U.S. patent application number 15/097356 was filed with the patent office on 2016-11-10 for sensor system.
The applicant listed for this patent is Sensirion AG. Invention is credited to Markus GRAF, Vincent HESS, Dominik NIEDERBERGER.
Application Number | 20160327418 15/097356 |
Document ID | / |
Family ID | 43302981 |
Filed Date | 2016-11-10 |
United States Patent
Application |
20160327418 |
Kind Code |
A1 |
GRAF; Markus ; et
al. |
November 10, 2016 |
SENSOR SYSTEM
Abstract
Disclosed is a method for adjusting a sensor signal and a
corresponding sensor system comprising a sensor for providing a
sensor signal representative of a measure other than temperature,
dynamic components of the sensor signal being dependent on
temperature. In addition there is provided a temperature sensor for
measuring the temperature. Dynamic components in the sensor signal
are adjusted subject to the temperature sensed, and a compensated
sensor signal is supplied. Such sensor system helps compensating
for long response times of sensors.
Inventors: |
GRAF; Markus; (Zurich,
CH) ; HESS; Vincent; (Zurich, CH) ;
NIEDERBERGER; Dominik; (Zurich, CH) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Sensirion AG |
Stafa |
|
CH |
|
|
Family ID: |
43302981 |
Appl. No.: |
15/097356 |
Filed: |
April 13, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13068628 |
May 17, 2011 |
9341499 |
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15097356 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01D 18/008 20130101;
G01D 3/0365 20130101 |
International
Class: |
G01D 18/00 20060101
G01D018/00 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 4, 2010 |
EP |
10005804.9 |
Claims
1. A sensor system, comprising a sensor providing a sensor signal
representative of a measure other than temperature, dynamic
components of the sensor signal being dependent on temperature, a
temperature sensor for providing a temperature signal, and a
compensation filter receiving the sensor signal and the temperature
signal, wherein the compensation filter is designed for adjusting
the dynamic components in the sensor signal subject to the
temperature signal, and for providing a compensated sensor signal,
and wherein the compensation filter is modeled based on an inverse
of a transfer function of a sensor model of the sensor, which
compensation filter contains temperature dependent terms, said
model being provided in a spectral domain.
2. The sensor system of claim 1, wherein the sensor model modelled
for building the compensation filter is a sensor model of second
order.
3. The sensor system of claim 2, wherein the sensor comprises a
housing, wherein the sensor comprises a sensor element sensitive to
a component in a medium outside the housing, wherein the sensor
model of second order represents two diffusion processes, a first
one of which diffusion processes is a diffusion process from the
outside into the housing, a second one of which diffusion processes
is a diffusion process from within the housing into the sensor
element.
4. The sensor system of claim 2, wherein the transfer function of
the sensor model of second order is G 2 ( s ) = Ks + 1 ( T 1 s + 1
) ( T 2 s + 1 ) ##EQU00037## where s denotes the complex Laplace
variable, K, T.sub.1, T.sub.2 are constants to be identified,
T.sub.1 and T.sub.2 are time constants of respective diffusion
processes, and K defines a coupling between the two diffusion
processes.
5. The sensor system of claim 2, wherein the compensation filter is
a compensation filter of second order.
6. The sensor system of claim 4, wherein a transfer function
C.sub.2(s) of the compensation filter is: C 2 ( s ) = ( T 1 s + 1 )
( T 2 s + 1 ) ( Ks + 1 ) ( Ps + 1 ) ##EQU00038##
7. The sensor system of claim 1, wherein the sensor model modelled
for building the compensation filter is a sensor model of first
order.
8. The sensor system of claim 7, wherein the sensor comprises a
sensor element sensitive to a component in a medium outside the
housing, wherein the sensor model of first order represents a
dominant diffusion process for the medium to reach the sensor
element.
9. The sensor system of claim 7, wherein the transfer function of
the sensor model of first order is G 1 ( s ) = 1 ( T 1 s + 1 )
##EQU00039## where s denotes the complex Laplace variable, and
T.sub.1 is a time constant of the respective diffusion process.
10. The sensor system of claim 7, wherein the compensation filter
is a compensation filter of first order.
11. The sensor system of claim 9, wherein a transfer function
C.sub.1(s) of the compensation filter is: C 1 ( s ) = ( T 1 s + 1 )
( Ps + 1 ) ##EQU00040##
12. The sensor system of claim 1, wherein the compensation filter
comprises a temperature continuous compensation model.
13. The sensor system according to claim 1, wherein the sensor is a
humidity sensor.
14. The sensor system according to claim 13, wherein the humidity
sensor and the temperature sensor are arranged close to a pane of a
vehicle for detecting fogging of the pane.
15. The sensor system of claim 1, wherein the compensation filter
is designed to decrease a response time of the sensor signal
subject to the temperature signal.
16. The sensor system of claim 1, wherein the same order selected
for the transfer function of the sensor model is applied to the
transfer function of the compensating filter.
17. A method for adjusting a sensor signal, comprising the steps
of: (a) sensing a temperature, (b) providing a sensor signal
representative of a measure other than temperature, dynamic
components of the sensor signal being dependent on temperature, and
(c) by a computing device configured for doing so, (i) adjusting
the dynamic components in the sensor signal subject to the
temperature sensed, and (ii) providing a compensated sensor signal,
wherein the computing device comprises a compensation filter
receiving the sensor signal and the temperature signal, wherein the
compensation filter is designed for adjusting the dynamic
components in the sensor signal subject to the temperature signal,
and for providing a compensated sensor signal, and wherein the
compensation filter is modeled based on an inverse of a transfer
function of a sensor model of the sensor, which compensation filter
contains temperature dependent terms, said model being provided in
a spectral domain, and wherein said steps are executed on a sensor
system according to claim 1.
18. The method according to claim 17, wherein the dynamic
components in the sensor signal are adjusted by applying a
temperature continuous compensation model.
