensor 5.
[0107] Details of the observer 21 are disclosed in Japanese
laid-open patent publication No. 7-83094 and U.S. Pat. No.
5,531,208, and will not be described below.
[0108] Each of the PID controllers 22 of the local feedback
controller 16 divides the output signal KACT from the LAF sensor 5
by an average value of the feedback correction coefficients #nKLAF
determined by the respective PID controllers 22 in a preceding
control cycle to produce a quotient value, and uses the quotient
value as a target air-fuel ratio for the corresponding cylinder.
Each of the PID controllers 22 then determines a feedback
correction coefficient #nKLAF in a present control cycle so as to
eliminate any difference between the target air-fuel ratio and the
corresponding real air-fuel ratio #nA/F determined by the observer
21.
[0109] The local feedback controller 16 multiplies a value, which
has been produced by multiplying the demand fuel injection quantity
Tcyl by the selected feedback correction coefficient KFB produced
by the general feedback controller 15, by the feedback correction
coefficient #nKLAF for each of the cylinders, thereby determining
an output fuel injection quantity #nTout (n=1, 2, 3, 4) for each of
the cylinders.
[0110] The output fuel injection quantity #nTout thus determined
for each of the cylinders is corrected for accumulated fuel
particles on intake pipe walls of the internal combustion engine 1
by a fuel accumulation corrector 23 in the engine-side control unit
7b. The corrected output fuel injection quantity #nTout is applied
to each of fuel injectors (not shown) of the internal combustion
engine 1, which injects fuel into each of the cylinders with the
corrected output fuel injection quantity #nTout.
[0111] The correction of the output fuel injection quantity in view
of accumulated fuel particles on intake pipe walls is disclosed in
detail in Japanese laid-open patent publication No. 8-21273 and
U.S. Pat. No. 5,568,799, and will not be described in detail
below.
[0112] A sensor output selector 24 shown in FIG. 1 serves to select
the output KACT from the LAF sensor 5, which is suitable for the
estimation of a real air-fuel ratio #nA/F of each cylinder with the
observer 21, depending on the operating conditions of the internal
combustion engine 1. Details of the sensor output selector 24 are
disclosed in detail in Japanese laid-open patent publication No.
7-259588 and U.S. Pat. No. 5,540,209, and will not be described in
detail below.
[0113] The exhaust-side control unit 7a has a subtractor 11 for
determining a difference kact (=KACT-FLAF/BASE) between the output
KACT from the LAF sensor 5 and a predetermined reference value
FLAF/BASE and a subtractor 12 for determining a difference VO2
(=VO2/OUT-VO2/TARGET) between the output VO2/OUT from the O.sub.2
sensor 6 and a target value VO2/TARGET therefor.
[0114] The catalytic converter 3 achieves an optimum purifying
capability irrespective of its deteriorated state at the air-fuel
ratio of the internal combustion engine 1 which causes the output
VO2/OUT from the O.sub.2 sensor 6 to settle on a certain constant
value VO2/TARGET (see FIG. 2). In the present embodiment,
therefore, the constant value VO2/TARGET is used as the target
value VO2/TARGET for the output VO2/OUT from the O.sub.2 sensor 6.
The reference value FLAF/BASE with respect to the output KACT from
the LAF sensor 5 is set to a "stoichiometric air-fuel ratio".
[0115] The differences kact, VO2 determined respectively by the
subtractors 11, 12 are referred to as a differential output kact of
the LAF sensor 5 and a differential output VO2 of the O.sub.2
sensor 6, respectively.
[0116] The exhaust-side control unit 7a also has an exhaust-side
main processor 13 which is supplied with the data of the
differential outputs kact, VO2 as the data of the output from the
LAF sensor 5 and the output of the O.sub.2 sensor 6.
[0117] The exhaust-side main processor 13 has a function
(hereinafter referred to as "target air-fuel ratio calculating
function) for sequentially calculating a target air-fuel ratio KCMD
for the internal combustion engine 1, or more specifically a target
value for the air-fuel ratio detected by the LAF sensor 5, based on
the data of the differential outputs kact, VO2, and a function
(hereinafter referred to as "deteriorated state evaluating
function) for evaluating the deteriorated state of the catalytic
converter 3.
[0118] The target air-fuel ratio calculating function serves to
control an object exhaust system (denoted by E in FIG. 1) including
the catalytic converter 3, which ranges from the LAF sensor 5 to
the O.sub.2 sensor 6 along the exhaust pipe 2. The target air-fuel
ratio calculating function sequentially determines the target
air-fuel ratio KCMD for the internal combustion engine 1 so as to
converge the output VO2/OUT of the O.sub.2 sensor 6 to the target
value VO2/TARGET therefor, or so as to converge the differential
output VO2 of the O.sub.2 sensor 6 to "0", according to an adaptive
sliding mode control process, in view of a dead time present in the
object exhaust system E to be controlled, a dead time present in
the internal combustion engine 1 and the engine-side control unit
7b, and behavioral changes of the object exhaust system E.
[0119] The deteriorated state evaluating function serves to
evaluate the deteriorated state of the catalytic converter 3 using
the data of identified values of parameters of a model, described
later on, that are sequentially obtained in the process of
calculating the target air-fuel ratio KCMD, and control the
operation of a deterioration indicator 29 connected to the
apparatus depending on the evaluation of the deteriorated state of
the catalytic converter 3. The deterioration indicator 29 may
comprise a lamp, a buzzer, or a display unit for displaying
characters, a graphic image, etc. to indicate the deteriorated
state of the catalytic converter 3.
[0120] In order to perform the target air-fuel ratio calculating
function and the deteriorated state evaluating function, the object
exhaust system E is regarded as a system for generating the output
VO2/OUT of the O.sub.2 sensor 6 (the detected value of the oxygen
concentration of the exhaust gas having passed through the
catalytic converter 3) from the output KACT of the LAF sensor 5
(the detected value of the air-fuel ratio) via a dead time element
and a response delay element, and the behavior of the system is
modeled as a discrete time system.
[0121] In addition, for the target air-fuel ratio calculating
function, the system comprising the internal combustion engine 1
and the engine-side control unit 7b is regarded as a system
(hereinafter referred to as "air-fuel ratio manipulating system")
for generating the output KACT of the LAF sensor 5 from the target
air-fuel ratio KCMD via a dead time element, and the behavior of
this system is modeled as a discrete time system.
[0122] The model (hereinafter referred to as "exhaust system
model") in which the behavior of the object exhaust system E is
expressed as a discrete time system is expressed, using the
differential output kact (=KACT-FLAF/BASE) from the LAF sensor 5
and the differential output VO2 (=VO2/OUT-VO2/TARGET) from the
O.sub.2 sensor 6, instead of the output KACT of the LAF sensor 5
and the output VO2/OUT of the O.sub.2 sensor 6, according to the
following equation (1):
VO2(k+1)=a1.multidot.VO2(k)+a2.multidot.VO2(k-1)+b1.multidot.kact(k-d1)
(1)
[0123] According to the equation (1), the object exhaust system E
is regarded as a system for generating the differential output VO2
from the O.sub.2 sensor 6 from the differential output kact from
the LAF sensor 5 via a dead time element and a response delay
element, and the behavior of the object exhaust system E is
expressed by the model of a discrete time system (more
specifically, an autoregressive model having a dead time in the
differential output kact as an input to the exhaust system E).
[0124] In the equation (1), "k" represents the ordinal number of a
discrete-time control cycle of the exhaust-side control unit 7a,
and udlll the dead time of the object exhaust system E as
represented by the number of control cycles. The dead time of the
object exhaust system E (more specifically, the dead time required
until the air-fuel ratio detected at each point of time by the LAF
sensor 5 is reflected in the output VO2/OUT of the O.sub.2 sensor
6) is generally equal to the time of 3-10 control cycles (d1=3-10)
if the period (constant in the present embodiment) of control
cycles of the exhaust-side control unit 7a ranges from 30 to 100
ms. In the present embodiment, a preset constant value (d1=7, for
example) which is equal to or slightly longer than the actual dead
time of the object exhaust system E is used as the dead time d1 in
the discretesystem model of the object exhaust system E as
represented by the equation (1).
[0125] The first and second terms of the right side of the equation
(1) correspond to a response delay element of the object exhaust
system E, the first term being a primary autoregressive term and
the second term being a secondary autoregressive term. In the first
and second terms, "a1", lia2"represent respective gain coefficients
of the primary autoregressive term and the secondary autoregressive
term. Stated otherwise, these gain coefficients a1, a2 are relative
to the differential output VO2 of the O.sub.2 sensor 6 as an output
of the control system E.
[0126] The third term of the right side of the equation (1)
represents the differential output kact of the LAF sensor 5 as an
input to the object exhaust system E, including the dead time d1 of
the object exhaust system E. In the third term, "b1" represents a
gain coefficient relative to the input to the object exhaust system
E, i.e., the differential output kact of the LAF sensor 5.
[0127] These gain coefficients "a1", "a2", "b1" are parameters
which define the behavior of the exhaust system model, and are
sequentially identified by an identifier which will be described
later on.
[0128] The model (hereinafter referred to as "air-fuel ratio
manipulating system model") of the discrete time system of the
air-fuel ratio manipulating system which comprises the internal
combustion engine 1 and the engine-side control unit 7b is
expressed, using the differential output kact (=KACT-FLAF/BASE)
from the LAF sensor 5 instead of the output KACT from the LAF
sensor 5 and also using a difference kcmd (=KCMD-FLAF/BASE, which
corresponds to a target value for the differential output kact of
the LAF sensor 5, and will be referred to as "target differential
air-fuel ratio kcmd") between the target air-fuel ratio KCMD and
the reference value FLAF/BASE instead of the target air-fuel ratio
KCMD, according to the following equation (2):
kact(k)=kcmd (k-d2) (2)
[0129] The equation (2) expresses the air-fuel ratio manipulating
system as the model of a discrete time system, regarding the
air-fuel ratio manipulating system as a system for generating the
differential output kact from the LAF sensor 5 from the target
differential air-fuel ratio kcmd via a dead time element, i.e., a
system in which the differential output kact in each control cycle
is equal to the target differential air-fuel ratio kcmd prior to
the dead time.
[0130] In the equation (2), "d2" represents the dead time of the
air-fuel ratio manipulating system in terms of the number of
control cycles of the exhaust-side control unit 7a. The dead time
of the air-fuel ratio manipulating system varies (more
specifically, the time required until the target air-fuel ratio
KCMD at each point of time is reflected in the output signal KACT
of the LAF sensor 5) varies with the rotational speed NE of the
internal combustion engine 1, and is longer as the rotational speed
NE of the internal combustion engine 1 is lower. In the present
embodiment, in view of the above characteristics of the dead time
of the air-fuel ratio manipulating system, a preset constant value
(for example, d2=3) which is equal to or slightly longer than the
actual dead time of the air-fuel ratio manipulating system at an
idling rotational speed of the internal combustion engine 1, which
is a rotational speed in a low speed range of the internal
combustion engine 1 (the actual dead time is a maximum dead time
which can be taken by the air-fuel ratio manipulating system at an
arbitrary rotational speed of the internal combustion engine 1), is
used as the value of the dead time d2 in the air-fuel ratio
manipulating system model expressed by the equation (2).
[0131] The air-fuel ratio manipulating system actually includes a
dead time element and a response delay element of the internal
combustion engine 1. Since a response delay of the output KACT of
the LAF sensor 5 with respect to the target air-fuel ratio KCMD is
basically compensated for by the feedback controller 14
(particularly the adaptive controller 18) of the engine-side
control unit 7b, there will arise no problem if a response delay
element of the internal combustion engine 1 is not taken into
account in the air-fuel ratio manipulating system as viewed from
the exhaust-side control unit 7a.
[0132] The exhaust-side main processor 13 performs the target
air-fuel ratio calculating function based on the exhaust system
model and the air-fuel ratio manipulating systen model expressed
respectively by the equations (1), (2) and the deterioration
evaluating function based on the exhaust system model expressed by
the equation (1) in constant control cycles of the exhaust-side
control unit 7a. In order to performs the above functions, the
exhaust-side main processor 13 has its functions as shown in FIG.
3.
[0133] As shown in FIG. 3, the exhaust-side main processor 13 has
an identifier 25 for sequentially identifying in each control cycle
the gain coefficients a1, a2, b1 that are parameters to be
established for the exhaust system model (the equation (1)).
[0134] The exhaust-side main processor 13 also has an estimator 26
for sequentially determining in each control cycle an estimated
value VO2 bar of the differential output VO2 from the O.sub.2
sensor 6 (hereinafter referred to as -estimated differential output
VO2 bar") after the total dead time d (=d1+d2) which is the sum of
the dead time d1 of the object exhaust system E and the dead time
d2 of the air-fuel ratio manipulating system, from the data of the
differential output kact of the LAF sensor 5, the differential
output VO2 of the O.sub.2 sensor 6, and the target air-fuel ratio
KCMD (more accurately, the target differential air-fuel ratio kcmd)
determined in the past by a sliding mode controller 27, using
identified values a1 hat, a2 hat, b1 hat of the gain coefficients
a1, a2, b1 (hereinafter referred to as "identified gain
coefficients a1 hat, a2 hat, b1 hat") calculated by the identifier
25.
[0135] The exhaust-side main processor 13 also has a sliding mode
controller 27 for sequentially determining in each control cycle a
target air-fuel ratio KCMD according to an adaptive slide mode
control process from the data of the estimated differential output
VO2 bar of the O.sub.2 sensor 6 determined by the estimator 26,
using the identified gain coefficients a1 hat, a2 hat, b1 hat.
[0136] The exhaust-side main processor 13 also has a catalytic
converter deterioration evaluator 28 for evaluating the
deteriorated state of the catalytic converter 3 using the data of
the identified gain coefficient b1 hat, for example, among the
identified gain coefficients a1 hat, a2 hat, b1 hat.
[0137] The algorithm of a processing operation to be carried out by
the identifier 25, the estimator 26, and the sliding mode
controller 27 is constructed as follows:
[0138] The identifier 25 serves to identify the gain coefficients
a1, a2, b1 sequentially on a real-time basis for the purpose of
minimizing a modeling error of the exhaust system model expressed
by the equation (1) with respect to the actual object exhaust
system E. The identifier 25 carries out its identifying process as
follows:
[0139] In each control cycle, the identifier 25 determines an
identified value VO2(k) hat of the differential output VO2 (the
output of the exhaust system model) from the O.sub.2 sensor 6
(hereinafter referred to as "identified differential output VO2(k)
hat") on the exhaust system model, using the data of the present
values of the identified gain coefficients a1 hat, a2 hat, b1 hat
of the exhaust system model, i.e., the values of identified gain
coefficients a1(k-1) hat, a2(k-1) hat, b1(k-1) hat determined in a
preceding control cycle, and the data of the past values of the
differential output kact from the LAF sensor 5 and the differential
output VO2 from the O.sub.2 sensor 6, according to the following
equation (3): 1 V O ^ 2 ( k ) = a1 ^ ( k - 1 ) VO2 ( k - 1 ) + a2 ^
( k - 1 ) VO2 ( k - 2 ) + b1 ^ ( k - 1 ) kact ( k - d1 - 1 ) ( 3
)
[0140] The equation (3) corresponds to the equation (1) which is
shifted into the past by one control cycle with the gain
coefficients a1, a2, b1 being replaced with the respective
identified gain coefficients a1(k-1) hat, a2(k1) hat, b1(k-1) hat.
The constant value (d1=7) established as described above is used as
the value of the dead time d1 of the object exhaust system E in the
third term of the equation (3).
[0141] If vectors .THETA., .xi. defined by the following equations
(4), (5) are introduced (the letter T in the equations (4), (5)
represents a transposition), then the equation (3) is expressed by
the equation (6):
.THETA..sup.T(k)=[a{circumflex over (1)}(k)a{circumflex over
(2)}(k)b{circumflex over (1)}(k)] (4)
.xi..sup.T(k)=[VO2(k-1)VO2(k-2)kact(k-d1-1)] (5)
V2(k)=.THETA..sup.T(k-1).multidot..xi.(k) (6)
[0142] The identifier 25 also determines a difference id/e(k)
between the identified differential output VO2(k) hat from the
O.sub.2 sensor 6 which is determined by the equation (3) or (6) and
the present differential output VO2(k) from the O.sub.2 sensor 6,
as representing a modeling error of the exhaust system model with
respect to the actual object exhaust system E (hereinafter the
difference id/e will be referred to as "identified error id/e"),
according to the following equation (7):
id/e(k)=VO2(k)-V2(k) (7)
[0143] The identifier 25 further determines new identified gain
coefficients a1(k) hat, a2(k) hat, b1(k) hat, stated otherwise, a
new vector .THETA.(k) having these identified gain coefficients as
elements (hereinafter the new vector .THETA.(k) will be referred to
as "identified gain coefficient vector .THETA."), in order to
minimize the identified error id/e, according to the equation (8)
given below. That is, the identifier 25 varies the identified gain
coefficients a1 hat (k-1), a2 hat (k-1), b1 hat (k-1) determined in
the preceding control cycle by a quantity proportional to the
identified error id/e for thereby determining the new identified
gain coefficients a1(k) hat, a2(k) hat, b1(k) hat.
.THETA.(k)=.THETA.(k-1)+K.theta.(k).multidot.id/e(k) (8)
[0144] where K.theta. represents a cubic vector determined by the
following equation (9), i.e., a gain coefficient vector for
determining a change depending on the identified error id/e of the
identified gain coefficients a1 hat, a2 hat, b1 hat): 2 K ( k ) = P
( k - 1 ) ( k ) 1 + T ( k ) P ( k - 1 ) ( k ) ( 9 )
[0145] where P represents a cubic square matrix determined by a
recursive formula expressed by the following equation (10): 3 P ( k
) = 1 1 ( k ) [ I = 2 ( k ) P ( k - 1 ) ( k ) T ( k ) 1 ( k ) + 2 (
k ) T ( k ) P ( k - 1 ) ( k ) ] P ( k - 1 ) ( 10 )
[0146] where I represents a unit matrix.
[0147] In the equation (10), .lambda..sub.1, .lambda..sub.2 are
established to satisfy the conditions 0<80.sub.1.ltoreq.1 and
0.ltoreq..lambda..sub.2.ltoreq.2, and an initial value P(0) of P
represents a diagonal matrix whose diagonal components are positive
numbers.
[0148] Depending on how .lambda..sub.1, .lambda..sub.2 in the
equation (10) are established, any one of various specific
algorithms including a fixed gain method, a degressive gain method,
a method of weighted least squares, a method of least squares, a
fixed tracing method, etc. may be employed. According to the
present embodiment, a method of least squares
(.lambda..sub.1=.lambda..sub.2=1), for example, is employed.
[0149] Basically, the identifier 25 sequentially determines in each
control cycle the identified gain coefficients a1 hat, a2 hat, b1
hat in order to minimize the identified error id/e according to the
above algorithm (calculating operation). Through this operation, it
is possible to sequentially obtain the identified gain coefficients
a1 hat, a2 hat, b1 hat which match the actual object exhaust system
E.
[0150] The algorithm described above is the basic algorithm that is
carried out by the identifier 25. The identifier 25 performs
additional processes such as a limiting process, on the identified
gain coefficients a1 hat, a2 hat, b1 hat in order to determine
them. Such operations of the identifier 25 will be described later
on.
