U.S. patent application number 09/282416 was filed with the patent office on 2001-07-12 for device for controlling running behavior of vehicle by mathematical tire model.
Invention is credited to TSUBOI, TOSHIHIRO, YOKOYAMA, TATSUAKI.
Application Number | 20010007965 09/282416 |
Document ID | / |
Family ID | 26452959 |
Filed Date | 2001-07-12 |
United States Patent
Application |
20010007965 |
Kind Code |
A1 |
YOKOYAMA, TATSUAKI ; et
al. |
July 12, 2001 |
DEVICE FOR CONTROLLING RUNNING BEHAVIOR OF VEHICLE BY MATHEMATICAL
TIRE MODEL
Abstract
A control device for controlling the running behavior of a four
wheeled vehicle has a mathematical tire model of each wheel
defining a relationship between longitudinal and lateral forces vs.
slip ratio, synthesizes the mathematical tire model at zero slip
and a control input from an outside running behavior controller
such as a spin controller or a driftout controller to generate
nominal values of longitudinal force, lateral force and yaw moment
of the vehicle body, and controls the slip ratio of the wheels
through cyclic adjustment so as to approach the differences between
the nominal values and the actual values in the longitudinal force,
lateral force and yaw moment of the vehicle body to the
corresponding differences of those parameters due to
differentiation thereof by the slip ratio based upon the
mathematical tire model.
Inventors: |
YOKOYAMA, TATSUAKI;
(SUSONO-SHI, JP) ; TSUBOI, TOSHIHIRO;
(GOTENBA-SHI, JP) |
Correspondence
Address: |
OLIFF & BERRIDGE
P O BOX 19928
ALEXANDRIA
VA
22320
|
Family ID: |
26452959 |
Appl. No.: |
09/282416 |
Filed: |
March 31, 1999 |
Current U.S.
Class: |
701/70 ; 180/197;
303/140 |
Current CPC
Class: |
B60W 10/184 20130101;
B60W 2520/14 20130101; B60W 2520/125 20130101; B60T 2270/86
20130101; B60W 2050/0028 20130101; B60T 8/1755 20130101; B60W
2520/10 20130101; B60W 2530/20 20130101 |
Class at
Publication: |
701/70 ; 180/197;
303/140 |
International
Class: |
G06F 007/70 |
Foreign Application Data
Date |
Code |
Application Number |
Apr 9, 1998 |
JP |
10-114126 |
Nov 24, 1998 |
JP |
10-332652 |
Claims
1. A device for controlling a running behavior of a vehicle based
upon a force-slip performance of a tire, the vehicle having a
vehicle body, a pair of front wheels and a pair of rear wheels, and
brake means for selectively applying a controlled braking force to
at least either the front pair or the rear pair of the wheels
bearing the tires, comprising: first means for cyclically
calculating by a minute cycle period longitudinal force and lateral
force of each of the at least either the front pair or the rear
pair of the wheels in reference to slip ratio thereof according to
a mathematical tire model of a relationship therebetween, so as to
obtain a first longitudinal force and a first lateral force
corresponding to a first slip ratio and a second longitudinal force
and a second lateral force corresponding to zero slip ratio; second
means for cyclically calculating by the minute cycle period
longitudinal force, lateral force and yaw moment of the vehicle
body based upon the longitudinal forces and the lateral forces of
the at least either the front pair or the rear pair of the wheels,
so as to obtain a first longitudinal force, a first lateral force
and a first yaw moment of the vehicle body corresponding to the
first longitudinal forces and the first lateral forces of the at
least either the front pair or the rear pair of the wheels and a
second longitudinal force, a second lateral force and a second yaw
moment of the vehicle body corresponding to the second longitudinal
forces and the second lateral forces of the at least either the
front pair or the rear pair of the wheels; third means for
cyclically modifying by the minute cycle period the second
longitudinal force, the second lateral force and the second yaw
moment of the vehicle body calculated by the second means with a
longitudinal force, a lateral force and a yaw moment corresponding
to an output of an outside running behavior controller, so as to
obtain a nominal longitudinal force, a nominal lateral force and a
nominal yaw moment, respectively; fourth means for cyclically
calculating by the minute cycle period a difference between the
nominal longitudinal force and the first longitudinal force, a
difference between the nominal lateral force and the first lateral
force and a difference between the nominal yaw moment and the first
yaw moment; fifth means for cyclically calculating by the minute
cycle period differentials of the longitudinal and lateral forces
of each of the at least either the front pair or the rear pair of
the wheels on the basis of the slip ratio thereof according to the