19. The method according to claim 17, wherein the sensor signal
represents measured humidity, and wherein the compensated sensor
signal is used in an antifogging application in a vehicle.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the priority of European Patent
Application 10005804.9, filed Jun. 4, 2010, the disclosure of which
is incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] It is the nature of sensors that they react on real impacts
with a certain time lag. Especially, this is true in fast varying
environments in which the quantity to be measured may change in
form of a step function, for example. However, the corresponding
sensor signal may not step up to the new real measure value but
rather gets there with a certain response time.
[0003] There are many applications that only work properly with a
sensor supplying a fast response to fast varying measures. However,
for many sensors there are limitations in modifying the hardware in
order to improve the response time.
BRIEF SUMMARY OF THE INVENTION
[0004] The problem to be solved by the present invention is
therefore to provide a sensor and a method for providing a sensor
signal with improved response time. It is also desired to provide a
method for building such a sensor system or pieces of it
respectively.
[0005] The problem is solved by a sensor system according to the
features of claim 1, by a method for adjusting a sensor signal
according to the features of claim 7, and by a method for building
a compensation filter for use in a sensor system according to the
features of claim 12.
[0006] According to a first aspect of the present invention, there
is provided a sensor system comprising a sensor providing a sensor
signal representative of a measure other than temperature, wherein
dynamic components of the sensor signal are dependent on
temperature. The system further includes a temperature sensor for
providing a temperature signal. A compensation filter receives the
sensor signal and the temperature signal. The compensation filter
is designed for adjusting the dynamic components in the sensor
signal subject to the temperature signal, and for providing a
compensated sensor signal.
[0007] According to another aspect of the present invention, there
is provided a method for adjusting a sensor signal. According to
this method a temperature is sensed and a sensor signal
representative of a measure other than temperature is provided.
Dynamic components of this sensor signal typically are dependent on
temperature. The dynamic components in the sensor signal are
adjusted subject to the temperature sensed. A compensated sensor
signal is provided as a result of this adjustment.
[0008] Sensors may not immediately react to changes in a measure
but only react with a certain delay, also called response time.
Such time lag may be owed to the appearance of diffusion processes,
which may include a diffusion of the measure into the sensor--e.g.
into a housing of the sensor--and, in addition, possibly a
diffusion of the measure into a sensor element of the sensor. For
some sensors and applications, chemical reactions of the measure
with the sensor element may increase the response time, too. While
a sensor may perfectly map a static measure into its sensor signal,
dynamic components in the measure, such as swift changes, steps, or
other high-frequent changes may be followed only with a delay in
time.
[0009] For such sensors/applications it may be beneficial if the
sensor response is dynamically compensated. This means, that the
sensor signal, and in particular the dynamic components of the
sensor signal are adjusted such that the response time of the
sensor is decreased. Such effort in decreasing the response time of
a sensor is also understood as compensation of the sensor signal
and especially its dynamic components.
[0010] By using a dynamic compensation filter the response of a
sensor, i.e. its output in response to a change in the measure,
will be accelerated. If the dynamics of the sensor including its
housing are known, an observer, i.e. a compensation filter, can be
implemented to estimate the true physical value of the measure.
This observer compensates for the sensor dynamics such that the
response can be considerably accelerated in time, which means that
the response time can be considerably decreased. This is why the
proposed method and system enhance the system dynamics of
sensors.
[0011] It has been observed that the dynamic components of a sensor
response--e.g. the gradient in the sensor signal--may be dependent
on the ambient temperature, such that for example the response time
of the sensor may be shorter at higher temperatures, and may take
longer at lower temperatures. Consequently, in the present
embodiments, it is envisaged to apply a compensating filter to the
sensor output which compensating filter takes the measured
temperature into account. As a result the compensated sensor signal
supplied by the compensating filter is even more enhanced in that
its deviation from the real measure is improved for the reason that
temperature dependency of the sensor dynamics is taken into account
of the compensation filter modelling.
[0012] Another aspect of the invention provides a method for
building a compensation filter for use in a sensor system. In this
method, a sensor model of the sensor is built, the sensor model
being characterized by a transfer function. A compensation filter
is modelled based on an inverse of the transfer function of the
sensor model. Temperature dependent terms are applied to the
compensation filter.
[0013] In another aspect of the present invention, there is
disclosed a computer program element for adjusting a sensor signal,
the computer program element comprising computer program
instructions executable by a computer to receive a sensor signal
representative of a measure other than temperature, dynamic
components of the sensor signal being dependent on temperature, to
adjust the dynamic components in the sensor signal subject to the
temperature sensed, and to provide a compensated sensor signal.
[0014] Other advantageous embodiments are listed in the dependent
claims as well as in the description below. The described
embodiments similarly pertain to the system, the methods, and the
computer program element. Synergetic effects may arise from
different combinations of the embodiments although they might not
be described in detail.
[0015] Further on it shall be noted that all embodiments of the
present invention concerning a method might be carried out with the
order of the steps as described, nevertheless this has not to be
the only essential order of the steps of the method all different
orders of orders and combinations of the method steps are herewith
described.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] The aspects defined above and further aspects, features and
advantages of the present invention can also be derived from the
examples of embodiments to be described hereinafter and are
explained with reference to examples of embodiments. The invention
will be described in more detail hereinafter with reference of
examples of embodiments but to which the invention is not
limited.