[0151] The estimator 26 sequentially determines in each control
cycle the estimated differential output VO2 bar which is an
estimated value of the differential output VO2 from the O.sub.2
sensor 6 after the total dead time d (=d1+d2) in order to
compensate for the effect of the dead time dl of the object exhaust
system E and the effect of the dead time d2 of the air-fuel ratio
manipulating system for the calculation of the target air-fuel
ratio KCMD with the sliding mode controller 27 as described in
detail later on. The algorithm for the estimator 26 to determine
the estimated differential output VO2 bar is constructed as
described below. Since the estimator 26 has no direct bearing on
the present invention and its details are disclosed in Japanese
laid-open patent publication No. 11-324767 and U.S. patent
application Ser. No. 09/311353, the estimator 26 will briefly be
described below.
[0152] If the equation (2) expressing the model of the air-fuel
ratio manipulating system is applied to the equation (1) expressing
the model of the object exhaust system E, then the equation (1) can
be rewritten as the following equation (11): 4 VO2 ( k + 1 ) = a1
VO2 ( k ) + a2 VO2 ( k - 1 ) + b1 kcmd ( k - d1 - d2 ) = a1 VO2 ( k
) + a2 VO2 ( k - 1 ) + b1 kcmd ( k - d ) ( 11 )
[0153] The equation (11) expresses a system which is a combination
of the object exhaust system E and the air-fuel manipulating system
as the model of a discrete time system, regarding such a system as
a system for generating the differential output VO2 from the
O.sub.2 sensor 6 from the target differential air-fuel ratio kcmd
via dead time elements of the object exhaust system E and the
air-fuel manipulating system and a response delay element of the
object exhaust system E.
[0154] By using the equation (11), the estimated differential
output VO2(k+d) bar which is an estimated value of the differential
output VO2(k+d) of the O.sub.2 sensor 6 after the total dead time d
in each control cycle can be expressed using time-series data
VO2(k), VO2(k-1) of the present and past values of the differential
output VO2 of the O.sub.2 sensor 6 and time-series data kcmd(k-j)
(j=1, 2, . . . , d) of the past values of the target differential
air-fuel ratio kcmd (=KCMD-FLAF/BASE) which corresponds to the
target air-fuel ratio KCMD determined by the sliding mode
controller 27 (its specific process of determining the target
air-fuel ratio KCMD will be described later on), according to the
following equation (12): 5 VO2 _ ( k + d ) = 1 VO2 ( k ) + 2 VO2 (
k - 1 ) + j = 1 d j kcmd ( k - j ) ( 12 )
[0155] where
[0156] .alpha.1=the first-row, first-column element of A.sup.d,
[0157] .alpha.2=the first-row, second-column element of
A.sup.d,
[0158] .beta.j=the first-row elements of A.sup.j-1.multidot.B 6 A =
[ a1 a2 1 0 ] B = [ b1 0 ]
[0159] In the equation (12), ".alpha.1", ".alpha.2" represent the
first-row, first-column element and the first-row, secondcolumn
element, respectively, of the dth power A.sup.d (d: total dead
time) of the matrix A defined as described above with respect to
the equation (12), and ".beta.j" (j=1, 2, . . . , d) represents the
first-row elements of the product A.sup.j-1.multidot.B of the
(j-1)th power A.sup.j-1 (j=1, 2, . . . , d) of the matrix A and the
vector B defined as described above with respect to the equation
(12).
[0160] Of the time-series data of the past values of the target
combined differential air-fuel ratio kcmd according to the equation
(12), the time-series data kcmd(k-d2), kcmd(k-d2), . . . ,
kcmd(k-d) from the present prior to the dead time d2 of the
air-fuel manipulating system can be replaced respectively with data
kact(k), kact(k-1), , kact(k-d+d2) obtained prior to the present
time of the differential output kact of the LAF sensor 5 according
to the equation (2). When the time-series data are thus replaced,
the following equation (13) is obtained: 7 VO2 _ ( k + d ) = 1 VO2
( k ) + 2 VO2 ( k - 1 ) + j = 1 d2 - 1 j kcmd ( k - j ) + i = 0 d -
d2 i + d2 kact ( k - i ) = 1 VO2 ( k ) + 2 VO2 ( k - 1 ) + j = 1 d2
- 1 j kcmd ( k - j ) + i = 0 d1 i + d2 kact ( k - i ) ( 13 )
[0161] The equation (13) is a basic formula for the estimator 26 to
determine the estimated differential output VO2(k+d) bar. Stated
otherwise, the estimator 26 determines, in each control cycle of
the exhaust-side control unit 7a, the estimated differential output
VO2(k+d) bar of the O.sub.2 sensor 6 according to the equation
(13), using the time-series data VO2(k), VO2(k-1) of the present
and past values of the differential output VO2 of the O.sub.2
sensor 6, the time-series data kcmd(k-j) (j=1, . . . d2-1) of the
past values of the target differential air-fuel ratio kcmd which
represents the target air-fuel ratio KCMD determined in the past by
the sliding mode controller 27, and the time-series data kact(k-1)
(i=0, . . . , d2-1) of the present and past values of the
differential output kact of the LAF sensor 5.
[0162] In the present embodiment, the values of the coefficients
.alpha.1, .alpha.2, .beta.j (j=1, 2, . . . , d) required to
calculate the estimated differential output VO2(k+d) bar according
to the equation (13) are basically calculated using the identified
gain coefficients a1 hat, a2 hat, b1 hat which are the identified
values of the gain coefficients a1, a2, b1 (which are elements of
the vectors A, B defined with respect to the equation (12)). The
values of the dead times d1, d2 required in the equation (13)
comprise the preset values as described above.
[0163] The estimated differential output VO2(k+d) bar may be
determined according to the equation (12) without using the data of
the differential output kact of the LAF sensor 5. For increasing
the reliability of the estimated differential output VO2(k+d) bar,
however, it is preferable to determine the estimated differential
output VO2(k+d) bar according to the equation (13) using the data
of the differential output kact of the LAF sensor 5 which reflects
the actual behavior of the internal combustion engine 1. If the
dead time d2 of the air-fuel ratio manipulating system can be set
to "1", all the time-series data kcmd(k-j) (j=1, 2, . . . , d) of
the past values of the target differential air-fuel ratio kcmd in
the equation (12) may be replaced with the time-series data
kact(k), kact(k-1), . . . , kact(k-d+d1), respectively, of the
present and past values of the differential output kact of the LAF
sensor 5. In this case, the estimated differential output VO2(k+d)
bar can be determined according to the following equation (14)
which does not include the data of the target differential air-fuel
ratio kcmd: 8 VO2 _ ( k + d ) = 1 VO2 ( k ) + 2 VO2 ( k - 1 ) + j =
0 d - 1 j + 1 kact ( k - j ) ( 14 )
[0164] The sliding mode controller 27 will be described in detail
below. Since the details of the sliding mode controller 27 are
disclosed in Japanese laid-open patent publication No. 11-324767
and U.S. patent application Ser. No. 09/311353, the sliding mode
controller 27 will briefly be described below.
[0165] The sliding mode controller 27 determines an input quantity
to be given to the object exhaust system E (which is specifically a
target value for the difference between the output KACT of the LAF
sensor 5 (the detected value of the air-fuel ratio) and the
reference value FLAF/BASE, which target value is equal to the
target differential air-fuel ratio kcmd) (the input quantity will
be referred to as "SLD manipulating input Usl") in order to cause
the output VO2/OUT of the O.sub.2 sensor 6 to settle on the target
value VO2/TARGET, i.e., to converge the differential output VO2 of
the O.sub.2 sensor 6 to "0" according to an adaptive sliding mode
control process which incorporates an adaptive control law for
minimizing the effect of a disturbance, in a normal sliding mode
control process, and determines the target air-fuel ratio KCMD from
the determined SLD manipulating input Us1. An algorithm for
carrying out the adaptive sliding mode control process is
constructed as follows:
[0166] A switching function required for the algorithm of the
adaptive sliding mode control process carried out by the sliding
mode controller 27 and a hyperplane defined by the switching
function (also referred to as a slip plane) will first be described
below.
[0167] According to a basic concept of the sliding mode control
process, the differential output VO2(k) of the O.sub.2 sensor 6
obtained in each control cycle and the differential output VO2(k-1)
obtained in a preceding control cycle are used as a state quantity
to be controlled, and a switching function a for the sliding mode
control process is defined as a linear function according to the
following equation (15): 9 ( k ) = s1 VO2 ( k ) + s2 VO2 ( k - 1 )
= S X ( 15 )
[0168] where
[0169] S=[s1s2], 10 X = [ VO2 ( k ) VO2 ( k - 1 ) ]
[0170] A vector X defined above with respect to the equation (15)
as a vector whose elements are represented by the differential
outputs VO2(k), VO2(k-1) will hereinafter be referred to as a state
quantity X.
[0171] The coefficients s1, s2 of the switching function .sigma. is
set in order to meet the condition of the following equation (16):
11 - 1 < s2 s1 < 1 ( 16 )
[0172] (when s1=1, -1<s2<1)
[0173] In the present embodiment, for the sake of brevity, the
coefficient s1 is set to s1=1 (s2/s1=s2), and the coefficient s2 is
established to satisfy the condition: -1<s2<1.
[0174] With the switching function .sigma. thus defined, the
hyperplane for the sliding mode control process is defined by the
equation .sigma.=0. Since the state quantity X is of the second
degree, the hyperplane .sigma.=0 is represented by a straight line
as shown in FIG. 4. At this time, the hyper-plane is called a
switching line or a switching plane depending on the degree of a
topological space.
[0175] In the present embodiment, the time-series data of the
estimated differential output VO2 bar determined by the estimator
26 is actually used as the variable components of the switching
function for the sliding mode control process, as described later
on.
[0176] The adaptive sliding mode control process serves to converge
the state quantity X onto the hyperplane .sigma.=0 according to a
reaching control law which is a control law for converging the
state quantity x (=VO2(k), VO2(k-1)) onto the hyperplane .sigma.=0,
and an adaptive control law which is a control law for compensating
for the effect of a disturbance in converging the state quantity X
onto the hyperplane .sigma.=0 (mode 1 in FIG. 4). While holding the
state quantity X onto the hyperplane .sigma.=0 according to an
equivalent control input, the state quantity X is converged to a
balanced point on the hyperplane .sigma.=0 where VO2(k)=VO2(k-1)
=0, i.e., a point where time-series data VO2/OUT(k), VO2/OUT(k-1)
of the output VO2/OUT of the O.sub.2 sensor 6 are equal to the
target value VO2/TARGET (mode 2 in FIG. 4).
[0177] The SLD manipulating input Us1 (=the target differential
air-fuel ratio kcmd) to be generated by the sliding mode controller
27 for converging the state quantity X toward the balanced point on
the hyperplane .sigma.=0 is expressed as the sum of an equivalent
control input Ueq to be applied to the object exhaust system E
according to the control law for converging the state quantity X
onto the hyperplane .sigma.=0, an input Urch (hereinafter referred
to as "reaching control law input Urch") to be applied to the
object exhaust system E according to the reaching control law, and
an input Uadp (hereinafter referred to as "adaptive control law
Uadp") to be applied to the object exhaust system E according to
the adaptive control law (see the following equation (17)).
Us1=Ueq+Urch+Uadp (17)
[0178] The equivalent control input Ueq, the reaching control law
input Urch, and the adaptive control law input Uadp are determined
on the basis of the model of the discrete time system expressed by
the equation (11), i.e., the model in which the differential output
kact(k-d1) of the LAF sensor 5 in the equation (1) is replaced with
the target differential air-fuel ratio kcmd(k-d) using the total
dead time d, as follows:
[0179] The equivalent control input Ueq which is an input component
to be applied to the object exhaust system E for converging the
state quantity X onto the hyperplane .sigma.=0 is the target
differential air-fuel ratio kcmd which satisfies the condition:
.sigma.(k+1)=.sigma.(k)=0. Using the equations (11), (15), the
equivalent control input Ueq which satisfies the above condition is
given by the following equation (18): 12 Ueq ( k ) = - ( S B ) - 1
{ S ( A - 1 ) } X ( k + d ) = - 1 s1b1 { [ s1 ( a1 - 1 ) + s2 ] VO2
( k + d ) + ( s1 a2 - s2 ) VO2 ( k + d - 1 ) } ( 18 )
[0180] The equation (18) is a basic formula for determining the
equivalent control law input Ueq(k) in each control cycle.
[0181] According to the present embodiment, the reaching control
law input Urch is basically determined according to the following
equation (19): 13 Urch ( k ) = - ( S B ) - 1 F ( k + d ) = - 1 s1b1
F ( k + d ) ( 19 )
[0182] Specifically, the reaching control law input Urch is
determined in proportion to the value .sigma.(k+d) of the switching
function .sigma. after the total dead time d, in view of the effect
of the total dead time d.
[0183] The coefficient F in the equation (19) which determines the
gain of the reaching control law is established to satisfy the
condition expressed by the following equation (20):
0<F<2 (20)
[0184] The value of the switching function .sigma. may possibly
vary in an oscillating fashion (so-called chattering) with respect
to the hyperplane .sigma.=0. In order to suppress such chattering,
it is preferable that the coefficient F relative to the reaching
control law input Urch be established to further satisfy the
condition of the following equation (21):
0<F<1 (21)
[0185] The adaptive control law input Uadp is basically determined
according to the following equation (22) (.DELTA.T in the equation
(22) represents the period of the control cycles of the
exhaust-side control unit 7a): 14 Uadp ( k ) = - ( S B ) - 1 G i =
0 k + d ( ( i ) T ) = - 1 s1b1 G i = 0 k + d ( ( i ) T ) ( 22 )
[0186] The adaptive control law input Uadp is determined in
proportion to an integrated value (which corresponds to an integral
of the values of the switching function .sigma.) over control
cycles of the product of values of the switching function .sigma.
and the period .DELTA.T of the exhaust-side control unit 7a until
after the total dead time d, in view of the effect of the total
dead time d.
[0187] The coefficient G (which determines the gain of the adaptive
control law) in the equation (22) is established to satisfy the
condition of the following equation (23): 15 G = J 2 - F T ( 0 <
J < 2 ) ( 23 )
[0188] A specific process of deriving conditions for establishing
the equations (16), (20), (21), (23) is described in detail in
Japanese patent application No. 11-93741 and U.S. Pat. No.
6,082,099, and will not be described in detail below.
[0189] In the present embodiment, the sliding mode controller 27
determines the sum (Ueq+Urch+Uadp) of the equivalent control input
Ueq, the reaching control law input Urch, and the adaptive control
law Uadp determined according to the respective equations (18),
(19), (22) as the SLD manipulating input Us1 to be applied to the
object exhaust system E. However, the differential outputs VO2
(K+d), VO2(k+d-1) of the O.sub.2 sensor 6 and the value
.sigma.(k+d) of the switching function .sigma., etc. used in the
equations (18), (19), (22) cannot directly be obtained as they are
values in the future.
[0190] According to the present embodiment, therefore, the sliding
mode controller 27 actually uses the estimated differential outputs
VO2(k+d) bar, VO2(k+d-1) bar determined by the estimator 26,
instead of the differential outputs VO2 (K+d), VO2(k+d-1) from the
O.sub.2 sensor 6 for determining the equivalent control input Ueq
according to the equation (18), and calculates the equivalent
control input Ueq in each control cycle according to the following
equation (24): 16 Ueq ( k ) = - 1 s1b1 { [ s1 ( a1 - 1 ) + s2 ] VO2
_ ( k + d ) + ( s1 a2 - s2 ) VO2 _ ( k + d - 1 ) } ( 24 )
[0191] According to the present embodiment, furthermore, the
sliding mode controller 27 actually uses time-series data of the
estimated differential output VO2 bar sequentially determined by
the estimator 26 as described above as a state quantity to be
controlled, and defines a switching function .sigma. bar according
to the following equation (25) (the switching function .sigma. bar
corresponds to time-series data of the differential output VO2 in
the equation (15) which is replaced with time-series data of the
estimated differential output VO2 bar), in place of the switching
function a established according to the equation (25):
{overscore (.sigma.(k))}=s1.multidot.{overscore
(VO2)}(k)+s2.multidot.{ove- rscore (VO2)}(k-1) (25)
[0192] The sliding mode controller 27 calculates the reaching
control law input Urch in each control cycle according to the
following equation (26), using the switching function .sigma. bar
represented by the equation (25), rather than the value of the
switching function .sigma. for determining the reaching control law
input Urch according to the equation (19): 17 Urch ( k ) = - 1 s1
b1 F _ ( k + d ) ( 26 )
[0193] Similarly, the sliding mode controller 27 calculates the
adaptive control law input Uadp in each control cycle according to
the following equation (27), using the value of the switching
function .sigma. bar represented by the equation (25), rather than
the value of the switching function .sigma. for determining the
adaptive control law input Uadp according to the equation (22): 18
Uadp ( k ) = - 1 s1 b1 G i = 0 k + d ( _ ( i ) T ) ( 27 )
[0194] The latest identified gain coefficients a1(k) hat, a2(k)
hat, b1(k) hat which have been determined by the identifier 25 are
basically used as the gain coefficients a1, a2, b1 that are
required to calculate the equivalent control input Ueq, the
reaching control law input Urch, and the adaptive control law input
Uadp according to the equations (24), (26), (27).
[0195] The sliding mode controller 27 determines the sum of the
equivalent control input Ueq, the reaching control law input Urch,
and the adaptive control law input Uadp determined according to the
equations (24), (26), (27), as the SLD manipulating input Us1 to be
applied to the object exhaust system E (see the equation (17)). The
conditions for establishing the coefficients s1, s2, F, G used in
the equations (24), (26), (27) are as described above.
[0196] The above process is a basic algorithm for determining the
SLD manipulating input Us1 (=target differential air-fuel ratio
kcmd) to be applied to the object exhaust system E with the sliding
mode controller 27. According to the above algorithm, the SLD
manipulating input Us1 is determined to converge the estimated
differential output VO2 bar from the O.sub.2 sensor 6 toward "O",
and as a result, to convert the output VO2/OUT from the O.sub.2
sensor 6 toward the target value VO2/TARGET.
[0197] The sliding mode controller 27 eventually sequentially
determines the target air-fuel ratio KCMD in each control cycle.
The SLD manipulating input Us1 determined as described above
signifies a target value for the difference between the air-fuel
ratio of the exhaust gas detected by the LAF sensor 5 and the
reference value FLAF/BASE, i.e., the target differential air-fuel
ratio kcmd. Consequently, the sliding mode controller 27 eventually
determines the target air-fuel ratio KCMD by adding the reference
value FLAF/BASE to the determined SLD manipulating input Us1 in
each control cycle according to the following equation (28): 19
KCMD ( k ) = Usl ( k ) + FLAF / BASE = Ueq ( k ) + Urch ( k ) +
Uadp ( k ) + FLAF / BASE ( 28 )
[0198] The above process is a basic algorithm for determining the
target air-fuel ratio KCMD with the sliding mode controller 27
according to the present embodiment.
[0199] In the present embodiment, the stability of the adaptive
sliding mode control process carried out by the sliding mode
controller 27 is checked for limiting the value of the SLD
manipulating input Us1. Details of such a checking process will be
described later on.
[0200] The catalytic converter deterioration evaluator 28 will be
described below.
[0201] Various studies conducted by the inventors of the present
invention have revealed that the time-series data of the identified
gain coefficients a1 hat, a2 hat, b1 hat sequentially calculated by
the identifier 25 during operation of the internal combustion
engine 1 exhibit a characteristic tendency depending on the
deteriorated state of the catalytic converter 3.