mathematical tire model; sixth means for cyclically calculating by
the minute cycle period differentials of the longitudinal force,
lateral force and yaw moment of the vehicle body based upon
differentials of the longitudinal and lateral forces of each of the
at least either the front pair or the rear pair of the wheels on
the basis of the slip ratio; seventh means for cyclically
calculating by the minute cycle period a difference in the
longitudinal force, a difference in the lateral force and a
difference in the yaw moment of the vehicle body based upon the
differentials thereof; eighth means for cyclically calculating by
the minute cycle period a first difference between the difference
in the longitudinal force calculated by the fourth means and the
difference in the longitudinal force calculated by the seventh
means, a second difference between the difference in the lateral
force calculated by the fourth means and the differential-based
difference in the lateral force calculated by the seventh means,
and a third difference between the difference in the yaw moment
calculated by the fourth means and the differential-based
difference in the yaw moment calculated by the seventh means; ninth
means for calculating by the minute cycle period differences in the
slip ratio of each of the at least either the front pair or the
rear pair of the wheels which minimize a weighted sum of squares of
the first, second and third differences; and tenth means for
selectively operating the brake means to change the slip ratio of
each of the at least either the front pair or the rear pair of the
wheels according to the difference thereof calculated by the ninth
means.
2. A device according to claim 1, further comprising: eleventh
means for cyclically calculating by the minute cycle period a
weighted sum of a square of each of the differences in the slip
ratio calculated by the ninth means; wherein the ninth means are
modified to calculate the differences in the slip ratio so that a
sum of the weighted sum calculated by the ninth means and the
weighted sum calculated by the eleventh means is minimized.
3. A device according to claim 1, further comprising: twelfth means
for cyclically calculating by the minute cycle period a weighted
sum of a square of each of respective sums of the slip ratio and
the change thereof calculated by the ninth means; wherein the ninth
means are modified to calculate the differences in the slip ratio
so that a sum of the weighted sum calculated by the ninth means and
the weighted sum calculated by the twelfth means is minimized.
4. A device according to claim 2, further comprising: twelfth means
for cyclically calculating by the minute cycle period a weighted
sum of a square of each of respective sums of the slip ratio and
the change thereof calculated by the ninth means; wherein the ninth
means are modified to calculate the differences in the slip ratio
so that a sum of the weighted sum calculated by the ninth means,
the weighted sum calculated by the eleventh means and the weighted
sum calculated by the twelfth means is minimized.
5. A device according to claim 1, wherein the third means modify
the second longitudinal force, the second lateral force and the
second yaw moment of the vehicle body calculated by the second
means with the longitudinal force, the lateral force and the yaw
moment corresponding to the output of the outside running behavior
controller, so as to obtain the nominal longitudinal force, the
nominal lateral force and the nominal yaw moment, respectively, by
adding the longitudinal force, the lateral force and the yaw moment
corresponding to the output of the outside running behavior
controller to the second longitudinal force, the second lateral
force and the second yaw moment, respectively.
6. A device according to claim 5, wherein the third means
substantially cancel the lateral force corresponding to the output
of the outside running behavior controller in obtaining the nominal
lateral force.
7. A device according to claim 2, wherein the ninth means apply a
variable weighting factor on each of the difference in the slip
ratio of each of the at least the front pair of the wheels
calculated thereby before outputting the calculated slip ratio
difference such that a slip ratio difference applied with a larger
weighting factor affects less in the running behavior control than
a slip ratio difference applied with a smaller weighting factor,
the weighting factor being varied such that, when the nominal yaw
moment calculated by the third means is directed to assist a turn
of the vehicle, the weighting factor on the slip ratio difference
of one of the pair of front wheels serving at the inside of a turn
is made larger.