[0017] FIG. 1 shows a diagram illustrating a change in a measure
and associated sensor signals for different ambient
temperatures,
[0018] FIG. 2 shows a schematic illustration of a sensor system
according to an embodiment of the present invention in a block
diagram,
[0019] FIG. 3A illustrates diagrams with sample measures,
associated sensor signals, and associated compensated sensor
signals,
[0020] FIG. 3B illustrates diagrams with sample measures,
associated sensor signals, and associated compensated sensor
signals,
[0021] FIG. 4A shows a graph of signals in the discrete time domain
which signals appear in a sensor system of an embodiment according
to the present invention,
[0022] FIG. 4B shows graphs of signals in the discrete time domain
which signals appear in a sensor system of an embodiment according
to the present invention,
[0023] FIG. 4C shows a graph of a signal in the discrete time
domain which signals appear in a sensor system of an embodiment
according to the present invention,
[0024] FIG. 5A illustrates graphs for supporting the understanding
of how to build a compensation filter according to an embodiment of
the present invention,
[0025] FIG. 5B illustrates graphs for supporting the understanding
of how to build a compensation filter according to an embodiment of
the present invention,
[0026] FIG. 6A illustrates graphs for supporting the understanding
of how to build a compensation filter according to another
embodiment of the present invention,
[0027] FIG. 6B illustrates graphs for supporting the understanding
of how to build a compensation filter according to another
embodiment of the present invention,
[0028] FIG. 6C illustrates graphs for supporting the understanding
of how to build a compensation filter according to another
embodiment of the present invention, and
[0029] FIG. 7 illustrates on a temperature scale with different
temperature sub-ranges a measure may be exposed to.
DETAILED DESCRIPTION OF THE DRAWINGS
[0030] FIG. 1 shows a diagram with a step function st representing
an immediate change in the quantity of a measure to be measured. An
x-axis of the diagram indicates time in s, the y axis indicates the
quantity of the measure to be measured, in this particular case the
relative humidity RH(t) in %. Accordingly, at t=0 the relative
humidity RH steps up from 20% to 80%. The other graphs in the
diagram indicate sensor signals over time provided by a relative
humidity sensor in response to the step function st of the relative
humidity. It can be derived from these graphs that the humidity
sensor cannot immediately follow the change in the measure and
approaches the new relative humidity of 80% only with a delay which
delay is also called response time. The various graphs represent
sensor signals subject to different ambient temperatures in Celsius
degrees. Basically, the higher the ambient temperature is the
faster the response time of the sensor signal is. The lower the
ambient temperature is the longer the response time of the sensor
signal is.
[0031] FIG. 2 shows a schematic illustration of a sensor system
according to an embodiment of the present invention. A relative
humidity sensor 1 senses the ambient relative humidity RH. In the
following, the term humidity is used as a synonym for relative
humidity. The physics of the humidity sensor 1 is such that
dynamics of the sensor signal RH.sub.sensor at its output is
temperature dependent. Insofar, the humidity sensor 1 of FIG. 2 may
behave according to a humidity sensor providing a temperature
dependent output according to the graphs in FIG. 1. This means that
the response time of the humidity sensor is dependent from the
ambient temperature T. Accordingly, in FIG. 2 the ambient
temperature T is illustrated as input to the humidity sensor 1
although the humidity sensor 1 is not meant to measure the ambient
temperature 1 but rather the dynamics of the sensor signal
RH.sub.sensor at its output is varying subject to the ambient
temperature T.
[0032] A second sensor is provided, which is a temperature sensor 2
for measuring the ambient temperature T. The output of the
temperature sensor 2 provides a temperature signal T representing
the ambient temperature T.
[0033] A compensator 3 receives the sensor signal RH.sub.sensor(t)
over time--which sensor signal is also denoted as u(t)--and the
temperature signal T(t) over time, and adjusts the dynamics in the
sensor signal RH.sub.sensor(t) subject to the temperature signal
T(t). As a result of this adjustment, the compensator 3 provides at
its output a compensated sensor signal RH.sub.compensated(t) over
time. In qualitative terms, the compensated sensor signal
RH.sub.compensated(t) shall compensate for the response time of the
humidity sensor 1 at its best and take a gradient that is more
close to the gradient of the measure to be measured. As such, the
compensator 3 adjusts for the dynamics of the sensor signal
RH.sub.sensor(t) and consequently for the physics of the sensor 1
not allowing for better response times.
[0034] In order to build a compensator 3 that actually compensates
for the dynamics of the sensor 1 in the desired way, the behaviour
of the sensor 1 needs to be understood. While the following
sections are described in connection with humidity sensing, it is
understood that the principles can be generalized to any other
sensor which shows a response time not satisfying for an
application the sensor is used in and in particular a temperature
dependent response time.
[0035] Modelling the Sensor:
[0036] The following desrcibes the modelling of a humidity sensor
out of which model a suitable compensator may be derived. Such
compensator may be applied downstream to the real sensor and
compensate for dynamics in the sensor signal output by such
sensor.
[0037] For a humidity sensor, the humidity as the relevant measure
needs to reach a sensing element of the humidity sensor. Such
sensing element of a humidity sensor preferably is a membrane. For
further information on humidity sensing background it is referred
to EP 1 700 724. Consequently, the humidity to be measured needs to
diffuse into the membrane of the humidity sensor. Prior to this,
the humidity needs to diffuse into a housing of the humidity sensor
provided the humidity sensor has such housing.
[0038] For humidity sensors for which both of these diffusion
processes--i.e. from the outside into the housing and from the
housing into the sensor element--are relevant both processes are
preferred to be respected in a corresponding sensor model.
[0039] Both of the processes may be described with a differential
diffusion equation with two independent diffusion time constants.
In a first approximation, the sensor can be described by a transfer
function in the frequency domain with two poles and one zero such
that the generic design of a corresponding transfer function
G.sub.2(s) may look like, specifically in a second order model:
G 2 ( s ) = Ks + 1 ( T 1 s + 1 ) ( T 2 s + 1 ) , ( Eq . 1 )
##EQU00001##
[0040] where s denotes the complex Laplace variable and K, T.sub.1,
T.sub.2 are constants to be identified. T.sub.1 and T.sub.2 are
time constants of the respective diffusion processes and K defines
a coupling between the two processes. The transfer function G(s)
generally describes the characteristics of the sensor in the
frequency domain by
RH.sub.sensor(s)=G(s)*RH(s)
[0041] If the housing of the humidity sensor is very complex, an
additional pole and zero may be added, and the transfer function of
the humidity sensor may be amended accordingly.