[0202] For example, the value of the identified gain coefficient b1
hat that is sequentially calculated by the identifier 25 varies a
small extent when the deterioration of the catalytic converter 3 is
relatively small, i.e., when the catalytic converter 3 is nearly
brand-new, as shown in a left half portion of FIG. 5. When the
deterioration of the catalytic converter 3 is relatively large, the
variation of the calculated value of the identified gain
coefficient b1 hat becomes larger. Thus, as the deterioration of
the catalytic converter 3 progresses, the variation of the
calculated value of the identified gain coefficient b1 hat becomes
larger, resulting in a wider distribution range. This is considered
to arise from the fact that as the deterioration of the catalytic
converter 3 progresses, the matching between the equation (1) of
the exhaust system model and the actual behavioral characteristics
of the object exhaust system E including the catalytic converter
3.
[0203] Such a tendency is also exhibited by the other identified
gain coefficients a1 hat, a2 hat. However, the tendency occurs
greatly particularly for the identified gain coefficient b1 hat
because the deteriorated state of the catalytic converter 3 has a
greater effect on the dead time element of the object exhaust
system E than on the response delay element thereof.
[0204] For the above reasons, the catalytic converter deterioration
evaluator 28 uses the value of the identified gain coefficient b1
hat determined by the identifier 25 in order to evaluate the
deteriorated state of the catalytic converter 3.
[0205] An algorithm for evaluating the deteriorated state of the
catalytic converter 3 is constructed as follows:
[0206] The catalytic converter deterioration evaluator 28
sequentially updates and determines a central value B1LS of the
value of the identified gain coefficient b1 hat (hereinafter
referred to as "identified central value BlLS"), i.e., a central
value of the distribution range of calculated values of the
identified gain coefficient b1 hat, in each control cycle of the
exhaust-side control unit 7a, according to a low-pass filtering
process based on a sequential statistical algorithm represented by
the following equation (29): 20 B1LS ( k ) = B1LS ( k - 1 ) + BP (
k - 1 ) 1 + BP ( k - 1 ) ( b1 ^ ( k ) - B1LS ( k - 1 ) ) ( 29 )
[0207] where BP represents a parameter sequentially updated in each
control cycle according to the equation (30): 21 BP ( k ) = 1 1 ( 1
- 2 BP ( k - 1 ) 1 + 2 BP ( k - 1 ) ) BP ( k - 1 ) ( 30 )
[0208] In the equation (30), .eta.1, .eta.2 are set to values that
satisfy the conditions: 0<.eta.1.ltoreq.1 and
0.ltoreq..eta.2<2. Depending on how the values of .eta.1, .eta.2
are set, various specific algorithms including a fixed gain method,
a method of least squares, a degression gain method, a method of
weighted least squares, etc. are constructed. According to the
present embodiment, .eta.1=1, and .eta.2 is set to a given value
smaller than "1" (e.g., 0.9999), and the algorithm of the method of
weighted least squares is employed.
[0209] According to the above algorithm, a low-pass filtering
process is effected on the time-series data of the identified gain
coefficient b1 hat to sequentially determine the identified central
value B1LS as indicated by the broken line in FIG. 5.
[0210] Concurrent with the determination of the identified central
value B1LS, the catalytic converter deterioration evaluator 28
determines the square B1MT of the difference between the identified
gain coefficient b1 hat and the identified central value B1LS as a
basic value representing the degree of variation of the identified
gain coefficient b1 hat (hereinafter referred to as "variation
basic parameter BLMT") according to the following equation
(31):
B1MT(k)=(b{circumflex over (1)}(k)-B1LS(k).sup.2) (31)
[0211] At this time, due to the above tendency of the identified
gain coefficient b1 hat with respect to the deteriorated state of
the catalytic converter 3, the variation basic parameter B1MT is of
a relatively small value when the deterioration of the catalytic
converter 3 is relatively small, as indicated in a left half
portion of FIG. 6. When the deterioration of the catalytic
converter 3 is larger, the variation basic parameter BLMT is of a
large value, as indicated in a right half portion of FIG. 6.
Therefore, as the deterioration of the catalytic converter 3
progresses, the value of the variation basic parameter BLMT
increases.
[0212] In the present invention, the square BLMT of the difference
between the identified gain coefficient b1 hat and the identified
central value B1LS is used as the variation basic parameter B1MT
which represents the degree of variation of the identified gain
coefficient b1 hat. However, the absolute value of the difference
may be used as a variation basic parameter. Such a variation basic
parameter exhibits the same tendency as the above variation basic
parameter BLMT against the deterioration of the catalytic converter
3.
[0213] The value of the variation basic parameter BLMT exhibits a
characteristic tendency with respect to the deterioration of the
catalytic converter 3. In general, however, the value of the
variation basic parameter BLMT tends to vary to a certain extent
even if the deteriorated state of the catalytic converter 3 remains
substantially the same.
[0214] According to the present invention, the catalytic converter
deterioration evaluator 28 further determines a central value
BLMTLS of the variation basic parameter BLMT (see the broken line
in FIG. 6) according to the equation (32) given below based on a
sequential statistical algorithm (an algorithm of the degression
gain method) which is the same low-pass filter process as used to
determine the identified central value B1LS, and obtains the
central value BlMTLS as a deterioration evaluating parameter for
finally evaluating the deteriorated state of the catalytic
converter 3.
[0215] 22 B1MTLS ( k ) = B1MTLS ( k - 1 ) + BP ( k - 1 ) 1 + BP ( k
- 1 ) ( B1MT ( k ) - B1MTLS ( k - 1 ) ) ( 32 )
B1MTLS(k)=B1MTLS(k-1)+BP-
(k-1)/1+BP(k-1).multidot.(B1MT(k)-B1MTLS(k-1) (32)
[0216] where BP represents a parameter sequentially updated by the
recursive formula according to the above equation (31). In the
present embodiment, the statistical algorithm for determining the
identified central value B1LS and the statistical algorithm for
determining the deterioration evaluating parameter BLMTLS (the
central value of the variation basic parameter B1MT) are the same
as each other. However, different algorithms may be used to
determine the identified central value B1LS and the deterioration
evaluating parameter B1MTLS, respectively.
[0217] The value of the deterioration evaluating parameter BLMTLS
thus determined is highly correlated to the deteriorated state of
the catalytic converter 3, and monotonously increases as the
deterioration of the catalytic converter 3 progresses. Therefore,
the deteriorated state of the catalytic converter 3, or the extent
to which the catalytic converter 3 is deteriorated, can be
recognized based on the value of the deterioration evaluating
parameter BLMTLS.
[0218] In the present embodiment, the deteriorated state of the
catalytic converter 3 is evaluated to judge whether the catalytic
converter 3 is in a state where it has been deteriorated to the
extent that it needs to be replaced immediately or soon (such a
deteriorated state will hereinafter be referred to as
"deterioration-in-progress state", or not (a state of the catalytic
converter 3 which is not in the deterioration-in-progress state
will hereinafter be referred to as "non-deteriorated state").
[0219] The catalytic converter deterioration evaluator 28 compares
the deterioration evaluating parameter B1MTLS with a predetermined
threshold CA TAGELMT as shown in FIG. 6. If B1MTLS>CATAGELMT,
then the catalytic converter deterioration evaluator 28 judges the
catalytic converter 3 as being in the deterioration-in-progress
state. If B1MTLS <CATAGELMT, then the catalytic converter
deterioration evaluator 28 judges the catalytic converter 3 as
being in the non-deteriorated state. When the catalytic converter
deterioration evaluator 28 judges the catalytic converter 3 as
being in the deterioration-in-progress state, the catalytic
converter deterioration evaluator 28 operates the deterioration
indicator 29 to indicate the deterioration-inprogress state.
[0220] The algorithm described above is a basic algorithm for
evaluating the deteriorated state of the catalytic converter 3 with
catalytic converter deterioration evaluator 28.
[0221] The general feedback controller 15 of the engine-side
control unit 7b, particularly, the adaptive controller 18, will
further be described below.
[0222] In FIG. 1, the general feedback controller 15 effects a
feedback control process to converge the output KACT (the detected
value of the air-fuel ratio) from the LAF sensor 5 toward the
target air-fuel ratio KCMD as described above. If such a feedback
control process were carried out under the known PID control only,
it would be difficult keep stable controllability against dynamic
behavioral changes including changes in the operating conditions of
the internal combustion engine 1, characteristic changes due to
aging of the internal combustion engine 1, etc.
[0223] The adaptive controller 18 is a recursive-type controller
which makes it possible to carry out a feedback control process
while compensating for dynamic behavioral changes of the internal
combustion engine 1. As shown in FIG. 7, the adaptive controller 18
comprises a parameter adjuster 30 for establishing a plurality of
adaptive parameters using the parameter adjusting law proposed by
I. D. Landau, et al., and a manipulated variable calculator 31 for
calculating the feedback manipulated variable KSTR using the
established adaptive parameters.
[0224] The parameter adjuster 30 will be described below. According
to the parameter adjusting law proposed by I. D. Landau, et al.,
when polynomials of the denominator and the numerator of a transfer
function B(Z.sup.-1)/A(Z.sup.-1) of a discrete-system object to be
controlled are generally expressed respectively by equations (33),
(34), given below, an adaptive parameter .theta. hat (j) (j
indicates the ordinal number of a control cycle) established by the
parameter adjuster 30 is represented by a vector (transposed
vector) according to the equation (35) given below. An input
.xi.(j) to the parameter adjuster 30 is expressed by the equation
(36) given below. In the present embodiment, it is assumed that the
internal combustion engine 1, which is an object to be controlled
by the general feedback controller 15, is considered to be a plant
of a first-order system having a dead time dp corresponding to the
time of three combustion cycles of the internal combustion engine
1, and m=n=1, dp=3 in the equations (33)-(36), and five adaptive
parameters s0, r1, r2, r3, b0 are established (see FIG. 7). In the
upper and middle expressions of the equation (36), us, ys generally
represent an input (manipulated variable) to the object to be
controlled and an output (controlled variable) from the object to
be controlled. In the present embodiment, the input is the feedback
manipulated variable KSTR and the output from the object (the
internal combustion engine 1) is the output KACT (detected air-fuel
ratio) from the LAF sensor 5, and the input .xi.(j) to the
parameter adjuster 30 is expressed by the lower expression of the
equation (36) (see FIG. 7).
A(Z.sup.-1)=1+a1Z.sup.-1+. . . +anZ.sup.-n (33)
B(Z.sup.-1)=b0+b1Z.sup.-1+. . . +bmZ.sup.-m (34)
{circumflex over (.theta.)}.sup.T(j)=[{circumflex over (b)}0(j),
{circumflex over (B)}R(Z.sup.-1, j), (Z.sup.-1, j)]=[b0(j), r1(j) .
. . , rm+dp-1(j), s0(j), . . . , sn-1(j)]=[b0(j),
R1(j),r2(j),r3(j), s0(j)] (35)
[0225] 23 ^ T ( j ) = [ b ^ 0 ( j ) , B ^ R ( Z - 1 , j ) , S ( Z -
1 , j ) ] = [ b0 ( j ) , r1 ( j ) , , rm + dp - 1 ( j ) , s0 ( j )
, , sn - 1 ( j ) ] = [ b0 ( j ) , r1 ( j ) , r2 ( j ) , r3 ( j ) ,
s0 ( j ) ] ( 35 ) T ( j ) = [ us ( j ) , , us ( j - m - dp + 1 ) ,
ys ( j ) , , ys ( j - n + 1 ) ] = [ us ( j ) , us ( j - 1 ) , us (
j - 2 ) , us ( j - 3 ) , ys ( j ) ] = [ KSTR ( j ) , KSTR ( j - 1 )
, KSTR ( j - 2 ) , KSTR ( j - 3 ) , KACT ( j ) ] ( 36 )
[0226] The adaptive parameter .theta. hat expressed by the equation
(35) is made up of a scalar quantity element b0 hat (j) for
determining the gain of the adaptive controller 18, a control
element BR hat (Z.sup.-1,j) expressed using a manipulated variable,
and a control element S (Z.sup.-1,j) expressed using a controlled
variable, which are expressed respectively by the following
equations (37)-(39) (see the block of the manipulated variable
calculator 31 shown in FIG. 7): 24 b ^ 0 - 1 ( j ) = 1 b0 ( 37 ) B
^ R ( Z - 1 , j ) = r1Z - 1 + r2Z - 2 + + rm + dp - 1 Z - ( n + dp
- 1 ) = r1Z - 1 + r2Z - 2 + r3Z - 3 ( 38 ) S ^ ( Z - 1 , j ) = s0 +
s1Z - 1 + + sn - 1 Z - ( n - 1 ) = s0 ( 39 )
[0227] The parameter adjuster 30 establishes coefficients of the
scalar quantity element and the control elements, described above,
and supplies them as the adaptive parameter .theta. hat expressed
by the equation (35) to the manipulated variable calculator 31. The
parameter adjuster 30 calculates the adaptive parameter .theta. hat
so that the output KACT from the LAF sensor 5 will agree with the
target air-fuel ratio KCMD, using time-series data of the feedback
manipulated variable KSTR from the present to the past and the
output KACT from the LAB sensor 5.
[0228] Specifically, the parameter adjuster 30 calculates the
adaptive parameter .theta. hat according to the following equation
(40):
{circumflex over (.theta.)}(j)={circumflex over
(.theta.)}(j-1)+.GAMMA.(j-- 1).multidot..xi.(j-dp).multidot.e* (j)
(40)
[0229] where .GAMMA.(j) represents a gain matrix (whose degree is
indicated by m+n+dp) for determining a rate of establishing the
adaptive parameter .theta. hat, and e*(j) an estimated error of the
adaptive parameter .theta. hat. .GAMMA.(j) and e*(j) are expressed
respectively by the following recursive formulas (41), (42): 25 ( j
) = 1 1 ( j ) [ ( j - 1 ) - 2 ( j ) ( j - 1 ) ( j - dp ) T ( j - dp
) ( j - 1 ) 1 ( j ) + 2 ( j ) T ( j - dp ) ( j - 1 ) ( j - dp ) ] (
41 )
[0230] where 0<.lambda.1(j).ltoreq.1,
0.ltoreq..lambda.2(j)<2, .GAMMA.(0)>0. 26 e * ( j ) = D ( Z -
1 ) KACT ( j ) - ^ T ( j - 1 ) ( j - dp ) 1 + T ( j - dp ) ( j - 1
) ( j - dp ) ( 42 )
[0231] where D(Z.sup.-1) represents an asymptotically stable
polynomial for adjusting the convergence. In the present
embodiment, D(Z.sup.-1)=1.
[0232] Various specific algorithms including the degressive gain
algorithm, the variable gain algorithm, the fixed tracing
algorithm, and the fixed gain algorithm are obtained depending on
how .lambda.1(j), .lambda.2(j) in the equation (41) are selected.
For a time-dependent plant such as a fuel injection process, an
air-fuel ratio, or the like of the internal combustion engine 1,
either one of the degressive gain algorithm, the variable gain
algorithm, the fixed gain algorithm, and the fixed tracing
algorithm is suitable.
[0233] Using the adaptive parameter .theta. hat (s0, r1, r2, r3,
b0) established by the parameter adjuster 30 and the target
air-fuel ratio KCMD determined by the exhaust-side main processor
13, the manipulated variable calculator 31 determines the feedback
manipulated variable KSTR according to a recursive formula
expressed by the following equation (43): 27 KSTR = KCMD ( j ) - s0
KACT ( j ) - r1 KSTR ( j - 1 ) - r2 KSTR ( j - 2 ) - r3 KSTR ( j -
3 ) b0 ( 43 )
[0234] The manipulated variable calculator 31 shown in FIG. 7
represents a b1 ock diagram of the calculations according to the
equation (43).
[0235] The feedback manipulated variable KSTR determined according
to the equation (43) becomes the target air-fuel ratio KCMD insofar
as the output KACT of the LAF sensor 4 agrees with the target
air-fuel ratio KCMD. Therefore, the feedback manipulated variable
KSTR is divided by the target air-fuel ratio KCMD by the divider 19
for thereby determining the feedback manipulated variable kstr that
can be used as the feedback correction coefficient KFB.
[0236] As is apparent from the foregoing description, the adaptive
controller 18 thus constructed is a recursive-type controller
taking into account dynamic behavioral changes of the internal
combustion engine 1 which is an object to be controlled. Stated
otherwise, the adaptive controller 18 is a controller described in
a recursive form to compensate for dynamic behavioral changes of
the internal combustion engine 1, and more particularly a
controller having a recursive-type adaptive parameter adjusting
mechanism.
[0237] A recursive-type controller of this type may be constructed
using an optimum regulator. In such a case, however, it generally
has no parameter adjusting mechanism. The adaptive controller 18
constructed as described above is suitable for compensating for
dynamic behavioral changes of the internal combustion engine 1.
[0238] The details of the adaptive controller 18 have been
described above.
[0239] The PID controller 17, which is provided together with the
adaptive controller 18 in the general feedback controller 15,
calculates a proportional term (P term), an integral term (I term),
and a derivative term (D term) from the difference between the
output KACT of the LAF sensor 5 and the target air-fuel ratio KCMD,
and calculates the total of those terms as the feedback manipulated
variable KLAF, as is the case with the general PID control process.
In the present embodiment, the feedback manipulated variable KLAF
is set to "1" when the output KACT of the LAF sensor 5 agrees with
the target air-fuel ratio KCMD by setting an initial value of the
integral term (I term) to "1", so that the feedback manipulated
variable KLAF can be used as the feedback correction coefficient
KFB for directly correcting the fuel injection quantity. The gains
of the proportional term, the integral term, and the derivative
term are determined from the rotational speed NE and intake
pressure PB of the internal combustion engine 1 using a
predetermined map.
[0240] The switcher 20 of the general feedback controller 15
outputs the feedback manipulated variable KLAF determined by the
PID controller 17 as the feedback correction coefficient KFB for
correcting the fuel injection quantity if the combustion in the
internal combustion engine 1 tends to be unstable as when the
temperature of the coolant of the internal combustion engine 1 is
low, the internal combustion engine 1 rotates at high speeds, or
the intake pressure is low, or if the output KACT of the LAF sensor
5 is not reliable due to a response delay of the LAF sensor 5 as
when the target air-fuel ratio KCMD changes largely or immediately
after the air-fuel ratio feedback control process has started, or
if the internal combustion engine 1 operates highly stably as when
it is idling and hence no high-gain control process by the adaptive
controller 18 is required. Otherwise, the switcher 20 outputs the
feedback manipulated variable kstr which is produced by dividing
the feedback manipulated variable KSTR determined by the adaptive
controller 18 by the target air-fuel ration KCMD, as the feedback
correction coefficient KFB for correcting the fuel injection
quantity. This is because the adaptive controller 18 effects a
high-gain control process and functions to converge the output KACT
of the LAF sensor 5 quickly toward the target air-fuel ratio KCMD,
and if the feedback manipulated variable KSTR determined by the
adaptive controller 18 is used when the combustion in the internal
combustion engine 1 is unstable or the output KACT of the LAF
sensor 5 is not reliable, then the air-fuel ratio control process
tends to be unstable.
[0241] Such operation of the switcher 20 is disclosed in detail in
Japanese laid-open patent publication No. 8-105345 or U.S. Pat. No.
5,558,075, and will not be described in detail below.
[0242] Operation of the entire apparatus according to the present
embodiment will be described below.