8. A device according to claim 1, wherein the tenth means are
adapted to cancel a braking of the rear wheels by overriding the
difference of the slip ratio calculated by the ninth means when the
yaw rate of the vehicle has changed its direction from a first
direction conforming to a turning of the vehicle to a second
direction opposite to the first direction during a turn running of
the vehicle.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a device for controlling a
running behavior of vehicles, and more particularly, to a device
for conducting such a control of a four wheeled vehicle based upon
a mathematical tire model simulating the performance of
longitudinal and lateral forces vs. slip ratio of the tire of each
wheel.
[0003] 2. Description of the Prior Art
[0004] It is known in the art that the tires of the wheels of
vehicles such as automobiles generally exhibit a performance such
as exemplarily shown in the map of FIG. 5 with respect to the
relationship between the longitudinal or lateral force and the slip
ratio. Of course, the actual performance of each particular tire
differs from the shown performance in the shape of the curves as
well as in the magnitude of the scales according to its tread
pattern and respective operational conditions such as a road
surface condition, etc.
[0005] Further, it is also known in the art that such a performance
between the longitudinal or lateral force and the slip ratio of the
tires of wheels of vehicles can be mathematically simulated by the
following equations: 1 Ftxi = - i 2 Ks 1 - Si Si - Wi cos i ( 1 - 3
i 2 + 2 i 3 ) ( 1 ) Ftyi = - i 2 Kb tan i 1 - Si - Wi sin i ( 1 - 3
i 2 + 2 i 3 ) ( 2 )
[0006] when .xi.i.gtoreq.0,
[0007]
[0008] or
Ftxi=-.mu.Wi cos .theta.i (3)
Ftyi=-.mu.Wi sin .theta.i (4)
[0009] when .xi.i<0.
[0010] wherein, generalizing by i such suffixes as fr, fl, rr and
rl indicating the pertinency to front right, front left, rear right
and rear left wheels of a common four wheeled vehicle each bearing
the tire, Ftxi and Ftyi are the longitudinal and lateral components
of a force Fti acting at a tire (wheel) as illustrated in FIG. 6,
and .theta.i is the angle between Fti and Ftxi, Si is a slip ratio
of the tire defined as below by equation 5, and other parameters
are as defined by the following: 2 Si = u - R u ( 5 )
[0011] wherein u is vehicle speed at the tire, R is radius of the
tire, and .omega.is angular speed of the tire
(-.infin.<Si.ltoreq.1.0) 3 cos i = Si i ( 6 ) sin i = Kb tan i
Ks i ( 7 ) i = Si 2 + Kb 2 tan 2 i Ks 2 ( 8 ) i = 1 - Ks i 3 Wi ( 1
- Si ) ( 9 )
[0012] where .beta.i is slip angle of the wheel, Wi is vertical
load on each wheel, Kb is the inclination at .beta.i=0 of a curve
of the slip angle .beta.i vs. the lateral force Ftyi such as shown
in FIG. 7 and Ks is the inclination at Si=0 of a curve of the slip
angle Si vs. the longitudinal force Ftxi such as shown in FIG.
8.
[0013] The above equations are mathematical analyses of the
relationships among such parameters as the longitudinal and lateral
forces, the slip ratio, the slip angle, the vertical load and the
friction coefficient with respect to each single tire. On the other
hand, the running behavior of a four wheeled vehicles is a matter
of interrelations among such respective performances of the four
wheels. FIG. 9 shows an example of the yaw moment applied to the
vehicle body of a four wheeled vehicle by a braking of each of the
four wheels when the vehicle is running out of a straight
course.
[0014] It would be contemplated to apply the above mathematical
analyses to the running behavior control of four wheeled vehicles
by preparing certain maps of relationships between or among each
two or three of those parameters. However, if a four wheeled
vehicle is mathematically controlled of its running behavior based
upon a mathematical tire model such as expressed by the
above-mentioned equations 1-9, since at least 11 parameters will be
incorporated in the mathematical control calculations even when
only one of the front and rear pairs of the wheels are controlled
about their braking, only a very rough discrete points simulation
would be available even by using the most modern microcomputers
employable for an automobile running behavior control from the view
point of the convenience of construction and economy.