[0042] Some other applications may require a less complex sensor
representation. In this case, a first order model may approximate
the sensor, which first order model is characterized by a transfer
function in the frequency domain with one pole such that the
generic design of such transfer function G.sub.1(s) may look like,
specifically in a first order model:
G 1 ( s ) = 1 ( T 1 s + 1 ) . ( Eq . 2 ) ##EQU00002##
[0043] Such model may be sufficient, for example, if the humidity
sensor does not include a housing such that the diffusion process
into the housing can be neglected, or, if one of the two diffusion
processes--either from the outside into the housing or from the
housing into the sensor element--is dominant over the other, such
that the transfer function may be approximated by the dominant
diffusion process only.
[0044] There are different ways for identifying the parameters
T.sub.1, T.sub.2 and K. One approach is to find the parameters by
trial and error. In a first trial, the sensor output is simulated
by the sensor model wherein the sensor model makes use of a first
estimation of the parameters. The output of the sensor model then
is compared with the sensor signal supplied by the real sensor.
Afterwards, the parameters are adjusted until a deviation between
the simulated sensor output and the real sensor signal is
acceptably small.
[0045] For implementing the sensor model in a digital system such
as a microcontroller the sensor model preferably is implemented in
the discrete time domain rather than in the continuous frequency
domain as described by equations 1 or 2. Therefore, the sensor
model needs to be digitised, i.e. transformed into a set of
difference equations.
[0046] First, the differential equations in the frequency domain,
e.g. the equations 1 and 2, can be reverse transformed into the
time continuous domain by the Laplace back-transform.
[0047] For the second order model of the sensor according to
equation 1 the equivalent time continuous state space description
in the control canonical form is:
[ x 1 ( t ) t x 2 ( t ) t ] = A c M [ x 1 ( t ) x 2 ( t ) ] + B c M
w ( t ) ##EQU00003## v ( t ) = C c M x ( t ) + D c M w ( t )
##EQU00003.2##
[0048] with
[0049] w(t) denoting the real relative humidity RH at time t in the
time domain,
[0050] x1(t) and x2(t) denoting internal states of the second order
sensor model, and
[0051] v(t) denoting the sensor model output over time t.
[0052] In this time continuous state space representation, the
coefficients A, B, C and D are determined by:
A c M = [ - T 1 + T 2 T 1 T 2 1 T 1 T 2 1 0 ] , B c M [ 1 0 ]
##EQU00004## C c M = [ K T 1 T 2 1 T 1 T 2 ] , D c M = 0
##EQU00004.2##
[0053] For a first order sensor model the time continuous state
space description in the control canonical form is:
x ( t ) t = A c M x ( t ) + B c M w ( t ) ##EQU00005## v ( t ) = C
c M x ( t ) + D c M w ( t ) ##EQU00005.2##
[0054] again, with
[0055] w(t) denoting the real relative humidity RH at time t in the
time domain,
[0056] x(t) denoting an internal state of the first order sensor
model, and
[0057] v(t) denoting the sensor model output over time t.
[0058] In this time continuous state space representation, the
coefficients A, B, C and D are determined by:
A c M = - 1 T 1 , B c M = 1 , C c M = 1 T 1 , D c M = 0
##EQU00006##
[0059] Second, the representation in the time continuous domain may
be transformed into the time discrete domain.
[0060] A time discrete state space representation equivalent to the
time continuous state space representation for the second order
sensor model may be:
[ x 1 ( k + 1 ) x 2 ( k + 1 ) ] = A d M [ x 1 ( k ) x 2 ( k ) ] + B
d M w ( k ) ##EQU00007## v ( t ) = C d M [ x 1 ( k ) x 2 ( k ) ] +
D d M w ( k ) [ x 1 ( 0 ) x 2 ( 0 ) ] = ( I - A d M ) - 1 B d M w (
0 ) ##EQU00007.2##
[0061] where w denotes the measured relative humidity at time step
k with the sampling time t(k+1)-t(k)=T.sub.s. There are two
internal states x.sub.1(k), x.sub.2(k) of the second order sensor
model. This means x(k)=(x.sub.1(k), x.sub.2(k)).sup.T. v(k) denotes
the sensor model output in the discrete time domain.
[0062] In this time discrete state space representation, the
coefficients A, B, C and D are determined by:
A.sub.d.sup.M=e.sup.A.sup.c.sup.M.sup.T.sup.s,
B.sub.d.sup.M=(A.sub.c.sup.M).sup.-1(e.sup.A.sup.c.sup.M.sup.T.sup.s-I)B.-
sub.c.sup.M
C.sub.d.sup.M=C.sub.c.sup.M, D.sub.d.sup.M=D.sub.c.sup.M
[0063] In addition,
I = [ 1 0 0 1 ] ##EQU00008##
and T.sub.s is the sampling time.
[0064] A time discrete state space representation of the time
continuous state space representation for the first order sensor
model may be:
x ( k + 1 ) = A d M x ( k ) + B d M w ( k ) ##EQU00009## v ( k ) =
C d M x ( k ) + D d M w ( k ) ##EQU00009.2## x ( 0 ) = B d M 1 - A
d M w ( 0 ) ##EQU00009.3##
[0065] where w(k) denotes the measured relative humidity RH at time
step k with the sampling time t(k+1)-t(k)=T.sub.s. There is an
internal state x(k) of the first order sensor model. v(k) denotes
the modelled sensor output in the discrete time domain.