[0243] First, control cycles of the processing sequence carried out
by the control unit 7 will be described below. The process of
controlling the air-fuel ratio of the internal combustion engine 1,
i.e., the process of adjusting the fuel injection quantity, needs
to be in synchronism with the rotational speed of the internal
combustion engine 1. Therefore, the processing sequence carried out
by the engine-side control unit 7b is performed in control cycles
in synchronism with the crankshaft angle period (so-called TDC) of
the internal combustion engine 1. The output data from various
sensors including the LAF sensor 5 and the O.sub.2 sensor 6 are
also read in control cycles in synchronism with the crankshaft
angle period (so-called TDC).
[0244] It is preferable that the process performed by the
exhaust-side control unit 7a for calculating the target air-fuel
ratio KCMD and evaluating the deteriorated state of the catalytic
converter 3 be carried out in control cycles of a constant period
in view of the dead time present in the catalytic converter 3,
calculating loads, etc. In the present embodiment, the above
process of the exhaust-side control unit 7a is carried out in
control cycles of a constant period (e.g., 30-100 ms).
[0245] The constant period may be determined depending on the type,
reaction rate, volume, etc. of the catalytic converter 3 to be
controlled. In the present embodiment, the time interval of the
above constant period is selected to be greater than the time
interval of the crankshaft angle period (TDC) in a general
operating state, i.e., at a general rotational speed of the
internal combustion engine 1.
[0246] First, a process, carried out by the engine-side control
unit 7b, of calculating an output fuel injection quantity #nTout
(n=1, 2, 3, 4) for each of the cylinders of the internal combustion
engine 1 for controlling the air-fuel ratio of the internal
combustion engine 1 will be described below with reference to FIG.
8. The engine-side control unit 7b calculates an output fuel
injection quantity #nTout (n=1, 2, 3, 4) for each of the cylinders
in synchronism with a crankshaft angle period (TDC) of the internal
combustion engine 1 as follows:
[0247] In FIG. 8, the engine-side control unit 7b reads outputs
from various sensors including the LAF sensor 5 and the O.sub.2
sensor 6 in STEPa. At this time, the output KACT of the LAF sensor
5 and the output VO2/OUT of the O.sub.2 sensor 6, including data
obtained in the past, are stored in a timeseries fashion in a
memory (not shown).
[0248] Then, the basic fuel injection quantity calculator 8
corrects a fuel injection quantity corresponding to the rotational
speed NE and intake pressure PB of the internal combustion engine 1
depending on the effective opening area of the throttle valve,
thereby calculating a basic fuel injection quantity Tim in STEPb.
The first correction coefficient calculator 9 calculates a first
correction coefficient KTOTAL depending on the coolant temperature
and the amount by which the canister is purged in STEPc.
[0249] The engine-side control unit 7b decides whether the target
air-fuel ratio KCMD generated by the exhaust-side main processor 13
is to be used or not, i.e., determines ON/OFF of the exhaust-side
main processor 13, and sets a value of a flag f/prism/on which
represents ON/OFF of the exhaust-side main processor 13 in STEPd.
When the value of the flag f/prism/on is "0", it means that the
target air-fuel ratio KCMD generated by the exhaust-side main
processor 13 is not to be used (OFF), and when the value of the
flag f/prism/on is "1", it means that the target air-fuel ratio
KCMD generated by the exhaust-side main processor 13 is to be used
(ON).
[0250] In the above deciding step, activated states of the O.sub.2
sensor 6 and the LAF sensor 5 and an operating state (operating
mode) of the internal combustion engine 1 are determined. If these
states satisfy given conditions, then the value of the flag
f/prism/on is set to "1" in order to use the target air-fuel ratio
KCMD generated by the exhaustside main processor 13 for controlling
the supply of fuel to the internal combustion engine 1. If the
above states do not satisfy given conditions, e.g., if the O.sub.2
sensor 6 or the LAF sensor 5 is not sufficiently activated, the
supply of fuel to the internal combustion engine 1 is being cut
off, or the internal combustion engine 1 is being operated with a
lean air-fuel mixture, then the value of the flag f/prism/on is set
to "0". Basically, the value of the flag f/prism/on is set to "1"
while the internal combustion engine 1 is normally operating.
[0251] After the value of the flag f/prism/on has been set, the
engine-side control unit 7b determines the value of the flag
f/prism/on in STEPe. If f/prism/on=1, then the engine-side control
unit 7b reads the target air-fuel ratio KCMD generated by the
exhaust-side main processor 13 in STEPf. If f/prism/on=0, then the
engine-side control unit 7b sets the target air-fuel ratio KCMD to
a predetermined value in STEPg. The predetermined value to be
established as the target air-fuel ratio KCMD is determined from
the rotational speed NE and intake pressure PB of the internal
combustion engine 1 using a predetermined map, for example.
[0252] In the local feedback controller 16, the PID controllers 22
calculate respective feedback correction coefficients #nKLAF in
order to eliminate variations between the cylinders, based on
actual air-fuel ratios #nA/F of the respective cylinders which have
been estimated from the output KACT of the LAF sensor 5 by the
observer 21, in STEPh. Then, the general feedback controller 15
calculates a feedback correction coefficient KFB in STEPi.
[0253] Depending on the operating conditions of the internal
combustion engine 1, the switcher 20 selects either the feedback
manipulated variable KLAF determined by the PID controller 17 or
the feedback manipulated variable kstr which has been produced by
dividing the feedback manipulated variable KSTR determined by the
adaptive controller 18 by the target air-fuel ratio KCMD (normally,
the switcher 20 selects the feedback manipulated variable kstr).
The switcher 20 then outputs the selected feedback manipulated
variable KLAF or kstr as a feedback correction coefficient KFB for
correcting the fuel injection quantity.
[0254] When switching the feedback correction coefficient KFB from
the feedback manipulated variable KLAF from the PID controller 17
to the feedback manipulated variable kstr from the adaptive
controller 18, the adaptive controller 18 determines a feedback
manipulated variable KSTR in a manner to hold the correction
coefficient KFB to the preceding correction coefficient KFB (=KLAF)
as long as in the control cycle for the switching. When switching
the feedback correction coefficient KFB from the feedback
manipulated variable kstr from the adaptive controller 18 to the
feedback manipulated variable KLAF from the PID controller 17, the
PID controller 17 calculates a present correction coefficient KLAF
in a manner to regard the feedback manipulated variable KLAF
determined by itself in the preceding cycle time as the preceding
correction coefficient KFB (=kstr).
[0255] After the feedback correction coefficient KFB has been
calculated, the second correction coefficient calculator 10
calculates in STEPj a second correction coefficient KCMDM depending
on the target air-fuel ratio KCMD determined in STEPf or STEPg.
[0256] Then, the engine-side control unit 7b multiplies the basic
fuel injection quantity Tim determined as described above, by the
first correction coefficient KTOTAL, the second correction
coefficient KCMDM, the feedback correction coefficient KFB, and the
feedback correction coefficients #nKLAF of the respective
cylinders, determining output fuel injection quantities #nTout of
the respective cylinders in STEPk. The output fuel injection
quantities #nTout are then corrected for accumulated fuel particles
on intake pipe walls of the internal combustion engine 1 by the
fuel accumulation corrector 23 in STEPm. The corrected output fuel
injection quantities #nTout are applied to the non-illustrated fuel
injectors of the internal combustion engine 1 in STEPn.
[0257] In the internal combustion engine 1, the fuel injectors
inject fuel into the respective cylinders according to the
respective output fuel injection quantities #nTout.
[0258] The above calculation of the output fuel injection
quantities #nTout and the fuel injection of the internal combustion
engine 1 are carried out in successive cycle times synchronous with
the crankshaft angle period of the internal combustion engine 1 for
controlling the air-fuel ratio of the internal combustion engine 1
in order to converge the output KACT of the LAF sensor 5 (the
detected air-fuel ratio) toward the target air-fuel ratio KCMD.
While the feedback manipulated variable kstr from the adaptive
controller 18 is being used as the feedback correction co-efficient
KFB, the output KACT of the LAF sensor 5 is quickly converged
toward the target air-fuel ratio KCMD with high stability against
behavioral changes such as changes in the operating conditions of
the internal combustion engine 1 or characteristic changes thereof.
A response delay of the internal combustion engine 1 is also
appropriately compensated for.
[0259] Concurrent with the above fuel control (the fuel injection
quantity adjustment) for the internal combustion engine 1, the
exhaust-side main processor 13 of the exhaustside control unit 7a
executes a main routine shown in FIG. 9 in control cycles of a
constant period.
[0260] As shown in FIG. 9, the exhaust-side main processor 13
decides whether the processing thereof (the processing of the
identifier 25, the estimator 26, the sliding mode controller 27,
and the catalytic converter deterioration evaluator 28) is to be
executed or not, and sets a value of a flag f/prism/cal indicative
of whether the processing is to be executed or not in STEP1. When
the value of the flag f/prism/cal is "", it means that the
processing of the exhaust-side main processor 13 is not to be
executed, and when the value of the flag f/prism/cal is "1", it
means that the processing of the exhaust-side main processor 13 is
to be executed.
[0261] The deciding subroutine in STEP1 is shown in detail in FIG.
10. As shown in FIG. 10, the exhaust-side main processor 13 decides
whether the O.sub.2 sensor 6 and the LAF sensor 5 are activated or
not respectively in STEP1-1, STEP1-2. If neither one of the O.sub.2
sensor 6 and the LAF sensor 5 is activated, since detected data
from the O.sub.2 sensor 6 and the LAF sensor 5 for use by the
exhaust-side main processor 13 are not accurate enough, the value
of the flag f/prism/cal is set to "0" in STEP1-6. Then, in order to
initialize the identifier 25 as described later on, the value of a
flag f/id/reset indicative of whether the identifier 25 is to be
initialized or not is set to "1" in STEP1-7. When the value of the
flag f/id/reset is "1", it means that the identifier 25 is to be
initialized, and when the value of the flag f/id/reset is "0", it
means that the identifier 25 is not to be initialized.
[0262] The exhaust-side main processor 13 decides whether the
internal combustion engine 1 is operating with a lean air-fuel
mixture or not in STEP1-3. The exhaust-side main processor 13
decides whether the ignition timing of the internal combustion
engine 1 is retarded for early activation of the catalytic
converter 3 immediately after the start of the internal combustion
engine 1 or not in STEP1-4. If the conditions of these steps are
satisfied, then since the target air-fuel ratio KCMD calculated to
adjust the output VO2/OUT of the O.sub.2 sensor 6 to the target
value VO2/TARGET is not used for the fuel control for the internal
combustion engine 1, the value of the flag f/prism/cal is set to
fior in STEP1-6, and the value of the flag f/id/reset is set to "1"
in order to initialize the identifier 25 in STEP1-7.
[0263] If the conditions of STEPl-1, STEP1-2 are satisfied and the
conditions of STEP1-3, STEP1-4 are not satisfied, then the value of
the flag f/prism/cal is set to "1" in order to perform the
processing sequence of the exhaustside main processor 13 in
STEP1-5.
[0264] In FIG. 9, after the above deciding subroutine, the
exhaust-side main processor 13 decides whether a process of
identifying (updating) the gain coefficients a1, a2, b1 with the
identifier 25 is to be executed or not, and sets a value of a flag
f/id/cal indicative of whether the process of identifying
(updating) the gain coefficients a1, a2, b1 is to be executed or
not in STEP2. When the value of the flag f/id/cal is "0", it means
that the process of identifying (updating) the gain coefficients
a1, a2, b1 is not to be executed, and when the value of the flag
f/id/cal is "1", it means that the process of identifying
(updating) the gain coefficients a1, a2, b1 is to be executed.
[0265] The deciding subroutine of STEP2 is shown in detail in FIG.
11.
[0266] The exhaust-side main processor 13 decides whether the
throttle valve of the internal combustion engine 1 is fully open or
not in STEP2-1. The exhaust-side main processor 13 decides whether
the supply of fuel to the internal combustion engine 1 is being
stopped or not in STEP2-2. If either one of the conditions of these
steps is satisfied, then since it is difficult to adjust the gain
coefficients a1, a2, b1 appropriately, the value of the flag
f/id/cal is set to "0" in STEP2-4. If neither one of the conditions
of these steps is satisfied, then the value of the flag f/id/cal is
set to "1" to identify (update) the gain coefficients a1, a2, b1
with the identifier 25 in STEP2-3.
[0267] Referring back to FIG. 9, the exhaust-side main processor 13
acquires the latest differential outputs kact(k) (=KACT-FLAF/BASE),
VO2(k) (=VO2/OUT VO2/TARGET) respectively from the subtractors 11,
12 in STEP3. Specifically, the subtractors 11, 12 select latest
ones of the time-series data read and stored in the non-illustrated
memory in STEPa shown in FIG. 8, calculate the differential outputs
kact(k), VO2(k), and give the calculated differential outputs
kact(k), VO2(k) to the exhaust-side main processor 13. The
differential outputs kact(k), VO2(k) given to the exhaust-side main
processor 13, as well as data given in the past, are stored in a
time-series manner in a memory (not shown) in the exhaust-side
control unit 7a.
[0268] Then, in STEP4, the exhaust-side main processor 13
determines the value of the flag f/prism/cal set in STEP1. If the
value of the flag f/prism/cal is "0", i.e., if the processing of
the exhaust-side main processor 13 is not to be executed, then the
exhaust-side main processor 13 "forcibly sets the SLD manipulating
input Us1 (the target differential air-fuel ratio kcmd) to be
determined by the sliding mode controller 27, to a predetermined
value in STEP13. The predetermined value may be a fixed value
(e.g., "0") or the value of the SLD manipulating input Us1
determined in a preceding control cycle.
[0269] After the SLD manipulating input Us1 is set to the
predetermined value in STEP13, the exhaust-side main processor 13
adds the reference value FLAF/BASE to the SLD manipulating input
Us1 for thereby determining a target air-fuel ratio KCMD in the
present control cycle in STEP14. Then, the processing in the
present control cycle is finished.
[0270] If the value of the flag f/prism/cal is "1" in STEP4, i.e.,
if the processing of the exhaust-side main processor 13 is to be
executed, then the exhaust-side main processor 13 effects the
processing of the identifier 25 in STEP5.
[0271] The processing subroutine of STEP5 is shown in detail in
FIG. 12.
[0272] The identifier 25 determines the value of the flag f/id/cal
set in STEP2 in STEP5-1. If the value of the flag f/id/cal is "0",
then since the process of identifying the gain coefficients a1, a2,
b1 with the identifier 25 is not carried out, control immediately
goes back to the main routine shown in FIG. 9.
[0273] If the value of the flag f/id/cal is "1", then the
identifier 25 determines the value of the flag f/id/reset set in
STEP1 with respect to the initialization of the identifier 25 in
STEP5-2. If the value of the flag f/id/reset is "1", the identifier
25 is initialized in STEP5-3. When the identifier 25 is
initialized, the identified gain coefficients a1 hat, a2 hat, b1
hat are set to predetermined initial values (the identified gain
coefficient vector .THETA. according to the equation (4) is
initialized), and the elements of the matrix P (diagonal matrix)
according to the equation (10) are set to predetermined initial
values. The value of the flag f/id/reset is reset to Then, the
identifier 25 calculates the identified differential output VO2(k)
hat, which is the output of the exhaust system model that is
expressed using the present identified gain coefficients al(k-1)
hat, a2(k-1) hat, b1(k-1) hat, using the past data VO2(k-1),
VO2(k-2), kact(k-d-1) of the differential outputs VO2, kact
calculated in each control cycle in STEP3, and the values of the
identified gain coefficients a1(k-1) hat, a2(k-1)hat, b1(k-1) hat,
according to the equation (3) or the equation (6) equivalent
thereto in STEP5-4.
[0274] The identifier 25 then calculates the vector KO(k) to be
used in determining the new identified gain coefficients a1 hat, a2
hat, b1 hat according to the equation (9) in STEP5-5. Thereafter,
the identifier 25 carries out a management process described below
in STEP5-6.
[0275] When the gain coefficients a1, a2, b1 of the exhaust system
model are to be sequentially identified, they should preferably be
identified in a particular behavioral state of the object exhaust
system E. For example, it is easier to obtain identified gain
coefficients a1 hat, a2 hat, b1 hat that are appropriate for
calculating the target air-fuel ratio and evaluating the
deteriorated state of the catalytic converter 3 by identifying the
gain coefficients a1, a2, b1 in a behavioral state of the object
exhaust system E in which the air-fuel ratio is changed from a
leaner value to a richer value than by identifying the gain
coefficients a1, a2, b1 in a behavioral state of the object exhaust
system E in which the air-fuel ratio is changed from a richer value
to a leaner value.
[0276] In the present invention, therefore, the process of
identifying the gain coefficients a1, a2, b1, or more precisely the
process of updating the identified gain coefficients a1 hat, a2
hat, b1 hat, is carried out in a behavioral state of the object
exhaust system E in which the air-fuel ratio is changed from a
leaner value to a richer value. The management process is a process
of specifying such a behavioral state of the object exhaust system
E.
[0277] As shown in FIG. 13, according to the control process of the
present embodiment which uses the adaptive sliding mode control
process, the state quantity X (VO2(k), VO2(k-1)) of the
differential output VO2 of the O.sub.2 sensor 6 changes from its
initial state at a point Q along a path W with respect to the
hyperplane .sigma.=0 (see FIG. 4). Basically, a state in which the
state quantity X changes above the hyperplane .sigma.=0 (at this
time, the value of the switching function a determined by the state
quantity X is positive) is equal to a state in which the air-fuel
ratio is changed from a leaner value to a richer value, and a state
in which the state quantity x changes below the hyperplane
.sigma.=0 (at this time, the value of the switching function a
determined by the state quantity X is negative) is equal to a state
in which the air-fuel ratio is changed from a richer value to a
leaner value.
[0278] Consequently, whether the object exhaust system E is in a
behavioral state in which the air-fuel ratio recognized by the
output VO2/OUT (the detected value of the oxygen concentration) of
the O.sub.2 sensor 6 is changed from a leaner value to a richer
value or not can be determined based on whether the value of the
switching function .sigma. is positive or negative. However, if
whether the object exhaust system E is in a behavioral state in
which the air-fuel ratio is changed from a leaner value to a richer
value or not is determined based on whether the value of the
switching function .sigma. is positive or not, then the decision
about whether the object exhaust system E is in a behavioral state
in which the air-fuel ratio is changed from a leaner value to a
richer value or not may be changed when the state quantity X
slightly varies from above the hyperplane .sigma.=0. Therefore, it
is not preferable to carry out the process of identifying the gain
coefficients a1, a2, b1, i.e., updating the identified gain
coefficients a1 hat, a2 hat, b1 hat, depending on that
decision.
[0279] In the present embodiment, a management function .lambda.
defined using the time-series data of the differential output VO2
according to the following equation (44) is introduced:
.gamma.(k)=m1.multidot.VO2(k)+m2.multidot.VO2(k-1)+m3 (44)
[0280] The coefficients ml, m2, m3 of the management function
.gamma. are established such that a management hyperplane (in this
case, a straight line) expressed by .gamma.=0 is positioned
slightly above (in the region of .sigma.>0) the sliding mode
control hyperplane .sigma.=0. In this embodiment, the coefficient
m1 of the management function y is set to "1" in view of the fact
that the coefficient s1 of the switching function a is set to
"1".
[0281] If the management function .gamma. is .gamma.>0, then the
object exhaust system E is certainly in a behavioral state in which
the air-fuel ratio is changed from a leaner value to a richer
value. Therefore, whether the object exhaust system E is in such a
behavioral state or not can stably be determined based on whether
the management function .gamma. is of a positive value (including
"0") or not.