SUMMARY OF THE INVENTION
[0015] In view of such an estrangement between the self-closed
mathematical analyses applicable only to the performance of a
single tire and the complicated interrelations of the performances
of the pairs of front and rear wheels in the actual running
behavior controls of four wheeled vehicles, it is a primary object
of the present invention to provide a device for controlling a
running behavior of four wheeled vehicles which can utilize a
self-closed mathematical performance analysis of a single wheel
tire such as described above effectively for a running behavior
control of four wheeled vehicles even by using a microcomputer of a
limited capacity.
[0016] According to the present invention, the above-mentioned
primary object is accomplished by a device for controlling a
running behavior of a vehicle based upon a force-slip performance
of a tire, the vehicle having a vehicle body, a pair of front
wheels and a pair of rear wheels, and brake means for selectively
applying a controlled braking force to at least either the front
pair or the rear pair of the wheels bearing the tires,
comprising:
[0017] first means for cyclically calculating by a minute cycle
period longitudinal force and lateral force of each of the at least
either the front pair or the rear pair of the wheels in reference
to slip ratio thereof according to a mathematical tire model of a
relationship therebetween, so as to obtain a first longitudinal
force and a first lateral force corresponding to a first slip ratio
and a second longitudinal force and a second lateral force
corresponding to zero slip ratio;
[0018] second means for cyclically calculating by the minute cycle
period longitudinal force, lateral force and yaw moment of the
vehicle body based upon the longitudinal forces and the lateral
forces of the at least either the front pair or the rear pair of
the wheels, so as to obtain a first longitudinal force, a first
lateral force and a first yaw moment of the vehicle body
corresponding to the first longitudinal forces and the first
lateral forces of the at least either the front pair or the rear
pair of the wheels and a second longitudinal force, a second
lateral force and a second yaw moment of the vehicle body
corresponding to the second longitudinal forces and the second
lateral forces of the at least either the front pair or the rear
pair of the wheels;
[0019] third means for cyclically modifying by the minute cycle
period the second longitudinal force, the second lateral force and
the second yaw moment of the vehicle body calculated by the second
means with a longitudinal force, a lateral force and a yaw moment
corresponding to an output of an outside running behavior
controller, so as to obtain a nominal longitudinal force, a nominal
lateral force and a nominal yaw moment, respectively;
[0020] fourth means for cyclically calculating by the minute cycle
period a difference between the nominal longitudinal force and the
first longitudinal force, a difference between the nominal lateral
force and the first lateral force and a difference between the
nominal yaw moment and the first yaw moment;
[0021] fifth means for cyclically calculating by the minute cycle
period differentials of the longitudinal and lateral forces of each
of the at least either the front pair or the rear pair of the
wheels on the basis of the slip ratio thereof according to the
mathematical tire model;
[0022] sixth means for cyclically calculating by the minute cycle
period differentials of the longitudinal force, lateral force and
yaw moment of the vehicle body based upon differentials of the
longitudinal and lateral forces of each of the at least either the
front pair or the rear pair of the wheels on the basis of the slip
ratio;
[0023] seventh means for cyclically calculating by the minute cycle
period a difference in the longitudinal force, a difference in the
lateral force and a difference in the yaw moment of the vehicle
body based upon the differentials thereof;
[0024] eighth means for cyclically calculating by the minute cycle
period a first difference between the difference in the
longitudinal force calculated by the fourth means and the
difference in the longitudinal force calculated by the seventh
means, a second difference between the difference in the lateral
force calculated by the fourth means and the differential-based
difference in the lateral force calculated by the seventh means,
and a third difference between the difference in the yaw moment
calculated by the fourth means and the differential-based
difference in the yaw moment calculated by the seventh means;
[0025] ninth means for calculating by the minute cycle period
differences in the slip ratio of each of the at least either the
front pair or the rear pair of the wheels which minimize a weighted
sum of squares of the first, second and third differences; and
[0026] tenth means for selectively operating the brake means to
change the slip ratio of each of the at least either the front pair
or the rear pair of the wheels according to the difference thereof
calculated by the ninth means.