[0066] In this time discrete state space representation, the
coefficients A, B, C and D are determined by:
A d M = - T 1 T s , B d M = - 1 T 1 ( - T 1 T s - 1 ) ##EQU00010##
C d M = 1 , D d M = 0 ##EQU00010.2##
where T.sub.s is the sampling time.
[0067] The derivation of the matrices for the first and the second
order sensor model requires Schur decomposition or series expansion
and matrix inversion. Computer software may help to calculate the
coefficients.
[0068] The time discrete state space representations of the first
or the second order sensor model may be run on a microprocessor,
and the parameters T.sub.1 or T.sub.1, T.sub.2 and K respectively
may be varied until the sensor model output v(k) is close enough to
the real sensor signal u(t) which may be present in digitized form
u(k), too, or may be digitized for comparing purposes.
[0069] More sophisticated methodologies for determining the
parameters of the sensor model may use system identification tools
that automatically build dynamical models from measured data.
[0070] Modelling the Compensator:
[0071] In a next step, the compensator 3 out of FIG. 2 is
determined and implemented. When the humidity sensor 1 is modelled
by a second order model then, advantageously, the compensator is
modelled by a second order model, too. The transfer function
C.sub.2(s) of such a second order compensation filter 3--also
denoted as compensator--in the frequency domain may be described
by:
C 2 ( s ) = ( T 1 s + 1 ) ( T 2 s + 1 ) ( Ks + 1 ) ( Ps + 1 ) ( Eq
. 3 ) ##EQU00011##
[0072] If a first order sensor model is applied, the following
first order compensation filter is proposed, which may be described
by a transfer function C.sub.1(s) in the frequency domain by:
C 1 ( s ) = ( T 1 s + 1 ) ( Ps + 1 ) . ( Eq . 4 ) ##EQU00012##
[0073] For both models, s denotes the complex Laplace variable and
K, T.sub.1, T.sub.2 are the constants that were identified when
determining the sensor model.
[0074] C(s) generally denotes the transfer function of the
compensation filter in the frequency domain, wherein
RH.sub.compensated(s)=C(s)*RH.sub.sensor(s)
[0075] Preferably, the compensation filter transfer function C(s)
is the inverse to the sensor model transfer function G(s), i.e. the
diffusion function, such that
C(s)=1/G(s)
[0076] The term (Ps+1) is introduced in the compensator transfer
function to make the function physically applicable. Parameter P is
kept small in order to keep impact on filter function low, but can
be used to filter measurement noise.
[0077] An important feature of the compensation filter transfer
function C(s) is that the final value of C(s) converges to 1,
i.e.
lim s .fwdarw. 0 C ( s ) = 1 ##EQU00013##
[0078] This means that the compensation filter 3 only changes the
sensor output characteristic during transition. When the
compensation filter 3 is in steady state, it does not affect the
sensor output, even if the modelling of the sensor and its housing
is inaccurate. Please note that overshoots may occur if the real
system response RH(t) is faster than modelled.
[0079] Typically, the compensation filter 3 is implemented in a
digital system such as a microcontroller which operates on samples
of the measured humidity rather than on the continuous signal. As a
consequence, microcontrollers cannot integrate and not implement
differential equations like those in equation 3 or 4. Therefore,
the compensator needs to be digitised, i.e. transformed into a set
of difference equations.
[0080] First, the differential equations in the spectral domain,
i.e. the equations 3 and 4 in the present example, can be reverse
transformed into the time continuous domain by the Laplace
back-transform.
[0081] For the second order compensation filter the time continuous
state space description in the control canonical form is:
[ x 1 ( t ) t x 2 ( t ) t ] = A c C [ x 1 ( t ) x 2 ( t ) ] + B c C
u ( t ) ##EQU00014## y ( t ) = C c C x ( t ) + D c C u ( t )
##EQU00014.2##
[0082] with u(t) denoting the measured humidity at time t in the
time domain, i.e. the sensor signal RH.sub.sensor(t),
[0083] x1(t) and x2(t) denoting internal states of the second order
compensation filter, and
[0084] y(t) denoting the compensated sensor signal, i.e.
RH.sub.compensated(t) according to FIG. 2.
[0085] In this time continuous state space representation, the
coefficients A, B, C and D are determined by:
A c C = [ K + P KP 1 KP 1 0 ] , B c C = [ 1 0 ] , D c C = T 1 T 2
KP ##EQU00015## C c C = [ T 1 + T 2 KP - T 1 T 2 ( K + P ) ( KP ) 2
1 KP - T 1 T 2 ( KP ) 2 ] ##EQU00015.2##
[0086] For the first order compensation filter the time continuous
state space description in the control canonical form is:
x ( t ) t = A c C x ( t ) + B c C u ( t ) ##EQU00016## y ( t ) = C
c C x ( t ) + D c C u ( t ) ##EQU00016.2##
[0087] with u(t) denoting the measured humidity at time t in the
time domain, i.e. the sensor signal RH.sub.sensor(t) in FIG. 2,
[0088] x(t) denoting an internal state of the second order
compensation filter, and
[0089] y(t) denoting the compensated sensor signal, i.e.
RH.sub.compensated(t) in FIG. 2.
[0090] In this time continuous state space representation, the
coefficients A, B, C and D are determined by:
A c C = - 1 P , B c C = 1 , C c C = P - T 1 P 2 , D c C = T 1 P
##EQU00017##
[0091] Second, the representation in the time continuous domain may
be transformed into the time discrete domain.
[0092] A time discrete state space representation of the time
continuous state space representation for the second order
compensation filter may be:
[ x 1 ( k + 1 ) x 2 ( k + 1 ) ] = A d C [ x 1 ( k ) x 2 ( k ) ] + B
d C u ( k ) y ( t ) = C d C [ x 1 ( k ) x 2 ( k ) ] + D d C u ( k )
[ x 1 ( 0 ) x 2 ( 0 ) ] = ( I - A d C ) - 1 B d C u ( 0 ) Equ . 5
##EQU00018##
[0093] where u(k) denotes the measured humidity at time step k with
the sampling time t(k+1)-t(k)=T.sub.s. There are two internal
states of the second order compensator, i.e. x(k)=(x.sub.1(k),
x.sub.2(k)).sup.T. y(k) denotes the compensated sensor signal in
the discrete time domain.