[0282] The management process in STEP5-6 determines, using the
management function .gamma. thus defined, whether the object
exhaust system E is in a behavioral state in which the air-fuel
ratio recognized by the output VO2/OUT (the detected value of the
oxygen concentration) of the O.sub.2 sensor 6 is changed from a
leaner value to a richer value or not, i.e., whether the object
exhaust system E is in a behavioral state that is suitable for the
identifier 25 to identify the gain coefficients a1, a2, b1 or not.
The management process is specifically carried out as follows:
[0283] The identifier 25 calculates the value of the management
function .gamma. according to the above equation (44), using the
latest differential output VO2(k) acquired in STEP3 (see FIG. 9)
and the differential output VO2(k-1) in the preceding control
cycle. If the management function y thus determined is
.gamma..gtoreq.0, then the identifier 25 sets a flag f/id/mng to
"1", and if the management function .gamma. is .gamma.<0, then
the identifier 25 sets the flag f/id/mng to "0". When the flag
f/id/mng is "1", it indicates that the object exhaust system E is
in a behavioral state in which the air-fuel ratio is changed from a
leaner value to a richer value. When the flag f/id/mng is "0", it
indicates otherwise.
[0284] Thus, the value of the flag f/id/mng indicates whether the
object exhaust system E is in a behavioral state in which the
air-fuel ratio is changed from a leaner value to a richer value,
i.e., whether the object exhaust system E is in a behavioral state
that is suitable for the identifier 25 to identify the gain
coefficients a1, a2, b1, or to update the identified gain
coefficients a1 hat, a2 hat, b1 hat.
[0285] After having carried out the management process, the
identifier 25 determines the value of the flag f/id/mng in STEP5-7.
If f/id/mng=1, i.e., if the object exhaust system E is in a
behavioral state in which the air-fuel ratio is changed from a
leaner value to a richer value, then the identifier 25 calculates
the identified error id/e, i.e., the difference between the
identified differential output VO2 hat and the actual differential
output VO2 (see the equation (7)), in STEP5-8. If f/id/mng=0, then
the identifier 25 forcibly sets the value of the identified error
id/e to "0" in STEP5-9.
[0286] Thereafter, the identifier 25 calculates a new identified
gain coefficient vector @(k), i.e., new identified gain
coefficients a1(k) hat, a2(k) hat, b1(k) hat, according to the
equation (8) using the identified error id/e determined in STEP5-8
or STEP5-9 and KO calculated in SETP5-5 in STEP5-10.
[0287] The identified error id/e obtained in STEP5-8 may basically
be calculated according to the equation (7). In the present
embodiment, however, as shown in FIG. 14, a value (=VO2-VO2 hat)
calculated according to the equation (7) from the differential
output VO2 acquired in each control cycle in STEP3 (see FIG. 9),
and the identified differential output VO2 hat calculated in each
control cycle in STEP5-4 is filtered with low-pass characteristics
to calculate the identified error id/e.
[0288] This is because since the object exhaust system E including
the catalytic converter 3 generally has low-pass characteristics,
it is preferable to attach importance to the low-frequency behavior
of the exhaust system E in appropriately identifying the gain
coefficients a1, a2, b1 of the the exhaust system model.
[0289] Both the differential output VO2 and the identified
differential output VO2 hat may be filtered with the same low-pass
characteristics. For example, after the differential output VO2 and
the identified differential output VO2 hat have separately been
filtered, the equation (7) may be calculated to determine the
identified error id/e.
[0290] However, determining the identified error id/e by filtering
the result of the calculation of the equation (7) as with the
present embodiment offers the following advantages: If the
resolutions of the differential output kact of the LAF sensor 5 and
the differential output VO2 of the O.sub.2 sensor 6, which are
supplied to the exhaust-side main processor 13, are lower than the
calculating resolution of the exhaust-side main processor 13, then
the result of the calculation of the equation (7) exhibits
relatively large stepwise changes. By filtering the result of the
calculation of the equation (7), any changes of the identified
error id/e can be smoothed.
[0291] The above filtering is carried out by a moving average
process which is a digital filtering process, for example.
[0292] After having calculated the new identified gain coefficients
a1(k) hat, a2(k) hat, b1(k) hat, the identifier 25 limits the
values of the identified gain coefficients a1 hat, a2 hat, b1 hat
(elements of the identified gain coefficient vector .THETA.), are
limited to meet predetermined conditions in STEP5-11, as described
below.
[0293] The predetermined conditions for limiting the values of the
identified gain coefficients a1 hat, a2 hat, b1 hat include a
condition (hereinafter referred to as a first limiting condition)
for limiting combinations of the values of the identified gain
coefficients a1 hat, a2 hat, and a condition (hereinafter referred
to as a second limiting condition) for limiting the value of the
identified gain coefficient b1 hat.
[0294] Prior to describing the first and second limiting conditions
and the specific processing details of STEP5-11, the reasons for
limiting the values of the identified gain coefficients a1 hat, a2
hat, b1 hat will be described below.
[0295] The inventors of the present invention have found that if
the values of the identified gain coefficients al hat, a2 hat, b1
hat are not particularly limited, while the output signal VO2/OUT
of the O.sub.2 sensor 6 is being stably controlled at the target
value VO2/TARGET, there are developed a situation in which the
target air-fuel ratio KCMD determined by the sliding mode
controller 27 changes smoothly with time, and a situation in which
the target air-fuel ratio KCMD oscillates with time at a high
frequency. Neither of these situations poses problems in
controlling the output VO2/OUT of the O.sub.2 sensor 6 at the
target value VO2/TARGET. However, the situation in which the target
air-fuel ratio KCMD oscillates with time at a high frequency is not
preferable in smoothly operating the internal combustion engine 1
that is controlled on the basis of the target air-fuel ratio KCMD.
In this situation, the value of the identified gain coefficient b1
hat sequentially calculated by the identifier 25 may possible
become inadequate for evaluating the deteriorated state of the
catalytic converter 3.
[0296] A study of the above phenomenon by the inventors has shown
that whether the target air-fuel ratio KCMD determined by the
sliding mode controller 27 changes smoothly or oscillates at a high
frequency depends strongly on the combinations of the values of the
identified gain coefficients a1 hat, a2 hat identified by the
identifier 25 and the value of the identified gain coefficient b1
hat.
[0297] In the present embodiment, the first and second limiting
conditions are established appropriately, and the combinations of
the values of the identified gain coefficients a1 hat, a2 hat and
the value of the identified gain coefficient b1 hat are
appropriately limited to eliminate the situation in which the
target air-fuel ratio KCMD oscillates at a high frequency.
[0298] According to the present embodiment, the first and second
limiting conditions are established as follows:
[0299] With respect to the first limiting condition for limiting
the values of the identified gain coefficients a1 hat, a2 hat, the
study by the inventors indicates that whether the target air-fuel
ratio KCMD determined by the sliding mode controller 27 changes
smoothly or oscillates at a high frequency is closely related to
combinations of the coefficient values a1, a2 in the equations
(12)-(14) which are determined by the values of the gain
coefficients al, a2, i.e., the coefficient values .alpha.1,
.alpha.2 used for the estimator 26 to determine the estimated
differential output VO2(k+d) bar (the coefficient values .alpha.1,
.alpha.2 are the firstrow, first-column element and the first-row,
second-column element of the matrix A.sup.d which is a power of the
matrix A defined by the equation (12)).
[0300] Specifically, as shown in FIG. 15, when a coordinate plane
whose coordinate components or axes are represented by the
coefficient values .alpha.1, .alpha.2 is established, if a point on
the coordinate plane which is determined by a combination of the
coefficient values .alpha.1, .alpha.2 lies in a hatched range,
which is surrounded by a triangle Q.sub.1Q.sub.2Q.sub.3 (including
the boundaries) and will hereinafter be referred to as an
estimating coefficient stable range, then the target air-fuel ratio
KCMD tends to be smooth.
[0301] Therefore, the combinations of the values of the gain
coefficients a1, a2 identified by the identifier 25, i.e., the
combinations of the values of the identified gain coefficients a1
hat, a2 hat, should be limited such that the point on the
coordinate plane shown in FIG. 15 which corresponds to the
combination of the coefficient values a1, a2 determined by the
values of the gain coefficients a1, a2 or the values of the
identified gain coefficients a1 hat, a2 hat will lie within the
estimating coefficient stable range.
[0302] In FIG. 15, a triangular range Q.sub.1Q.sub.4Q.sub.3 on the
coordinate plane which contains the estimating coefficient stable
range is a range that determines combinations of the coefficient
values .alpha.1, .alpha.2 which makes theoretically stable a system
defined according to the following equation (45), i.e., a system
defined by an equation similar to the equation (12) except that
VO2(k), VO2(k-1) on the right side of the equation (12) are
replaced respectively with VO2(k) bar, VO2(k-1) bar VO2(k) bar,
VO2(k-1) bar mean respectively an estimated differential output
determined before the dead time d by the estimator 26 and an
estimated differential output determined in a preceding cycle by
the estimator 26). 28 VO2 _ ( k + d ) = 1 VO2 _ ( k ) + 2 VO2 _ ( k
- 1 ) + j = 1 d j kcmd ( k - j ) ( 45 )
[0303] The condition for the system defined according to the
equation (45) to be stable is that a pole of the system (which is
given by the following equation (46)) exists in a unit circle on a
complex plane: 29 Pole of the system according to the equation ( 45
) = 1 a1 2 + 4 2 2 ( 46 )
[0304] The triangular range Q.sub.1Q.sub.4Q.sub.3 shown in FIG. 15
is a range for determining the combinations of the coefficient
values .alpha.1, .alpha.2 which satisfy the above condition.
Therefore, the estimating coefficient stable range is a range
indicative of those combinations where .alpha.1.ltoreq.0 of the
combinations of the coefficient values .alpha.1, .alpha.2 which
make stable the system defined by the equation (45).
[0305] Since the coefficient values .alpha.1, .alpha.2 are
determined by a combination of the values of the gain coefficients
a1, a2, a combination of the values of the gain coefficients a1, a2
is determined by a combination of the coefficient values .alpha.1,
.alpha.2. Therefore, the estimating coefficient stable range shown
in FIG. 15 which determines preferable combinations of the
coefficient values .alpha.1, .alpha.2 can be converted into a range
on a coordinate plane shown in FIG. 16 whose coordinate components
or axes are represented by the gain coefficients a1, a2.
Specifically, the estimating coefficient stable range shown in FIG.
15 is converted into a range enclosed by the imaginary lines in
FIG. 16, which is a substantially triangular range having an
undulating lower side and will hereinafter be referred to as an
identifying coefficient stable range, on the coordinate plane shown
in FIG. 16. Stated otherwise, when a point on the coordinate plane
shown in FIG. 16 which is determined by a combination of the values
of the gain coefficients a1, a2 resides in the identifying
coefficient stable range, a point on the coordinate plane shown in
FIG. 15 which corresponds to the combination of the coefficient
values .alpha.1, .alpha.2 determined by those values of the gain
coefficients a1, a2 resides in the estimating coefficient stable
range.
[0306] Consequently, the first limiting condition for limiting the
values of the identified gain coefficients a1 hat, a2 hat
determined by the identifier 25 should preferably be basically
established such that a point on the coordinate plane shown in FIG.
16 which is determined by those values of the identified gain
coefficients a1 hat, a2 hat reside in the identifying coefficient
stable range.
[0307] However, since a boundary (lower side) of the identifying
coefficient stable range indicated by the imaginary lines in FIG.
16 is of a complex undulating shape, a practical process for
limiting the point on the coordinate plane shown in FIG. 16 which
is determined by the values of the identified gain coefficients a1
hat, a2 hat is liable to be complex.
[0308] For this reason, according to the present embodiment, the
identifying coefficient stable range is substantially approximated
by a quadrangular range Q.sub.5Q.sub.6Q.sub.7Q.sub.8 enclosed by
the solid lines in FIG. 16, which has straight boundaries and will
hereinafter be referred to as an identifying coefficient limiting
range. As shown in FIG. 16, the identifying coefficient limiting
range is a range enclosed by a polygonal line (including line
segments Q.sub.5Q.sub.6 and Q.sub.5Q.sub.8) expressed by a
functional expression .vertline.a1.vertline.+a2=1, a straight line
(including a line segment Q.sub.6Q.sub.7) expressed by a
constantvalued functional expression a1=A1L (A1L: constant), and a
straight line (including a line segment Q.sub.7Q.sub.8) expressed
by a constant-valued functional expression a2=A2L (A2L: constant).
The first limiting condition for limiting the values of the
identified gain coefficients a1 hat, a2 hat is established such
that the point on the coordinate plane shown in FIG. 16 which is
determined by those values of the identified gain coefficients a1
hat, a2 hat lies in the identifying coefficient limiting range, and
the values of the identified gain coefficients a1 hat, a2 hat are
limited such that the point determined by those values of the
identified gain coefficients a1 hat, a2 hat lies in the identifying
coefficient limiting range. Although part of the lower side of the
identifying coefficient limiting range deviates from the
identifying coefficient stable range, it has experimentally been
confirmed that the point determined by the identified gain
coefficients a1 hat, a2 hat determined by the identifier 25 does
not actually fall in the deviating range. Therefore, the deviating
range will not pose any practical problem.
[0309] The above identifying coefficient limiting range is given
for illustrative purpose only, and may be equal to or may
substantially approximate the identifying coefficient stable range,
or may be of any shape insofar as most or all of the identifying
coefficient limiting range belongs to the identifying coefficient
stable range. Thus, the identifying coefficient limiting range may
be established in various configurations in view of the ease with
which to limit the values of the identified gain coefficients a1
hat, a2 hat and the practical controllability. For example, while
the boundary of an upper portion of the identifying coefficient
limiting range is defined by the functional expression
.vertline.a1.vertline.+a2=1 in the illustrated embodiment,
combinations of the values of the gain coefficients a1, a2 which
satisfy this functional expression are combinations of theoretical
stable limits where a pole of the system defined by the equation
(45) exists on a unit circle on a complex plane. Therefore, the
boundary of the upper portion of the identifying coefficient
limiting range may be determined by a functional expression
.vertline.a1.vertline.+a2=r (r is a value slightly smaller than
j"1" corresponding to the stable limits, e.g., 0.99) for higher
control stability.
[0310] The above identifying coefficient stable range shown in FIG.
16 as a basis for the identifying coefficient limiting range is
given for illustrative purpose only. The identifying coefficient
stable range which corresponds to the estimating coefficient stable
range shown in FIG. 15 is affected by the dead time d (more
precisely, its set value) and has its shape varied depending on the
dead time d, as can be seen from the definition of the coefficient
values a1, a2 (see the equation (12)). Irrespective of the shape of
the identifying coefficient stable range, the identifying
coefficient limiting range may be established, as described above,
in a manner to match the shape of the identifying coefficient
stable range.
[0311] In the present embodiment, the second limiting condition for
limiting the value of the gain coefficient b1 identified by the
identifier 25, i.e., the value of the identified gain coefficient
b1 hat, is established as follows:
[0312] The inventors have found that the situation in which the
time-depending change of the target air-fuel ratio KCMD is
oscillatory at a high frequency tends to happen also when the value
of the identified gain coefficient b1 hat is excessively large or
small. According to the present embodiment, an upper limit value
B1H and a lower limit value B1L (B1H>B1L>0) for the
identified gain coefficient b1 hat are determined in advance
through experimentation or simulation. Then, the second limiting
condition is established such that the identified gain coefficient
b1 hat is equal to or smaller than the upper limit value B1H and
equal to or greater than the lower limit value B1L (B1L.ltoreq.b1
hat<B1H).
[0313] A process of limiting the values of the identified gain
coefficients a1 hat, a2 hat, b1 hat according to the first and
second limiting conditions is carried out by in STEP5-11 as
follows:
[0314] As shown in FIG. 17, the identifier 25 limits combinations
of the identified gain coefficients a1(k) hat, a2(k) hat determined
in STEP5-10 shown in FIG. 12 according to the first limiting
condition in STEP5-11-1 through STEP5-11-8.
[0315] Specifically, the identifier 25 decides whether or not the
value of the identified gain coefficient a2(k) hat determined in
STEP5-10 is equal to or greater than a lower limit value A2L (see
FIG. 16) for the gain coefficient a2 in the identifying coefficient
limiting range in STEP5-11-1.
[0316] If the value of the identified gain coefficient a2(k) is
smaller than A2L, then since a point on the coordinate plane shown
in FIG. 16, which is expressed by (a1(k) hat, a2(k) hat),
determined by the combination of the values of the identified gain
coefficients a1(k) hat, a2(k) hat does not reside in the
identifying coefficient limiting range, the value of a2(k) hat is
forcibly changed to the lower limit value A2L in STEP5-11-2. Thus,
the point (a1(k) hat, a2(k) hat) on the coordinate plane shown in
FIG. 16 is limited to a point in a region on and above a straight
line, i.e., the straight line including the line segment
Q.sub.7Q.sub.8, expressed by at least a2=A2L.
[0317] Then, the identifier 25 decides whether or not the value of
the identified gain coefficient a1(k) hat determined in STEP5-10 is
equal to or greater than a lower limit value A1L (see FIG. 16) for
the gain coefficient a1 in the identifying coefficient limiting
range in STEP5-11-3, and then decides whether or not the value of
the identified gain coefficient a1(k) hat is equal to or smaller
than an upper limit value A1H (see FIG. 16) for the gain
coefficient al in the identifying coefficient limiting range in
STEP5-11-5. The upper limit value A1H for the gain coefficient a1
in the identifying coefficient limiting range is represented by
A1H=1-A2L because it is an a1 coordinate of the point Q.sub.8 where
the polygonal line .vertline.a1.vertline.+a2=1 (a1>0) and the
straight line a2=A2L intersect with each other, as shown in FIG.
16.
[0318] If the value of the identified gain coefficient a1(k) hat is
smaller than the lower limit value A1L or greater than the upper
limit value A1H, then since the point (a1(k) hat, a2(k) hat) on the
coordinate plane shown in FIG. 16 does not reside in the
identifying coefficient limiting range, the value of a1(k) hat is
forcibly changed to the lower limit value A1L or the upper limit
value A1H in STEP-5-11-4, STEP5-11-6.
[0319] Thus, the point (a1(k) hat, a2(k) hat) on the coordinate
plane shown in FIG. 16 is limited to a region on and between a
straight line, i.e., the straight line including the line segment
Q.sub.6A.sub.7, expressed by a1=A1L, and a straight line, i.e., the
straight line passing through the point Q.sub.8 and perpendicular
to the a1 axis, expressed by a1=A1H.
[0320] The processing in STEP5-11-3 and STEP5-11-4 and the
processing in STEP5-11-5 and STEP5-11-6 may be switched around. The
processing in STEP5-11-1 and STEP5-11-2 may be carried out after
the processing in STEP5-11-3 through STEP5-11-6.
[0321] Then, the identifier 25 decides whether the present values
of a1(k) hat, a2(k) hat after STEP5-11-1 through STEP5-11-6 satisfy
an inequality lall +a2 <1 or not, i.e., whether the point (a1(k)
hat, a2(k) hat) is positioned on or below or on or above the
polygonal line (including line segments Q.sub.5Q.sub.6 and Q5Q8)
expressed by the functional expression lall +a2 1 in
STEP5-11-7.