[0027] By the device of the above-mentioned construction, it is
possible to execute a running behavior control of a four wheeled
vehicle through mathematical control calculations based upon a
mathematical tire model defining a relationship between
longitudinal and lateral forces vs. slip ratio of each wheel such
that the desired running behavior control of the vehicle is
effectively accomplished with a minimum slip of at least a pair of
front wheels or a pair of rear wheels to which a controlled braking
is applied.
[0028] Since the running behavior control by the device according
to the present invention is executed based upon a standard
mathematical tire model, the control operation is continually
effective even when the vehicle is running in such an operation
range where the running behavior of the vehicle is so stabilized
that some conventional running stability control devices adapted to
be triggered by a certain parameter trespassing a threshold value
do not yet operate.
[0029] The above-mentioned device may further be modified such that
it further comprises:
[0030] eleventh means for cyclically calculating by the minute
cycle period a weighted sum of a square of each of the differences
in the slip ratio calculated by the ninth means;
[0031] wherein the ninth means are modified to calculate the
differences in the slip ratio so that a sum of the weighted sum
calculated by the ninth means and the weighted sum calculated by
the eleventh means is minimized.
[0032] Further, the above-mentioned device may further be modified
such that it further comprises:
[0033] twelfth means for cyclically calculating by the minute cycle
period a weighted sum of a square of each of respective sums of the
slip ratio and the change thereof calculated by the ninth
means;
[0034] wherein the ninth means are modified to calculate the
differences in the slip ratio so that a sum of the weighted sum
calculated by the ninth means and the weighted sum calculated by
the twelfth means is minimized.
[0035] In this case, the above-mentioned device may further be
modified such that the ninth means are modified to calculate the
differences in the slip ratio so that a sum of the weighted sum
calculated by the ninth means, the weighted sum calculated by the
eleventh means and the weighted sum calculated by the twelfth means
is minimized.
[0036] Further, the above-mentioned device may further be modified
such that the third means modify the second longitudinal force, the
second lateral force and the second yaw moment of the vehicle body
calculated by the second means with the longitudinal force, the
lateral force and the yaw moment corresponding to the output of the
outside running behavior controller, so as to obtain the nominal
longitudinal force, the nominal lateral force and the nominal yaw
moment, respectively, by adding the longitudinal force, the lateral
force and the yaw moment corresponding to the output of the outside
running behavior controller to the second longitudinal force, the
second lateral force and the second yaw moment, respectively.
[0037] In this case, the third means may substantially cancel the
lateral force corresponding to the output of the outside running
behavior controller in obtaining the nominal lateral force.
[0038] Further, the device may further be modified such that the
ninth means apply a variable weighting factor on each of the
difference in the slip ratio of each of the at least the front pair
of the wheels calculated thereby before outputting the calculated
slip ratio difference such that a slip ratio difference applied
with a larger weighting factor affects less in the running behavior
control than a slip ratio difference applied with a smaller
weighting factor, the weighting factor being varied such that, when
the nominal yaw moment calculated by the third means is directed to
assist a turn of the vehicle, the weighting factor on the slip
ratio difference of one of the pair of front wheels serving at the
inside of a turn is made larger.
[0039] Still further, the device may further be modified such that
the tenth means are adapted to cancel a braking of the rear wheels
by overriding the difference of the slip ratio calculated by the
ninth means when the yaw rate of the vehicle has changed its
direction from a first direction conforming to a turning of the
vehicle to a second direction opposite to the first direction
during a turn running of the vehicle.