[0094] In this time discrete state space representation, the
coefficients A, B, C and D are determined by:
A.sub.d.sup.C=e.sup.A.sup.c.sup.C.sup.T.sup.s
B.sub.d.sup.C=(A.sub.c.sup.C).sup.-1(e.sup.A.sup.c.sup.C.sup.T.sup.s-I)B-
.sub.c.sup.C
C.sub.d.sup.C=C.sub.c.sup.C
D.sub.d.sup.C=D.sub.c.sup.C
[0095] A time discrete state space representation of the time
continuous state space representation for the first order
compensation filter may be:
x ( k + 1 ) = A d C x ( k ) + B d C u ( k ) ##EQU00019## y ( k ) =
C d C x ( k ) + D d C u ( k ) ##EQU00019.2## x ( 0 ) = B d C 1 - A
d C u ( 0 ) ##EQU00019.3##
[0096] where u(k) denotes the measured humidity at time step k with
the sampling time t(k+1)-t(k)=T.sub.s. There is an internal state
x(k) of the first order compensator. y(k) denotes the compensated
sensor signal in the discrete time domain.
[0097] In this time discrete state space representation, the
coefficients A, B, C and D are determined by:
A d C = - PT s , B d C = - 1 P ( - PT s - 1 ) ##EQU00020## C d C =
P - T 1 P 2 , D d C = T 1 P ##EQU00020.2##
[0098] The derivation of the matrices for the first and the second
order compensation filter requires Schur decomposition or series
expansion and matrix inversion. Computer software may help to
calculate the coefficients.
[0099] FIGS. 4A, 4B, and 4C illustrate sample signals, primarily in
the discrete time domain. FIG. 4A illustrates a sample ambient
humidity RH over time t. The measured humidity as continuous signal
over time is denoted by u(t), i.e. the sensor signal u(t) supplied
by the humidity sensor. The sensor signal u(t) is sampled at points
k=0, k=1, . . . with the sampling time T.sub.s=t(k+1)-t(k). u(k)
denotes the sampled sensor signal which is a time discrete
signal.
[0100] For a second order compensation filter the internal states
x1 and x2 over sampling points k are illustrated in the graph in
FIG. 4B. In the last graph in FIG. 4C, the compensated sensor
signal is illustrated as step function in the discrete time domain.
For illustration purposes, an equivalent Y in the continuous time
domain is depicted as dot and dash line.
[0101] The compensation effect with respect to a sample humidity
characteristic over time is also illustrated in the diagrams of
FIGS. 3A, 3B and 3C. In FIG. 3A, the relative humidity in the
environment, denoted as "Ambient condition" is shown as a function
of time and includes three step wise changes and a gradient in form
of a ramp. The humidity sensor supplies a sensor signal--denoted as
"Sensor output"--which exhibits significant response times to the
fast changes in the Ambient condition. As mentioned before, the
Ambient condition is filtered within the sensor because of the
internal diffusion dynamics and the dynamics of the housing. A
compensation filter following the sensor supplies a compensated
sensor signal--denoted as "Compensated output". In the present
example, the compensation filter is implemented as a second order
model. As can be derived from the diagram, the Compensated output
much more resembles the Ambient condition than the sensor output
does without a compensator applied to the sensor output.
Consequently, the compensator helps in improving the quality of the
measuring system such that the overall output of the sensor system
including the compensator provides for a better quality output
especially for fast changes in the Ambient condition. FIG. 3B
illustrates the Sensor output and the Compensated Output for
another Ambient condition characteristic in form of a saw tooth. In
this example, the compensation filter is implemented as a first
order model.
[0102] The diagrams in FIGS. 5A and 5B support the illustration of
a method for implementing a sensor system according to an
embodiment of the present invention. In a first step, the sensor
itself is modelled for the purpose of deriving a compensator model
from the data that describes the sensor model. In this first step,
the real sensor again is exposed to a step wise increase of the
measure, i.e. the relative humidity denoted as "Ambient condition"
again. The relative humidity RH is increased in a single step from
about 15% to about 65%. The corresponding Sensor output is
measured, and preferably stored. The Sensor output exhibiting a
response time is plotted in both FIG. 5A and FIG. 5B. Up-front, it
is determined, that the humidity sensor used may best be
represented by a first order model. Consequently, in a second step,
the sensor model is built by means of the transfer function:
G 1 ( s ) = 1 ( T 1 s + 1 ) ##EQU00021##
[0103] and the parameter T.sub.1 needs to be determined. In order
to determine the parameter T.sub.1 such that the output of the
sensor model fits the real Sensor output as depicted in FIGS. 5A
and 5B best, the first order type sensor model is implemented on a
microcontroller in the time discrete state space according to the
equations that were explained previously:
x ( k + 1 ) = A d M x ( k ) + B d M w ( k ) ##EQU00022## v ( k ) =
C d M x ( k ) + D d M w ( k ) ##EQU00022.2## x ( 0 ) = B d M 1 - A
d M w ( 0 ) ##EQU00022.3##
[0104] With coefficients
A d M = - T 1 T s , B d M = - 1 T 1 ( - T 1 T s - 1 ) ##EQU00023##
C d M = 1 , D d M = 0 ##EQU00023.2##
[0105] In this time discrete state space representation of the
sensor model, an initial value of the parameter T.sub.1 is chosen,
e.g. T.sub.1=6s. The sensor model output with T.sub.1=6s is
illustrated in FIG. 5A. The sensor model is also run with
parameters T.sub.1=8s and T.sub.1=12s. The corresponding sensor
model output is illustrated in FIG. 5A, too.