[0322] If .vertline.a1.vertline.+a2.ltoreq.1, then the point (a1(k)
hat, a2(k) hat) determined by the values of a1(k) hat, a2(k) hat
after STEP5-11-1 through STEP5-11-6 exists in the identifying
coefficient limiting range (including its boundaries).
[0323] If .vertline.a1.vertline.+a2>1, then since the point
(a1(k) hat, a2(k) hat) deviates upwardly from the identifying
coefficient limiting range, the value of the a2(k) hat is forcibly
changed to a value (1-.vertline.a1(k) hat.vertline.) depending on
the value of a1(k) hat in STEP5-11-8. Stated otherwise, while the
value of a1(k) hat is being kept unchanged, the point (a1(k) hat,
a2(k) hat) is moved onto a polygonal line expressed by the
functional expression lall +a2=1, i.e., onto the line segment
Q.sub.5Q.sub.6 or the line segment Q.sub.5Q.sub.8 which is a
boundary of the identifying coefficient limiting range.
[0324] Through the above processing in STEP5-11-1 through 5-11-8,
the values of the identified gain coefficients a1(k) hat, a2(k) hat
are limited such that the point (a1(k) hat, a2(k) hat) determined
thereby resides in the identifying coefficient limiting range. If
the point (a1(k) hat, a2(k) hat) corresponding to the values of the
identified gain coefficients a1(k) hat, a2(k) hat that have been
determined in STEP5-10 exists in the identifying coefficient
limiting range, then those values of the identified gain
coefficients a1(k) hat, a2(k) hat are maintained.
[0325] The value of the identified gain coefficient a1(k) hat
relative to the primary autoregressive term of the discrete-system
model is not forcibly changed insofar as the value resides between
the lower limit value A1L and the upper limit value A1H of the
identifying coefficient limiting range. If a1(k) hat<A1L or
a1(k) hat>A1H, then since the value of the identified gain
coefficient a1(k) hat is forcibly changed to the lower limit value
A1L which is a minimum value that the gain coefficient a1 can take
in the identifying coefficient limiting range or the upper limit
value A1H which is a maximum value that the gain coefficient al can
take in the identifying coefficient limiting range, the change in
the value of the identified gain coefficient a1(k) hat is minimum.
Stated otherwise, if the point (a1(k) hat, a2(k) hat) corresponding
to the values of the identified gain coefficients a1(k) hat, a2(k)
hat that have been determined in STEP5-10 deviates from the
identifying coefficient limiting range, then the forced change in
the value of the identified gain coefficient a1(k) hat is held to a
minimum.
[0326] After having limited the values of the identified gain
coefficients a1(k) hat, a2(k) hat, the identifier 25 limits the
identified gain coefficient b1(k) hat according to the second
limiting condition in STEP5-11-9 through STEP5-11-12.
[0327] Specifically, the identifier 25 decides whether or not the
value of the identified gain coefficient b1(k) hat determined in
STEP5-10 is equal to or greater than the lower limit value B1L in
STEP5-11-9. If the lower limit value B1L is greater than the value
of the identified gain coefficient b1(k) hat, the value of b1(k)
hat is forcibly changed to the lower limit value B1L in
STEP5-11-10.
[0328] The identifier 25 decides whether or not the value of the
identified gain coefficient b1(k) hat is equal to or smaller than
the upper limit value B1H in STEP5-11-11. If the upper limit value
B1H is greater than the value of the identified gain coefficient
b1(k) hat, the value of b1(k) hat is forcibly changed to the upper
limit value B1H in STEP5-11-12.
[0329] Through the above processing in STEP5-11-9 through 5-11-12,
the value of the identified gain coefficient 1(k) hat is limited to
a range between the lower limit value B1L and the upper limit value
B1H.
[0330] After the identifier 25 has limited the combination of the
values of the identified gain coefficients a1(k) hat, a2(k) hat and
the identified gain coefficient b1(k) hat, control returns to the
sequence shown in FIG. 12.
[0331] The preceding values al(k-1) hat, a2(k-1) hat, 1(k-1) hat of
the identified gain coefficients used for determining the
identified gain coefficients a1(k) hat, a2(k) hat, b1(k) hat in
STEP5-10 shown in FIG. 12 are the values of the identified gain
coefficients limited according to the first and second limiting
conditions in STEP5-11 in the preceding control cycle.
[0332] Referring back to FIG. 12, after having limited the
identified gain coefficients a1(k) hat, a2(k) hat, b1(k) hat as
described above, the identifier 25 determines the value of the flag
f/id/mng set in the management process STEP5-6 in STEP5-12. If
f/id/mng=1, then the identifier 25 updates the matrix P(k)
according to the equation (10) for the processing of a next control
cycle in STEP5-13, after which control returns to the main routine
shown in FIG. 9. If f/id/mng=0, then since the values of the
identified gain coefficients a1(k) hat, a2(k) hat, b1(k) hat have
not been updated in STEP5-10, the identifier 25 maintains the
present matrix P(k-1) as the matrix P(k) in STEP5-14, after which
control returns to the main routine shown in FIG. 9.
[0333] The above process is the processing sequence of the
identifier 25 which is carried out in STEP5 shown in FIG. 9.
[0334] After the processing sequence of the identifier 25 has been
carried out as described above, the catalytic converter
deterioration evaluator 28 performs its own processing sequence in
STEP6 in FIG. 9. The processing sequence of the catalytic converter
deterioration evaluator 28 will be described below with reference
to FIG. 18.
[0335] The catalytic converter deterioration evaluator 28
determines the value of a flag F/DONE in STEP6-1. When the value of
the flag F/DONE is "1", then it indicates that the evaluation of
the deteriorated state of the catalytic converter 3 is completed
during the present operation of the internal combustion engine 1,
and when the value of the flag F/DONE is "0", then it indicates
that the evaluation of the deteriorated state of the catalytic
converter 3 is not completed during the present operation of the
internal combustion engine 1. When the internal combustion engine 1
starts to operate, the value of the flag F/DONE is initialized to
"0".
[0336] If F/DONE=0, i.e., if the evaluation of the deteriorated
state of the catalytic converter 3 is not completed, then the
catalytic converter deterioration evaluator 28 performs a process
of determining a varying state of the rate of flow of the exhaust
gas discharged from the internal combustion engine 1 into the
exhaust pipe 2 (hereinafter referred to as "exhaust gas volume") in
STEP6-2. More specifically, the catalytic converter deterioration
evaluator 28 determines whether the exhaust gas volume is kept at a
substantially constant level, i.e., in a cruise state, or not, and
sets the value of a flag F/CRS. When the value of the flag F/CRS is
"1", then it indicates that the exhaust gas volume is in the cruise
state, and when the value of the flag F/CRS is "0", then it
indicates that the exhaust gas volume is not in the cruise state.
The process of determining a varying state of the exhaust gas
volume is carried out in a period of 1 second, for example
(hereinafter referred to as "exhaust gas volume variation
determining period") longer than the period (30-100 ms) of the
control cycles of the exhaust-side control unit 7a, and is shown in
detail in FIG. 19.
[0337] As shown in FIG. 19, the catalytic converter deterioration
evaluator 28 calculates an estimated value ABSV of the present
exhaust gas volume (hereinafter referred to as "estimated exhaust
gas volume") from the detected data of the present rotational speed
NE and intake pressure PB of the internal combustion engine 1
according to the following equation (47) in STEP6-2-1: 30 ABSV = NE
1500 PB SVPRA ( 47 )
[0338] In the present embodiment, the exhaust gas volume when the
rotational speed of the internal combustion engine 1 is 1500 rpm is
used as a reference. Therefore, the detected value of the
rotational speed NE is divided by "1500" in the above equation
(47). In the equation (47), SVPRA represents a predetermined
constant depending on the displacement of the internal combustion
engine 1.
[0339] Instead of estimating the exhaust gas volume as described
above, the exhaust gas volume may be estimated from the fuel supply
quantity and intake air quantity of the internal combustion engine
1 or may be directly detected using a flow sensor.
[0340] Then, the catalytic converter deterioration evaluator 28
effects a predetermined filtering process on the estimated exhaust
gas volume calculated in STEP6-2-1 in each exhaust gas volume
variation determining period for thereby determining an exhaust gas
volume variation parameter SVMA that represents the varying state
of the exhaust gas volume in STEP6-2-2.
[0341] The above filtering process is expressed by the following
equation (48): 31 SVMA = ( ABSV ( n ) - ABSV ( n - 1 ) ) + ( ABSV (
n - 2 ) - ABSV ( n - 3 ) ) + ( ABSV ( n - 4 ) - ABSV ( n - 5 ) ) (
48 )
[0342] Specifically, the exhaust gas volume variation parameter
SVMA is calculated by determining a moving average of changes of
the estimated exhaust gas volume ABSV over a plurality of exhaust
gas volume variation determining periods (three exhaust gas volume
variation determining periods in the present embodiment). In the
equation (48), "n" represents the ordinal number of the cycle of
the exhaust gas volume variation determining period.
[0343] The exhaust gas volume variation parameter SVMA thus
calculated represents a rate of change in the estimated exhaust gas
volume ABSV. Consequently, as the value of the exhaust gas volume
variation parameter SVMA is closer to "0", the time-dependent
change of the estimated exhaust gas volume ABSV is smaller, i.e.,
the estimated exhaust gas volume ABSV is substantially
constant.
[0344] Then, the catalytic converter deterioration evaluator 28
compares the square of the exhaust gas volume variation parameter
SVMA, i.e., the square SVMA.sup.2, with a predetermined value
.delta. in STEP6-2-3. The predetermined value .delta. is a positive
value near "0".
[0345] If SVMA.sup.2.ltoreq..delta., i.e., if the present exhaust
gas volume suffers a relatively large variation, then the catalytic
converter deterioration evaluator 28 sets the value of a timer
counter (count-down timer) TMCRSJUD to a predetermined initial
value X/TMCRSJST in STEP6-2-4. As the exhaust gas volume is not in
the cruise state, i.e., the exhaust gas volume is not kept at a
substantially constant level, the catalytic converter deterioration
evaluator 28 sets the flag F/CRS to "0" in STEP6-2-5, after which
control returns to the routine shown in FIG. 18.
[0346] If SVMA.sup.2<.delta. in STEP6-2-3, i.e., if the present
exhaust gas volume suffers a relatively small variation, then the
catalytic converter deterioration evaluator 28 counts down the
value of the timer counter TMCRSJUD by a predetermined value in
each exhaust gas volume variation determining period as long as the
present exhaust gas volume suffers a relatively small variation, in
STEP6-2-6. Then, the catalytic converter deterioration evaluator 28
determines whether or not the value of the timer counter TMCRSJUD
becomes "0" or smaller, i.e., whether the set time of timer counter
TMCRSJUD has elapsed or not, in STEP6-2-7.
[0347] If TMCRSJUD.ltoreq.0, i.e., if the set time of the timer
counter TMCRSJUD has elapsed, then the catalytic converter
deterioration evaluator 28 decides that the exhaust gas volume is
in the cruise state, and holds the value of the timer counter
TMCRSJUD to "0" in STEP6-2-8. Then, the catalytic converter
deterioration evaluator 28 sets the value of the flag F/CRS to "1"
in STEP6-2-9, after which control returns to the routine shown in
FIG. 18.
[0348] If TMCRSJUD>0 in STEP6-2-7, i.e., if the set time of the
timer counter TMCRSJUD has not elapsed, then the catalytic
converter deterioration evaluator 28 sets the value of the flag
F/CRS to "0" in STEP6-2-5, after which control returns to the
routine shown in FIG. 18.
[0349] The processing sequence described above with reference to
FIG. 19 represents the processing in STEP6-2 shown in FIG. 18.
According to the processing in STEP6-2, if the square SVMA.sup.2 of
the exhaust gas volume variation parameter SVMA is
SVMA.sup.2<.delta., i.e., the variation of the exhaust gas
volume is small, continuously for a time, e.g., 10 to 15 seconds,
corresponding to the initial value X/TMCRSJST of the timer counter
TMCRSJUD, the catalytic converter deterioration evaluator 28
decides that the exhaust gas volume is in the cruise state, and
sets the value of the flag F/CRS to "1". Otherwise, the catalytic
converter deterioration evaluator 28 decides that the exhaust gas
volume is not in the cruise state, and sets the value of the flag
F/CRS to "0".
[0350] The processing in STEP6-2 allows a proper recognition of the
state in which the exhaust gas volume is maintained at a
substantially constant level. In each control cycle of the
exhaust-side control unit 7a in one exhaust gas volume variation
determining period, the value of the flag F/CRS is kept
constant.
[0351] Referring back to FIG. 18, the catalytic converter
deterioration evaluator 28 performs a process of determining
whether a condition to calculate the deterioration evaluating
parameter B1MTLS (hereinafter referred to as "deterioration
evaluating condition") is satisfied or not, or specifically a
process of setting a flag F/CALB1MT in STEP6-3. When the value of
the flag F/CALB1MT is "1", it indicates that the deterioration
evaluating condition is satisfied, and when the value of the flag
F/CALB1MT is "0", it indicates that the deterioration evaluating
condition is not satisfied. The process in STEP6-3 will be
described in detail below with reference to FIG. 20.
[0352] The catalytic converter deterioration evaluator 28
determines the value of the flag f/prism/on that is set by the
engine-side control unit 7b in STEPd shown in FIG. 8 in STEP6-3-1.
If f/prism/on=0, i.e., if the internal combustion engine 1 is in an
operating state in which the target air-fuel ratio KCMD determined
by the exhaust-side main processor 13 is not used for the control
of fuel in the internal combustion engine 1, e.g., if the internal
combustion engine 1 is operating with a lean air-fuel mixture, then
the catalytic converter deterioration evaluator 28 decides that the
deterioration evaluating condition is not satisfied, and sets the
flag F/CALB1MT to "0" in STEP6-3-7.
[0353] This is because if f/prism/on=0, it is often unable to
obtain the identified gain coefficient b1 hat which properly
reflects the deteriorated state of the catalytic converter 3.
[0354] If f/prism/on=1, then the catalytic converter deterioration
evaluator 28 determines the value of the flag F/CRS set in STEP6-2
in STEP6-3-2. If F/CRS=1, i.e., if the exhaust gas volume is in the
cruise state, then the catalytic converter deterioration evaluator
28 decides that the deterioration evaluating condition is not
satisfied, and sets the flag F/CALB1MT to "0" in STEP6-3-7.
[0355] Specifically, in the cruise state, the outputs of the
O.sub.2 sensor 6 and the LAF sensor 5 tend to be stably kept in a
steady state, i.e., in a substantially constant level. Therefore,
even when the deterioration of the catalytic converter 3
progresses, the identified gain coefficients a1 hat, a2 hat, b1 hat
determined by the identifier 25 are unlikely to vary. Thus, the
value of the identified gain coefficient b1 hat used as a basis for
the deterioration evaluating parameter B1MTLS does not tend to
reflect the effect of the deteriorated state of the catalytic
converter 3. In the cruise state, therefore, the catalytic
converter deterioration evaluator 28 decides that the deterioration
evaluating condition is not satisfied, and sets the flag F/CALB1MT
to "0".
[0356] Then, the catalytic converter deterioration evaluator 28
determines in STEP6-3-3 whether the present rotational speed NE and
intake pressure PB of the internal combustion engine 1, the latest
identified gain coefficient 1(k) hat determined by the identifier
25 in STEP5, and the present estimated exhaust gas volume ABSV
determined in STEP6-2 fall in respective given ranges, i.e., ranges
of ordinary values, or not in STEP6-3-3. The catalytic converter
deterioration evaluator 28 determines whether or not the
temperature of the internal combustion engine 1, i.e., the coolant
temperature, is a temperature equal to or higher than a
predetermined temperature, i.e., a normal temperature after the
internal combustion engine 1 has been warmed up, in STEP6-3-4. The
catalytic converter deterioration evaluator 28 determines whether a
given time has elapsed after the start of the internal combustion
engine 1, i.e., a state right after the start of the internal
combustion engine 1 has been over, or not in STEP6-3-5.
[0357] If the conditions of STEP6-3-3 through STEP6-3-5 are not
satisfied, then since the identified gain coefficient b1 hat
suitable for calculating the deterioration evaluating parameter
B1MTLS may not be obtained, the catalytic converter deterioration
evaluator 28 decides that the deterioration evaluating condition is
not satisfied and sets the flag F/CALB1MT to "0" in STEP6-3-7.
[0358] If f/prism/on=1 in STEP6-3-1, if F/CRS=0 in STEP6-3-2, and
also if the conditions of STEP6-3-3 through STEP6-3-5 are
satisfied, then the catalytic converter deterioration evaluator 28
decides that the deterioration evaluating condition is satisfied
and sets the flag F/CALB1MT to "1" in STEP6-3-6. Specifically, if
the fuel in the internal combustion engine 1 is controlled
depending on the target air-fuel ratio KCMD determined by the
sliding mode controller 27, if the exhaust gas volume of the
internal combustion engine 1 is not in the cruise sate, and if the
rotational speed NE and other parameters of the internal combustion
engine 1 are in an ordinary state, then the catalytic converter
deterioration evaluator 28 decides that the deterioration
evaluating condition is satisfied and sets the flag F/CALB1MT to
"1".
[0359] Referring back to FIG. 18, the catalytic converter
deterioration evaluator 28 determines the value of the flag
F/CALB1MT thus set in STEP6-4. If F/CALB1MT=0, i.e., if the
deterioration evaluating condition is not satisfied, then the
catalytic converter deterioration evaluator 28 does not calculate
the deterioration evaluating parameter B1MTLS, and control returns
to the main routine shown in FIG. 9.
[0360] If F/CALB1MT=1, i.e., if the deterioration evaluating
condition is satisfied, then the catalytic converter deterioration
evaluator 28 calculates the deterioration evaluating parameter
B1MTLS in STEP6-5. The process of calculating the deterioration
evaluating parameter B1MTLS will be described below with reference
to FIG. 21.
[0361] The catalytic converter deterioration evaluator 28
calculates (updates) the identified central value B1LS which is a
central value of the identified gain coefficient b1 hat according
to the equation (29) in STEP6-5-1. Specifically, the catalytic
converter deterioration evaluator 28 calculates a new identified
central value B1LS(k) according to the equation (29) from the value
b1(k) of the identified gain coefficient b1 hat determined in STEP5
in the present control cycle of the exhaust-side control unit 7a,
the present value B1LS(k-1) of the identified central value B1LS
(the value determined in the preceding control cycle), and the
present value BP(k-1) of the gain parameter BP determined by the
recursive formula according to the equation (30) (the value
determined in the preceding control cycle). Thus, the identified
central value B1LS is sequentially updated in each control cycle of
the exhaust-side control unit 7a.
[0362] The catalytic converter deterioration evaluator 28 then
determines the square B1MT(k) of the difference between the present
value b1(k) of the identified gain coefficient b1 hat and the
identified central value B1LS(k) determined in STEP6-5-1, i.e., the
variation basic parameter B1MT(k), according to the equation (31)
in STEP6-5-2.
[0363] Then, the catalytic converter deterioration evaluator 28
calculates (updates) the deterioration evaluating parameter B1MTLS
which is a central value of the variation basic parameter B1MT
according to the equation (32) in STEP6-5-3. Specifically, the
catalytic converter deterioration evaluator 28 calculates a new
deterioration evaluating parameter B1MTLS(k) according to the
equation (32) from the variation basic parameter B1MT(k) determined
in STEP6-5-2, the present value B1MTLS(k-1) of the deterioration
evaluating parameter B1MTLS (the value determined in the preceding
control cycle), and the present value BP(k-1) of the gain parameter
BP determined by the recursive formula according to the equation
(30) (the value determined in the preceding control cycle). In this
manner, the deterioration evaluating parameter B1MTLS is
sequentially updated in each control cycle of the exhaust-side
control unit 7a.