[0106] In a next step, the value of the parameter is chosen that
makes the sensor model output come closest to the real sensor
signal. From FIG. 5A it can be derived, that this is the case for
T.sub.1=8s. Accordingly, the complete transfer function of the
sensor model in the frequency domain is
G 1 ( s ) = 1 ( 8 s + 1 ) ##EQU00024##
[0107] While its representation in the time discrete domain is
x ( k + 1 ) = 0.8465 x ( k ) + 0.9211 w ( k ) ##EQU00025## v ( k )
= 0.1667 x ( k ) + 0 w ( k ) ##EQU00025.2## x ( 0 ) = 0.9211 1 -
0.8465 w ( 0 ) ##EQU00025.3##
[0108] The method can be modified in that the sensor is modelled
first with a first value of the parameter. If the deviation of the
sensor output based on the model with the first parameter value is
too large, another value for the parameter is chosen. Iteratively,
as many parameter values are chosen as long as there is considered
to be sufficient similarity between the sensor model output and the
real sensor signal, i.e. the deviation between those two is below a
threshold.
[0109] In a next step, the compensator model is determined to be a
first order model with a general representation in the frequency
domain of
C 2 ( s ) = T 1 s + 1 Ps + 1 ##EQU00026##
[0110] The representation in the time discrete state space
according to the above is:
x ( k + 1 ) = A d C x ( k ) + B d C u ( k ) ##EQU00027## y ( k ) =
C d C x ( k ) + D d C u ( k ) ##EQU00027.2## x ( 0 ) = B d C 1 - A
d C u ( 0 ) ##EQU00027.3##
[0111] with u(k) denoting the discrete input to the compensator,
i.e. the discrete representation of output of the real sensor, and
y(k) denoting the discrete output of the compensator, i.e. the
compensated sensor signal in the time discrete domain. The
corresponding coefficients are:
A d C = e - PT s , B d C = - 1 P ( e - PT s - 1 ) ##EQU00028## C d
C = P - T 1 P 2 , D d C = T 1 P ##EQU00028.2##
[0112] With the determination of the parameter T.sub.1 upon
implementation of the sensor model, the coefficients A-D of the
compensator can now be determined. In this step, parameter P is
chosen, too. Parameter P effects reducing the signal noise.
[0113] The compensator can now be implemented. In its time discrete
state space, the compensator is described by:
x ( k + 1 ) = 0.3679 x ( k ) + 0.6321 u ( k ) ##EQU00029## y ( k )
= 8.0 x ( k ) + - 7.0 u ( k ) ##EQU00029.2## x ( 0 ) = 0.6321 1 -
0.3679 u ( 0 ) ##EQU00029.3##
[0114] The compensator now can be validated on the data measured. P
can be adjusted to best performance in the signal to noise ratio
SNR.
[0115] In the present embodiment, parameter P is chosen as P=1.
[0116] The Compensated output is shown in FIG. 5B.
[0117] The response time is limited compared to the uncompensated
Sensor output. The compensator, of course works for all kinds of
signals
[0118] The diagrams in FIGS. 6A, 6B and 6C support the illustration
of a method for implementing a sensor system according to another
embodiment of the present invention. In contrast to the embodiment
of FIGS. 5A and 5B the sensor model and the compensator now are
described as a second order model. Besides, the steps of
implementing the sensor system including the compensator are the
same as described in connection with FIGS. 5A and 5B. Again, in a
first step, the sensor itself is modelled for the purpose of
deriving a compensator model from the data that describes the
sensor model. In this first step, the real sensor again is exposed
to a step wise increase of the measure, i.e. the relative humidity
denoted as "Ambient condition" again. The relative humidity RH is
increased in a single step from about 15% to about 65%. The
corresponding Sensor output is measured, and preferably stored. The
Sensor output exhibiting a response time is plotted in all FIGS.
5A, 5B and 5C. Consequently, in a second step, the sensor model is
built by means of the transfer function:
G 2 ( s ) = Ks + 1 ( T 1 s + 1 ) ( T 2 s + 1 ) ##EQU00030##
[0119] and the parameter T.sub.1, T2 and K need to be determined.
In order to determine the parameter such that the output of the
sensor model fits the real Sensor output as depicted in FIG. 6A
best, the sensor model is implemented on a microcontroller in the
time discrete state space according to the equations as given
above. Initial values of the parameters are chosen and in an
iterative way the parameters are set such that the output of the
sensor model fits the sensor signal of the real sensor best. In
FIG. 6A, there are illustrated multiple outputs of sensor models
implemented with different parameter settings. It can be derived,
that the parameter setting of T.sub.1=16, T.sub.2=155, and K=90
fits best. With such a parameter setting, the description of the
sensor model in the time discrete state space is finalized.
[0120] In a next step, the compensator model is built as a second
order model with a representation in the frequency
domain--including the parameters as determined while building the
sensor model, and assuming parameter P to be set to P=20:
C 2 ( s ) = ( 16 s + 1 ) ( 155 s + 1 ) ( 90 s + 1 ) ( 20 s + 1 )
##EQU00031##
[0121] This compensator model can be described in the time discrete
state space by:
[ x 1 ( k + 1 ) x 2 ( k + 1 ) ] = [ 9.78 10 - 1 - 2.20 10 - 4 1.98
10 - 1 1.00 10 - 1 ] [ x 1 ( k ) x 2 ( k ) ] + [ 0.198 0.020 ] u (
k ) ##EQU00032## y ( k ) = [ - 0.116 - 0.00195 ] [ x 1 ( k ) x 2 (
k ) ] + 2.756 u ( k ) [ x 1 ( 0 ) x 2 ( 0 ) ] = [ 0 1800 ] u ( 0 )
##EQU00032.2##
[0122] Again, the compensator now can be validated on the data
measured. The Compensated output is shown in FIG. 6B and FIG. 6C.