[0364] The catalytic converter deterioration evaluator 28 updates
the value of the gain parameter BP according to the equation (30)
in STEP6-5-4. Thereafter, the catalytic converter deterioration
evaluator 28 increments, by "1", the value of a counter CB1P which
counts the number of times that the deterioration evaluating
parameter B1MTLS and the gain parameter BP are updated, which
number corresponds to the number of values of the identified gain
coefficient b1 hat used to determine the deterioration evaluating
parameter B1MTLS, in STEP6-5-5. Thereafter, control returns to the
main routine shown in FIG. 18.
[0365] The values of the identified central value B1LS, the
deterioration evaluating parameter B1MTLS, and the gain parameter
BP which are determined respectively in STEP6-51, STEP6-5-3, and
STEP6-5-4 are stored in a nonvolatile memory such as an EEPROM or
the like (not shown) when the internal combustion engine 1 is shut
off, so that those values will not be lost when the internal
combustion engine 1 is not operating. When the internal combustion
engine 1 operates next time, the stored values of the identified
central value B1LS, the deterioration evaluating parameter B1MTLS,
and the gain parameter BP are used as their initial values. The
initial values of the identified central value B1LS, the
deterioration evaluating parameter B1MTLS, and the gain parameter
BP at the time the internal combustion engine 1 operates for the
first time are "0.2", "0", and "1", respectively. The value of the
counter CB1P is initialized to "0" at the time of the startup of
the internal combustion engine 1.
[0366] In FIG. 18, after calculating (updating) the value of the
deterioration evaluating parameter B1MTLS as described above, the
catalytic converter deterioration evaluator 28 evaluates the
deteriorated state of the catalytic converter 3 based on the
deterioration evaluating parameter B1MTLS in STEP6-6. The process
of evaluating the deteriorated state of the catalytic converter 3
will be described below with reference to FIG. 22.
[0367] The catalytic converter deterioration evaluator 28
determines whether the present value BP(k) of the gain parameter BP
and the preceding value BP(k-1) thereof are substantially equal to
each other or not, i.e., whether the gain parameter BP has
substantially been converged or not, in STEP6-6-1, and then
determines whether or not the value of the counter CB1P is equal to
or greater than a predetermined value CB1CAT, i.e., whether the
number of values of the identified gain coefficient b1 hat used to
determine the deterioration evaluating parameter B1MTLS has reached
the predetermined value CB1CAT or not, in STEP6-6-2.
[0368] In the present embodiment, if the data of the identified
central value B1LS, the deterioration evaluating parameter B1MTLS,
and the gain parameter BP are not held, i.e., if the values thereof
are initialized to "0", as when the battery of the vehicle (not
shown) is temporarily removed before the internal combustion engine
1 is started or as when the internal combustion engine 1 operates
for the first time, then the predetermined value to be compared
with the value of the counter CB1P in STEP6-6-2 is set to a value
greater than if the data of the identified central value B1LS, the
deterioration evaluating parameter B1MTLS, and the gain parameter
BP are held.
[0369] If either of the conditions in STEP6-6-1 and STEP6-6-2 is
not satisfied, then the deterioration evaluating parameter B1MTLS
determined in STEP6-5 in the present control cycle is considered to
be not sufficiently converged to the central value of the variation
basic parameter B1MT. Therefore, the processing in STEP6-6 is
finished without evaluating the deteriorated state of the catalytic
converter 3 based on the deterioration evaluating parameter
B1MTLS.
[0370] If either of the conditions in STEP6-6-1 and STEP6-6-2 is
satisfied, then since the deterioration evaluating parameter B1MTLS
determined in STEP6-5 in the control cycle is representative of the
central value of the variation basic parameter B1MT, the catalytic
converter deterioration evaluator 28 compares the deterioration
evaluating parameter B1MTLS with the threshold CATAGELMT shown in
FIG. 6 in STEP6-6-3.
[0371] If B1MTLS.ltoreq.CATAGELMT, then the catalytic converter
deterioration evaluator 28 decides that the deteriorated state of
the catalytic converter 3 is in the deterioration-in-progress state
in which it needs to be replaced immediately or soon. The catalytic
converter deterioration evaluator 28 controls the deterioration
indicator 29 to indicate the deteriorated state of the catalytic
conrverter 3 in STEP6-6-4. After setting the value of the flag
F/DONE to "1", indicating that the evaluation of the deteriorated
state of the catalytic converter 3 is completed, in STEP6-6-5, the
processing in STEP6-6 is finished.
[0372] If B1MTLS<CATAGELMT in STEP6-6-3, since the catalytic
converter 3 is in the non-deteriorated state, the catalytic
converter deterioration evaluator 28 does not control the
deterioration indicator 29, but sets the value of the flag F/DONE
to "1" in STEP6-6-5. The processing in STEP6-6 is now finished.
[0373] The above processing represents the process that is carried
out by the catalytic converter deterioration evaluator 28 in STEP6
shown in FIG. 9.
[0374] In FIG. 9, after the processing of the catalytic converter
deterioration evaluator 28 has been carried out, the exhaust-side
main processor 13 determines the values of the gain coefficients
a1, a2, b1 in STEP7. Specifically, if the value of the flag
f/id/cal set in STEP2 is 11", i.e., if the gain coefficients a1,
a2, b1 have been identified by the identifier 25, then the gain
coefficients a1, a2, b1 are set to the latest identified gain
coefficients a1(k) hat, a2(k) hat, b1(k) hat determined by the
identifier 25 in STEP5 (limited in STEP5-11). If the value of the
flag f/id/cal is "0", i.e., if the gain coefficients a1, a2, b1
have not been identified by the identifier 25, then the gain
coefficients a1, a2, b1 are set to predetermined values,
respectively.
[0375] Then, the exhaust-side main processor 13 effects a
processing operation of the estimator 26, i.e., calculates the
estimated differential output VO2 bar, in STEP8.
[0376] The estimator 26 calculates the coefficients .alpha.1,
.alpha.2, .beta.j (j=1, 2, . . , d) to be used in the equation
(13), using the gain coefficients a1, a2, b1 determined in STEP7
(these values are basically the identified gain coefficients a1
hat, a2 hat, b1 hat) as described above.
[0377] Then, the estimator 26 calculates the estimated differential
output VO2(k+d) bar (the estimated value of the differential output
VO2 after the total dead time d from the time of the present
control cycle) according to the equation (13), using the
time-series data VO2(k), VO2(k-1), from before the present control
cycle, of the differential output VO2 of the O.sub.2 sensor
calculated in each control cycle in STEP3, the time-series data
kact(k-j) (j=0, . . . d1), from before the present control cycle,
of the differential output kact of the LAF sensor 5, the
time-series data kcmd(k-j) (=Us1(k-j), j=1, . . . , d2-1), from
before the preceding control cycle, of the target differential
air-fuel ratio kcmd (=the SLD manipulating input Us1) given in each
control cycle from the sliding mode controller 27, and the
coefficients .alpha.1, .alpha.2, .beta.j calculated as described
above.
[0378] Then, the exhaust-side main processor 13 calculates the SLD
manipulating input Us1 (=the target differential air-fuel ratio
kcmd) with the sliding mode controller 27 in STEP9.
[0379] Specifically, the sliding mode controller 27 calculates a
value .sigma.(k+d) bar (corresponding to an estimated value, after
the total dead time d, of the linear function a defined according
to the equation (15)), after the total dead time d from the present
control cycle, of the switching function .sigma. bar defined
according to the equation (25), using the time-series data VO2(k+d)
bar, VO2(k+d-1) bar of the estimated differential output VO2 bar
(the present and preceding values of the estimated differential
output VO2 bar) determined by the estimator 26 in STEP8.
[0380] At this time, the sliding mode controller 27 keeps the value
of the switching function .sigma. bar within a predetermined
allowable range. If the value .sigma.(k+d) bar determined as
described above exceeds the upper or lower limit of the allowable
range, then the sliding mode controller 27 forcibly limits the
value .sigma.(k+d) bar to the upper or lower limit of the allowable
range. This is because if the value of the switching function
.sigma. bar were excessive, the reaching control law input Urch
would be excessive, and the adaptive control law Uadp would change
abruptly, tending to impair the stability of the process of
converging the output VO2/OUT of the O.sub.2 sensor 6 to the target
value VO2/TARGET.
[0381] Then, the sliding mode controller 27 accumulatively adds
values .sigma.(k+d) bar.multidot..DELTA.T, produced by multiplying
the value .sigma.(k+d) bar of the switching function .sigma. bar by
the period .DELTA.T (constant period) of the control cycles of the
exhaust-side control unit 7a. That is, the sliding mode controller
27 adds the product .sigma.(k+d) bar.multidot..DELTA.T of the value
.sigma.(k+d) bar and the period .DELTA.T calculated in the present
control cycle to the sum determined in the preceding control cycle,
thus calculating an integrated value .sigma. bar (hereinafter
represented by ".SIGMA..sigma. bar ") which is the calculated
result of the term .SIGMA.(.sigma.bar.multidot..D- ELTA.T) of the
equation (27).
[0382] In the present embodiment, the sliding mode controller 27
keeps the integrated value .SIGMA..sigma. bar in a predetermined
allowable range. If the integrated value .SIGMA..sigma. bar exceeds
the upper or lower limit of the allowable range, then the sliding
mode controller 27 forcibly limits the integrated value
.SIGMA..sigma. bar to the upper or lower limit of the allowable
range. This is because if the integrated value .SIGMA..sigma. bar
were excessive, the adaptive control law Uadp determined according
to the equation (27) would be excessive, tending to impair the
stability of the process of converging the output VO2/OUT of the
O.sub.2 sensor 6 to the target value VO2/TARGET.
[0383] Then, the sliding mode controller 27 calculates the
equivalent control input Ueq, the reaching control law input Urch,
and the adaptive control law Uadp according to the respective
equations (24), (26), (27), using the timeseries data VO2(k+d)bar,
VO2(k+d-1) bar of the present and past values of the estimated
differential output VO2 bar determined by the estimator 26 in
STEP8, the value .sigma.(k+d) bar of the switching function .sigma.
and its integrated value .SIGMA..sigma. bar which are determined as
described above, and the gain coefficients a1, a2, b1 determined in
STEP 7 (these values are basically the latest identified gain
coefficients a1(k) hat, a2(k) hat, b1(k) hat).
[0384] The sliding mode controller 27 then adds the equivalent
control input Ueq, the reaching control law input Urch, and the
adaptive control law Uadp to calculate the SLD manipulating input
Us1, i.e., the input (=the target differential air-fuel ratio kcmd)
to be applied to the object exhaust system E for converging the
output signal VO2/OUT of the O.sub.2 sensor 6 toward the target
value VO2/TARGET.
[0385] The above process represents the processing in STEP9.
[0386] After the SLD manipulating input Us1 has been calculated,
the exhaust-side main processor 13 determines the stability of the
adaptive sliding mode control process carried out by the sliding
mode controller 27, or more specifically, the ability of the
controlled state of the output VO2/OUT of the O.sub.2 sensor 6
based on the adaptive sliding mode control process (hereinafter
referred to as "SLD controlled state"), and sets a value of a flag
f/sld/stb indicative of whether the SLD controlled state is stable
or not in STEP10. The value of the flag f/sld/stb is "1" if the SLD
controlled state is stable, and "0" otherwise.
[0387] The determining subroutine of STEP10 is shown in detail in
FIG. 23.
[0388] As shown in FIG. 23, the exhaust-side main processor 13
calculates a difference .DELTA..sigma. bar (corresponding to a rate
of change of the switching function .sigma. bar ) between the
present value .sigma.(k+d) bar of the switching function .sigma.
bar calculated in STEP9 and a preceding value .sigma.(k+d-1) bar
thereof in STEP10-1.
[0389] Then, the exhaust-side main processor 13 decides whether or
not a product .DELTA..sigma.bar.multidot..sigma.(k+d) bar
(corresponding to the time-differentiated function of a Lyapunov
function a bar.sup.2/2 relative to the .sigma. bar ) of the
difference .DELTA..sigma. bar and the present value .sigma.(k+d)
bar is equal to or smaller than a predetermined value
.epsilon.(.gtoreq.0) in STEP10-2.
[0390] The difference .DELTA..sigma. bar.multidot..sigma.(k+d) bar
(hereinafter referred to as "stability determining parameter Pstb")
will be described below. If the stability determining parameter
Pstb is greater than 0 (Pstb>0), then the value of the switching
function .sigma. bar is basically changing away from "0". If the
stability determining parameter Pstb is equal to or smaller than 0
(Pstb<0), then the value of the switching function .sigma. bar
is basically converged or converging to "0". Generally, in order to
converge a controlled variable to its target value according to the
sliding mode control process, it is necessary that the value of the
switching function be stably converged to "0". Basically,
therefore, it is possible to determine whether the SLD controlled
state is stable or unstable depending on whether or not the value
of the stability determining parameter Pstb is equal to or smaller
than 0.
[0391] If, however, the stability of the SLD controlled state is
determined by comparing the value of the stability determining
parameter Pstb with "0", then the determined result of the
stability is affected even by slight noise contained in the value
of the switching function .sigma. bar . According to the present
embodiment, therefore, the predetermined value .epsilon. with which
the stability determining parameter Pstb is to be compared in
STEP10-2 is of a positive value slightly greater than "0".
[0392] If Pstb>.epsilon. in STEP10-2, then the SLD controlled
state is judged as being unstable, and the value of a timer counter
tm (count-down timer) is set to a predetermined initial value
T.sub.M (the timer counter tm is started) in order to inhibit the
determination of the target air-fuel ratio KCMD using the SLD
manipulating input Us1 calculated in STEP9 for a predetermined time
in STEP10-4. Thereafter, the value of the flag f/sld/stb is set to
"0" in STEP10-5, after which control returns to the main routine
shown in FIG. 9.
[0393] If Pstb.ltoreq..epsilon. in STEP10-2, then the exhaust-side
main processor 13 decides whether the present value .sigma.(k+d)
bar of the switching function .sigma. bar falls within a
predetermined range or not in STEP10-3.
[0394] If the present value .sigma.(k+d) bar of the switching
function .sigma. bar does not fall within the predetermined range,
then since the present value .sigma.(k+d) bar spaced widely apart
from "0", the SLD controlled state is considered to be unstable.
Therefore, if the present value .sigma.(k+d) bar of the switching
function .sigma. bar does not fall within the predetermined range
in STEP10-3, then the SLD controlled state is judged as being
unstable, and the processing of STEP10-4 and STEP10-5 is executed
to start the timer counter tm and set the value of the flag
f/sld/stb to "0".
[0395] In the present embodiment, since the value of the switching
function .sigma. bar is limited within the allowable range in
STEP9, the decision processing in STEP10-3 may be dispensed
with.
[0396] If the present value .sigma.(k+d) bar of the switching
function .sigma. bar falls within the predetermined range in
STEP10-3, then the exhaust-side main processor 13 counts down the
timer counter tm for a predetermined time .DELTA.tm in STEP10-6.
The exhaust-side main processor 13 then decides whether or not the
value of the timer counter tm is equal to or smaller than "S0",
i.e., whether a time corresponding to the initial value T.sub.M has
elapsed from the start of the timer counter tm or not, in
STEP10-7.
[0397] If tm>0, i.e., if the timer counter tm is still measuring
time and its set time has not yet elapsed, then since no
substantial time has elapsed after the SLD controlled state is
judged as unstable in STEP10-2 or STEP10-3, the SLD controlled
state tends to become unstable. Therefore, if tm>0 in STEP10-7,
then the value of the flag f/sld/stb is set to "0" in STEP10-5.
[0398] If tm<0 in STEP10-7, i.e., if the set time of the timer
counter tm has elapsed, then the SLD controlled stage is judged as
being stable, and the value of the flag f/sld/stb is set to "1" in
STEP10-8.
[0399] According to the above processing, if the SLD controlled
state is judged as being unstable, then the value of the flag
f/sld/stb is set to "0", and if the SLD controlled state is judged
as being stable, then the value of the flag f/sld/stb is set to
"1".
[0400] In the present embodiment, the above process of determining
the stability of the SLD controlled state is by way of illustrative
example only. The stability of the SLD controlled state may be
determined by any of various other processes. For example, in each
given period longer than the control cycle, the frequency with
which the value of the stability determining parameter Pstb in the
period is greater than the predetermined value e is counted. If the
frequency is in excess of a predetermined value, then the SLD
controlled state is judged as unstable. Otherwise, the SLD
controlled state is judged as stable.
[0401] Referring back to FIG. 9, after a value of the flag
f/sld/stb indicative of the stability of the SLD controlled state
has been set, the exhaust-side main processor 13 determines the
value of the flag f/sld/stb in STEP11. If the value of the flag
f/sld/stb is "1", i.e., if the SLD controlled state is judged as
being stable, then the sliding mode controller 27 limits the SLD
manipulating input Us1 calculated in STEP9 in STEP12. Specifically,
the sliding mode controller 27 determines whether the present value
of the SLD manipulating input Us1 calculated in STEP9 falls in a
predetermined allowable range or not. If the present value of the
SLD manipulating input Us1 exceeds the upper or lower limit of the
allowable range, then the sliding mode controller 27 forcibly
limits the present value Us1(k) of the SLD manipulating input Us1
to the upper or lower limit of the allowable range.
[0402] The SLD manipulating input Us1 (=the target differential
air-fuel ratio kcmd) limited in STEP12 is stored in a memory (not
shown) in a time-series fashion, and will be used in the processing
operation of the estimator 26.
[0403] Then, the exhaust-side main processor 13 adds the reference
value FLAF/BASE to the SLD manipulating input Us1 which has been
limited in STEP12 for thereby determining a target air-fuel ratio
KCMD in STEP 14. Then, the processing in the present control cycle
is finished.
[0404] If f/sld/stb=0 in STEP11, i.e., if the SLD controlled state
is judged as unstable, then the exhaust-side main processor 13
forcibly sets the SLD manipulating input Us1 in the present control
cycle to a predetermined value (the fixed value or the preceding
value of the SLD manipulating input Us1) in STEP13. The
exhaust-side main processor 13 calculates the target air-fuel ratio
KCMD according to the equation (28) in STEP 14. Then, the
processing in the present control cycle is finished.
[0405] The target air-fuel ratio KCMD finally determined in STEP14
is stored in a memory (not shown) in a time-series fashion in each
control cycle. When the general feedback controller 15 is to use
the target air-fuel ratio KCMD determined by the exhaust-side main
processor 13 (see STEPF in FIG. 8), the latest one of the
time-series data of the target air-fuel ratio KCMD thus stored is
selected.
[0406] Details of the operation of the apparatus shown in FIG. 1
have been described above.
[0407] The operation of the apparatus will be summarized as
follows: The exhaust-side main processor 13 sequentially determines
the target air-fuel ratio KCMD (the target value for the air-fuel
ratio detected by the LAF sensor 5) for the exhaust gas introduced
into the catalytic converter 3 so as to converge (adjust) the
output signal VO2/OUT of the O.sub.2 sensor 6 downstream of the
catalytic converter 3 to the target value VO2/TARGET therefor. The
amount of fuel injected into the internal combustion engine 1 is
adjusted depending on the target air-fuel ratio KCMD and the output
KACT (the detected value of the air-fuel ratio) of the LAF sensor 5
to manipulate the air-fuel ratio of the internal combustion engine
1. By adjusting the output signal VO2/OUT of the O.sub.2 sensor 6
downstream of the catalytic converter 3 to the target value
VO2/TARGET, the catalytic converter 3 can maintain its optimum
exhaust gas purifying performance without being affected by its own
aging.
[0408] Concurrent with the above fuel control for the internal
combustion engine 1, the catalytic converter deterioration
evaluator 28 of the exhaust-side main processor 13 determines the
deterioration evaluating parameter B1MTLS representing the degree
of variation of the time-series data of the identified gain
coefficient b1 hat, among the identified gain coefficients a1 hat,
a2 hat, b1 hat sequentially determined by the identifier 25, from
the timeseries data of the identified gain coefficient b1 hat. The
catalytic converter deterioration evaluator 28 then compares the
deterioration evaluating parameter B1MTLS with the threshold
CATAGELMT to evaluate whether the catalytic converter 3 is in the
deterioration-in-progress state or the non-deteriorated state. If
the catalytic converter 3 is in the deterioration-in-progress
state, the deterioration-inprogress state is indicated by the
deterioration indicator 29.
[0409] The apparatus according to the present embodiment is thus
capable of evaluating the deteriorated state of the catalytic
converter 3 without interrupting, but concurrent with, the control
of fuel in the internal combustion engine 1 while the internal
combustion engine 1 is operating in an ordinary state in which the
air-fuel ratio of the internal combustion engine 1 is controlled in
order to achieve an optimum purifying capability of the catalytic
converter 3.
[0410] For evaluating the deteriorated state of the catalytic
converter 3, the square B1MT (or the absolute value) of the
difference between each of the time-series data of the identified
gain coefficient b1 hat and the identified central value B1LS which
is a central value of those time-series data is determined as the
variation basic parameter B1MT representing the degree of variation
of the time-series data. Then, a central value of the variation
basic parameter B1MT is determined as the deterioration evaluating
parameter B1MTLS.
[0411] The deterioration evaluating parameter B1MTLS is highly
correlated to the deteriorated state of the catalytic converter 3,
and monotonously increases as the deterioration of the catalytic
converter 3 progresses. If the deteriorated state of the catalytic
converter 3 remains the same, the value of the deterioration
evaluating parameter B1MTLS also remains substantially the same.
Therefore, the deteriorated state of the catalytic converter 3 can
accurately and properly be evaluated by comparing the deterioration
evaluating parameter B1MTLS with the predetermined threshold
CATAGELMT.
[0412] In the present embodiment, the target air-fuel ratio KCMD
determined by the exhaust-side main processor 13 is calculated
using the sliding mode controller 27 which is resistant to the
effect of disturbances, the estimator 26 which compensates for the
effect of the dead times d1, d2 of the object exhaust system E and
the air-fuel manipulating system, and the identifier 25 which
sequentially identifies on a real-time basis the gain coefficients
a1, a2, b1 which are parameters of the exhaust system model that
expresses the behavior of the object exhaust system E. Therefore,
it is possible to accurately determine the target air-fuel ratio
KCMD optimum for controlling the output VO2/OUT of the O.sub.2
sensor 6 at the target value VO2/TARGET therefor. The air-fuel
ratio of the internal combustion engine 1 is controlled to converge
the output KACT of the LAF sensor 5 to the target air-fuel ratio
KCMD primarily by the adaptive controller 18 which is a controller
of the recursive type capable of accurately compensating for the
effect of behavioral changes of the internal combustion engine
1.
[0413] Thus, the output VO2/OUT of the O.sub.2 sensor 6 can stably
be controlled at the target value VO2/TARGET therefor while
minimizing the effect of disturbances. Therefore, the behavior of
the object exhaust system E is stabilized, preventing disturbances
other than the deteriorated state of the catalytic converter 3 from
affecting the identified gain coefficients a1 hat, a2 hat, b1 hat.
As a result, the correlation between the degree of variation of the
time-series data of the identified gain coefficient b1 hat and the
deteriorated state of the catalytic converter 3 is increased, and
hence the deteriorated state of the catalytic converter 3 can
accurately be evaluated based on the deterioration evaluating
parameter B1MTLS which represents the degree of variation of the
time-series data of the identified gain coefficient b1.
[0414] In the present invention, the identifier 25 calculates
(updates) the identified gain coefficients a1 hat, a2 hat, b1 hat
when the object exhaust system E is in a behavioral state in which
the air-fuel ratio is changed from a leaner value to a richer
value. The above behavioral state of the object exhaust system E
can simply and reliably be recognized using the management function
.gamma. defined using the time-series data of the differential
output VO2 of the O.sub.2 sensor 6. Therefore, it is possible to
control the air-fuel ratio of the internal combustion engine 1 and
also to determine the identified gain coefficients a1 hat, a2 hat,
b1 hat that are highly reliable and suitable for evaluating the
deteriorated state of the catalytic converter 3.
[0415] In calculating the identified error id/e used to
sequentially update the identified gain coefficients al hat, a2
hat, b1 hat, the identified differential output VO2 hat
corresponding to the output VO2/OUT of the O.sub.2 sensor 6 on the
exhaust system model and the actual differential output VO2 of the
O.sub.2 sensor 6 are subjected to a filtering process of the same
frequency characteristics (low-pass characteristics), in view of
the frequency characteristics (low-pass characteristics) of the
object exhaust system E.
[0416] Therefore, it is possible to identify the gain coefficients
a1, a2, b1 in a manner to cause the frequency characteristics of
the exhaust system model to match the actual frequency
characteristics of the object exhaust system E, for thereby
determining the identified gain coefficients a1 hat, a2 hat, b1 hat
that match the behavioral characteristics of the object exhaust
system E. Therefore, the reliability of the identified gain
coefficients a1 hat, a2 hat, b1 hat is increased. Particularly, the
identified gain coefficient b1 hat can properly reflects the effect
of the deteriorated state of the catalytic converter 3.
[0417] In sequentially calculating the identified gain coefficients
a1 hat, a2 hat, b1 hat, the above limiting process is performed to
determine the identified gain coefficients a1 hat, a2 hat, b1 hat
which are suitable to make smooth and stable the target air-fuel
ratio KCMD and the air-fuel ratio of the internal combustion engine
1 controlled thereby. At the same time, it is possible to stably
determine an identified gain coefficient b1 hat highly reflecting
the deteriorated state of the catalytic converter 3 while
eliminating an identified gain coefficient b1 hat which is not
suitable for evaluating the deteriorated state of the catalytic
converter 3.
[0418] Furthermore, in the exhaust system model and the processing
operation of the identifier 25, the output KACT from the LAF sensor
5 and the output VO2/OUT from the O.sub.2 sensor 6 are not directly
used, but the difference kact between the output KACT from the LAF
sensor 5 and the reference value FLAF/BASE and the difference VO2
between the output VO2/OUT from the O.sub.2 sensor 6 and the target
value VO2/TARGET (reference value) are used. Therefore, the
algorithm of the processing operation of the identifier 25 is
constructed easily, and the accuracy of the processing operation of
the identifier 25 is increased. This holds true for the processing
operation of the estimator 26 and the sliding mode controller
27.
[0419] In the cruise state in which the exhaust gas volume of the
internal combustion engine 1 is maintained at a substantially
constant level, the process of calculating the identified central
value B1LS and the deterioration evaluating parameter B1MTLS and
the process of evaluating the deteriorated state of the catalytic
converter 3 based on the deterioration evaluating parameter B1MTLS
(STEP6-5, STEP6-6) are not carried out. Stated otherwise, the
identified gain coefficient b1 hat determined by the identifier 25
is not used in the cruise state in calculating the deterioration
evaluating parameter B1MTLS for evaluating the deteriorated state
of the catalytic converter 3. In operating states of the internal
combustion engine 1 other than the cruise state, the identified
gain coefficient b1 hat determined by the identifier 25 is used to
calculate the deterioration evaluating parameter B1MTLS.
[0420] Therefore, it is possible to obtain the deterioration
evaluating parameter B1MTLS which is reliably correlated to the
deteriorated state of the catalytic converter 3, achieving the
reliability of the evaluation of the deteriorated state of the
catalytic converter 3.
[0421] The present invention is not limited to the above
embodiment, but may be modified as follows:
[0422] In the above embodiment, the deterioration evaluating
parameter B1MTLS is determined from the timeseries data of the
identified gain coefficient b1 hat, among the identified gain
coefficients a1 hat, a2 hat, b1 hat, and the deteriorated state of
the catalytic converter *3 is evaluated based on the deterioration
evaluating parameter B1MTLS. However, the deteriorated state of the
catalytic converter 3 may be evaluated using the identified gain
coefficient a1 hat or a2 hat. In such a case, a central value of
the time-series data of the identified gain coefficient a1 hat or
a2 hat is sequentially determined according to a sequential
statistical algorithm (more generally, a low-pass filtering
process) such as a degression gain method or a method of least
squares, and a central value of the square or absolute value of the
difference between the central value and each of the data of the
identified gain coefficient a1 hat or a2 hat is determined as a
deterioration evaluating parameter according to a sequential
statistical algorithm (more generally, a low-pass filtering
process) such as a degression gain method or a method of least
squares. The deterioration evaluating parameter thus determined is
correlated to the deteriorated state of the catalytic converter 3
in the same manner as with the deterioration evaluating parameter
BIMTLS in the above embodiment, and the deteriorated state of the
catalytic converter 3 can be evaluated based on the deterioration
evaluating parameter thus determined.
[0423] However, the inventors have found that of the identified
gain coefficients a1 hat, a2 hat, b1 hat, the identified gain
coefficient b1 hat has a largest tendency to vary more greatly as
the deterioration of the catalytic converter 3 progresses.
Therefore, it is preferable to determine the deterioration
evaluating parameter using the identified gain coefficient b1.
[0424] In the above embodiment, the deteriorated state of the
catalytic converter 3 is evaluated based on only the deterioration
evaluating parameter B1MTLS determined from the identified gain
coefficient b1. However, deterioration evaluating parameters may be
determined respectively from the identified gain coefficients a1
hat, a2 hat, b1 hat, the deteriorated state of the catalytic
converter 3 may be temporarily determined based on the respective
deterioration evaluating parameters, and the evaluated results may
be combined to finally evaluate the deteriorated state of the
catalytic converter 3.
[0425] In the above embodiment, in determining the deterioration
evaluating parameter B1MTLS, the central value (=the identified
central value B1LS) of the identified gain coefficient b1 hat is
determined according to a sequential statistical algorithm of a
degression gain method. However, the central value of the
identified gain coefficient b1 hat may be determined according to
any of various other statistical algorithms such as a method of
minimum squares, a method of weighted minimum squares, a fixed gain
method, etc. Furthermore, an arithmetic mean of the timeseries data
of the identified gain coefficient b1 hat may be determined as the
central value thereof. This also holds true for the determination
of a deterioration evaluating parameter using the other identified
gain coefficient a1 hat or a2 hat.
[0426] In the above embodiment, the central value of the square of
the difference B1MT between each of the identified gain coefficient
b1 hat and the identified central value B1LS is determined as the
deterioration evaluating parameter B1MTLS representing the degree
of variation of the time-series data of the identified gain
coefficient b1 hat. However, an arithmetic mean of the square of
the difference B1MT, which represents a variance of the timeseries
data of the identified gain coefficient b1 hat, or a standard
deviation which is the square root of the arithmetic mean or
variance may be determined as the deterioration evaluating
parameter, or the deterioration evaluating parameter may be
determined using the absolute value of the difference B1MT instead
of the square of the difference BIMT. Dependent on the operating
conditions of the internal combustion engine 1 and the accuracy
required of the evaluation of the deteriorated state of the
catalytic converter 3, it is possible to evaluate the deteriorated
state of the catalytic converter 3 using the square or absolute
value of the difference B1MT itself as the deterioration evaluating
parameter. This also holds true for the determination of a
deterioration evaluating parameter using the other identified gain
coefficient a1 hat or a2 hat.
[0427] In the above embodiment, the deteriorated state of the
catalytic converter 3 is evaluated as one of the two states, i.e.,
the deterioration-in-progress state and the non-deteriorated state.
However, if an increased number of thresholds are used for
comparison with the deterioration evaluating parameter, then the
deteriorated state of the catalytic converter 3 may be evaluated as
three or more deteriorated states. In this case, different
evaluations may be indicated depending on those three or more
deteriorated states.
[0428] In the above embodiment, the model of the object exhaust
system E (the exhaust system model) is expressed according to the
equation (1). However, the exhaust system model may be expressed
according to an equation in which the secondary autoregressive term
(the term of VO2(k-1) is be dispensed with, or more autoregressive
terms including the term of VO2(k-2), for example, are added.
[0429] In the above embodiment, the model of the object exhaust
system E used to determine the deteriorated state of the catalytic
converter 3 and the model of the object exhaust system E used to
control the air-fuel ratio of the internal combustion engine 1,
i.e., to calculate the target air-fuel ratio KCMD, are the same as
each other, and the parameters (gain coefficients) a1, a2, b1 of
the model are identified by the same identifier 25. However,
different models of the object exhaust system E may be established
to determine the deteriorated state of the catalytic converter 3
and control the air-fuel ratio of the internal combustion engine 1,
and the parameters of those models may be identified by respective
identifiers.
[0430] In the above embodiment, the deteriorated state of the
catalytic converter 3 is evaluated while controlling the air-fuel
ratio of the internal combustion engine 1 at an air-fuel ratio for
achieving an optimum purifying capability of the catalytic
converter 3. However, even while the internal combustion engine 1
is operating in another mode, it is possible to identify the
parameters (gain coefficients) a1, a2, b1 of the exhaust system
model and determine the deterioration evaluating parameter from the
identified values for evaluating the deteriorated state of the
catalytic converter 3.
[0431] In the above embodiment, the adaptive sliding mode control
process is employed to calculate the target air-fuel ratio KCMD.
However, the ordinary sliding mode control process which does not
use the adaptive control law may be employed to calculate the
target air-fuel ratio KCMD.
[0432] In the above embodiment, the effect of the total dead time d
is compensated for by the estimator 26 in calculating the target
air-fuel ratio KCMD for converging the output VO2/OUT of the
O.sub.2 sensor 6 to the target value VO2/TARGET. If the dead time
of the air-fuel ratio manipulating system, which is made up of the
internal combustion engine 1 and the engine-side control unit 7b,
is negligibly small, then only the dead time d1 of the object
exhaust system E may be compensated for. In this modification, the
estimator 26 sequentially determines in each control cycle the
estimated value VO2(k+d1) after the dead time d1 of the
differential output VO2 of the O.sub.2 sensor 6, according to the
following equation (49) which is similar to the equation (12)
except that "kcmd" and "d" are replaced respectively with "kact,"
and "d1": 32 VO2 _ ( k + d1 ) = 1 VO2 ( k ) + 2 VO2 ( k - 1 ) + j =
1 d1 j kact ( k - j ) ( 49 )
[0433] where
[0434] .alpha.1=the first-row, first-column element of
A.sup.d1,
[0435] .alpha.2=the first-row, second-column element of
A.sup.d1,
[0436] .beta.j=the first-row elements of A.sup.j-1B
[0437] 33 A = [ a1 a2 1 0 ] B = [ b1 0 ]
[0438] In this modification, the sliding mode controller 27
determines in each control cycle the equivalent control input Ueq,
the reaching control law input Urch, and the adaptive control law
input Uadp according to equations which are similar to the
equations (24)-(27) except that "d" is replaced with "d1", and adds
the equivalent control input Ueq, the reaching control law input
Urch, and the adaptive control law input Uadp to determine the
target differential air-fuel ratio kcmd for thereby determining the
target air-fuel ratio KCMD which has been compensated for the
effect of the dead time d1 of the object exhaust system E.
[0439] If the dead time d2 of the object exhaust system E as well
as the dead time d1 of the air-fuel ratio manipulating system is
negligibly small, then the estimator 26 may be dispensed with. In
this modification, the processing operation of the sliding mode
controller 27 and the identifier 25 may be performed with
d=d1=0.
[0440] In the above embodiment, the O.sub.2 sensor 6 is used as the
second exhaust gas sensor. However, for maintaining the desired
purifying performance of the catalytic converter 3, any of various
other sensors may be employed insofar as they can detect the
concentration of a certain component of the exhaust gas downstream
of the catalytic converter to be controlled. For example, a CO
sensor is employed if the carbon monoxide (CO) in the exhaust gas
downstream of the catalytic converter is controlled, an NOx sensor
is employed if the nitrogen oxide (NOx) in the exhaust gas
downstream of the catalytic converter is controlled, and an HC
sensor is employed if the hydrocarbon (HC) in the exhaust gas
downstream of the catalytic converter is controlled. If a three-way
catalytic converter is employed, then it can be controlled to
maximize its purifying performance irrespective of which of the
above gas components is detected for its concentration. If a
reducing catalytic converter or an oxidizing catalytic converter is
employed, then its purifying performance can be increased by
directly detecting a gas component to be purified.
[0441] For evaluating the deteriorated state of the catalytic
converter 3, an exhaust gas sensor other than the LAF sensor 5 may
be used as the first exhaust gas sensor, and may comprise a CO
sensor, an NOx sensor, a HC sensor, or the like. The first and
second exhaust gas sensors may be selected such that when the
object exhaust system E is modeled and the parameters of the model
are identified, the degree of variation of the time-series data of
the identified values varies depending on the deteriorated state of
the catalytic converter 3.
[0442] In the above embodiment, the differential output kact from
the LAF sensor 5, the differential output VO2 from the O.sub.2
sensor 6, and the target differential air-fuel ratio kcmd are
employed in performing the processing operation of the identifier
25, the estimator 26, and the sliding mode controller 27. However,
the output KACT of the LAF sensor 5, the output VO2/OUT of the
O.sub.2 sensor 6, and the target air-fuel ratio KCMD may directly
be employed in performing the processing operation of the
identifier 25, the estimator 26, and the sliding mode controller
27. The reference value FLAF/BASE relative to the differential
output kact (=KACT-FLAF/BASE) may not necessarily be of a constant
value, but may be established depending on the rotational speed NE
and intake pressure PB of the internal combustion engine 1.
[0443] In the above embodiment, in order to reliably achieve the
optimum purifying capability of the catalytic converter 3, the
identifier 25, the estimator 26, and the sliding mode controller 27
are used to calculate the target air-fuel ratio KCMD, and the
air-fuel ratio of the internal combustion engine 1 is
feedback-controlled using the adaptive controller 18. However, if
the purifying capability of the catalytic converter 3 is not
required to be so strict, the target air-fuel ratio KCMD may be
calculated and the air-fuel ratio of the internal combustion engine
1 may be feedback-controlled according to a general PID control
process.
[0444] In the above embodiment, the deteriorated state of the
catalytic converter 3 which is disposed in the exhaust pipe 2 of
the internal combustion engine 1 is evaluated. However, if the
deteriorated state of the catalytic converter 3 alone is to be
determined, then an air-fuel mixture which is the same as the
air-fuel mixture supplied to the internal combustion engine 1 may
be combusted by a combustion device other than the internal
combustion engine 1, and an exhaust gas produced by the combustion
device may be supplied to the catalytic converter 3 for the
evaluation of the deteriorated state of the catalytic converter
3.
[0445] Although a certain preferred embodiment of the present
invention has been shown and described in detail, it should be
understood that various changes and modifications may be made
therein without departing from the scope of the appended
claims.
* * * * *