Both Compensated outputs differ in that different parameters P are
applied. While in FIG. 6B, P is set to P=10, the Compensated output
is exposed to significant noise. In FIG. 6C P is set to P=20 which
provides a much better signal to noise ratio SNR.
[0123] However, diffusion processes in general depend very much on
temperature. Therefore, the model for the compensating filter
preferably takes temperature dependency into account--especially if
temperature varies by more than 10-20.degree. C. This can be easily
achieved by making the constants T1, T2, . . . , K, . . . time
dependent or by using a set of sensor models G.sub.i(s) and
corresponding compensator models C.sub.i(s) for different
temperature ranges and switching amongst them.
[0124] In a preferred embodiment, a second order temperature
dependent sensor model may be described in the frequency domain
by:
G 2 ( s , T ) = Ks + 1 ( T 1 ( T ) s + 1 ) ( T 2 ( T ) s + 1 )
##EQU00033##
[0125] with T being the temperature.
[0126] The corresponding compensation filter may be described
by
C 2 ( s , T ) = ( T 1 ( T ) s + 1 ) ( T 2 ( T ) s + 1 ) ( Ks + 1 )
( Ps + 1 ) ##EQU00034##
[0127] In the time continuous state space, the following equations
represent the temperature dependent compensator:
dx 1 ( t ) dt = a 11 ( T ) x 1 + a 12 ( T ) x 2 + b 1 ( T ) u ( t )
##EQU00035## dx 2 ( t ) dt = a 21 ( T ) x 1 + a 22 ( T ) x 2 + b 2
( T ) u ( t ) ##EQU00035.2## y ( t ) = c 1 x 1 + c 2 x 2
##EQU00035.3##
[0128] In the time discrete state space, the following equations
represent the temperature dependent compensator:
x(k+1)=A.sub.d.sup.C(T)x(k)+B.sub.d.sup.C(T)u(k)
y(k)=C.sub.c.sup.D(T)x(k)+D.sub.d.sup.C(T)u(k)
[0129] with coefficients
A d C ( T ) = [ a 11 1 + a 12 2 T a 12 1 + a 12 2 T a 21 1 + a 21 2
T a 22 1 + a 22 2 T ] ##EQU00036## B d C ( T ) = [ b 1 1 + b 1 2 T
b 2 1 + b 2 2 T ] ##EQU00036.2## C d C ( T ) = [ 1 1 ]
##EQU00036.3## D d C ( T ) = [ d 1 + d 2 T ] ##EQU00036.4##
[0130] The determination of A.sub.d.sup.C(T) may be complex. A
linear interpolation of matrix elements may be an appropriate way
to determine the coefficients.
[0131] Alternatively, the temperature range is divided into n
sub-ranges i, with temperature sub-range i=0 being the first one,
and temperature sub-range i=n being the last one spanning the
temperature range covered. For each sub-range i a different sensor
model and consequently a different compensator model is determined.
For example, the following compensation filter models are
determined in the frequency domain for temperature sub-ranges [i=0,
. . . , i=n]: [0132] C.sub.2.sup.1(s), C.sub.2.sup.2(s),
C.sub.2.sup.3(s), C.sub.2.sup.4(s), . . . , C.sub.2.sup.n(s)
[0133] And accordingly, the different transfer functions are
transformed each in the time discrete sate space such that for each
temperature range a corresponding compensator model, which may be
different from the compensator models for the other temperature
ranges, may be provided, stored, and applied whenever the ambient
temperature is identified to fall within the corresponding
temperature sub-range.
[0134] In execution, as illustrated in connection with FIG. 2, the
temperature sensor 2 determines the temperature T and supplies such
temperature signal to the compensator 3. The compensator 3
determines in which temperature sub-range i the measured
temperature T falls into, and applies the compensator model that is
defined for such temperature sub-range. The sensor signal u(t) is
then compensated by such selected compensator model 3. As a result
the entire sensor system comprising the sensor 1, the temperature
sensor 2 and the compensator 3 not only compensates for response
times, it compensates also for temperature dependencies in the
sensor signal. By this means, the sensor system can be applied to
environments with fast changing measures which environments are
also characterized to be operated under varying temperatures.
[0135] Whenever temperature is determined to be in sub-range i,
i.e. if T is in T.sub.i, then k=I and the corresponding compensator
model is applied:
x(k+1)=A.sub.d.sup.k(T)x(k)+B.sub.d.sup.k(T)u(k)
y(k)=C.sub.d.sup.k(T)x(k)+D.sub.d.sup.k(T)u(k)
[0136] In FIG. 7 there is illustrated a sample temperature range T
divided into i=4 sub-ranges, with [i=0, . . . i=n=4]. The dashed
line shows a temperature characteristic taken by the temperature
sensor 2 out of FIG. 2. The temperature rises first from a
temperature in sub-range i=2 to a temperature in sub-range i=3,
then falls back to a temperature in sub-range i=2, and further
drops to a temperature in sub-range i=1. Consequently, during this
measurement cycle, three compensator models are applied in sequence
to the humidity sensor signal, i.e. the models i=2, i=3, i=2 again
and finally i=1 corresponding to the temperature ranges.
[0137] The compensator 3 including its models may preferably be
implemented in software, in hardware, or in a combination of
software and hardware.
[0138] Preferably, the sensor system and the corresponding methods
may be applied in the antifogging detection for vehicles. In such
application, it is preferred that the sensor 1 is a humidity
sensor. The humidity sensor may be arranged on or close to a pane
such as a windscreen, for example. In addition, the temperature
sensor may be arranged on or close to the pane, too, for measuring
the ambient temperature, preferably at the same location the
humidity sensor covers.
[0139] The results of the measurements may be used to take action
against a fogged windscreen, for, example, and start operating a
blower.
* * * * *