BRIEF DESCRIPTION OF THE DRAWINGS
[0040] In the accompanying drawings,
[0041] FIG. 1 is a diagrammatical view showing a four wheeled
vehicle having a steering system, a brake system and a control
system in which an embodiment of the present invention herein shown
is incorporated;
[0042] FIG. 2 is a flowchart showing a main routine of the control
operation of the embodiment of the present invention;
[0043] FIG. 3 is a flowchart showing a subroutine of the control
operation executed in step 550 of the main routine;
[0044] FIG. 4 is a flowchart showing a subroutine of the control
operation executed in step 650 of the main routine;
[0045] FIG. 5 is a map showing an example of the relationships
among the longitudinal force, the lateral force, the slip ratio and
the slip angle of a common tire;
[0046] FIG. 6 is a diagrammatical illustration of a tire or wheel
for defining parameters concerned therewith;
[0047] FIG. 7 is a graph showing a general relationship between the
lateral force Ftyi and the slip angle .beta.i of a common tire or
wheel;
[0048] FIG. 8 is a graph showing a general relationship between the
longitudinal force Ftxi and the slip angle Si of a common tire or
wheel;
[0049] FIG. 9 is a map showing an example of the distribution of
the yaw moment born by each of the front right, front left, rear
right and rear left wheels of a four wheeled vehicle;
[0050] FIG. 10 is a map to be referred to in step 400 to obtain a
factor for estimating a longitudinal force to be applied to the
vehicle body for a yaw rate control;
[0051] FIG. 11A is a graph showing a general relationship between
the slip ratio of a front wheel and the longitudinal or lateral
force applied to the vehicle body corresponding to the slip ratio;
and
[0052] FIG. 11B is a graph showing a general relationship between
the slip ratio of a front wheel and the yaw moment applied to the
vehicle body corresponding to the slip ratio.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0053] In the following, the present invention will be described in
more detail with respect to a preferred embodiment thereof with
reference to the accompanying drawings.
[0054] Referring to FIG. 1 showing diagrammatically a vehicle in
which an embodiment of the vehicle running behavior control device
according to the present invention is incorporated. The vehicle has
a vehicle body 12, and front right wheel 10FR, front left wheel
10FL, rear right wheel 10RR and rear left wheel 10RL supporting the
vehicle body 12 via respective suspension means not shown in the
figure. The front right and front left wheels 10FR and 10FL are
steered by a rack-and-pinion type power steering means 16 according
to rotations of a steering wheel 14 by a driver via a pair of tie
rods 18R and 18L, respectively.
[0055] A brake system generally designated by 20 includes a
hydraulic circuit means 22, a brake pedal 26 adapted to be
depressed by the driver, a master cylinder 28 for supplying a
master cylinder pressure to the hydraulic circuit means 22
according to the depression of the brake pedal by the driver, and
wheel cylinders 24FR, 24FL, 24RR and 24RL each adapted to apply a
braking force to each corresponding one of the front right, front
left, rear right and rear left wheels according to a supply of a
hydraulic pressure thereto from the hydraulic circuit means 22.
[0056] The hydraulic circuit means 22 are electrically controlled
by electric control means 30 incorporating a microcomputer which
may be of an ordinary type including a central processor unit, a
read only memory, a random access memory, input and output port
means and a common bus interconnecting these elements.
[0057] The electric control means 30 are supplied with a signal
indicating steering angle .phi. inputted to the lack-and-pinion
type power steering means 16 from the steering wheel 14 according
to a rotation thereof by the driver from a steering angle sensor
34, a signal indicating yaw rate .gamma. of the vehicle body from a
yaw rate sensor 36, a signal indicating longitudinal acceleration
Gx of the vehicle body from a longitudinal acceleration sensor 38,
a signal indicating lateral acceleration Gy of the vehicle body
from a lateral acceleration sensor 40, a signal indicating vehicle
speed V from a vehicle speed sensor 42, signals indicating vehicle
wheel speeds Vwi of the front right, front left, rear right and
rear left wheels from wheel speed sensors 32FR, 32FL, 32RR and
32RL, respectively, and signals indicating static loads Wsi of the
front right, front left, rear right and rear left wheels from
static load sensors 44fr, 44fl, 44rr and 44rl, respectively, and
conduct control calculations according to the programs stored in
the read only memory based upon the parameters supplied by the
signals in the manner described in detail hereinbelow with
reference to the flowchart shown in FIG. 2 for stabilizing the
movement of the vehicle, then outputting control signals toward the
hydraulic circuit means 22 for executing pertinent braking of
wheels for the vehicle running behavior control.
[0058] The vehicle running behavior control device of the present
invention will be described hereinbelow in the form of its control
operation of an embodiment thereof by referring to the flowchart of
FIG. 2 showing the main routine of the control operation. The
control according to the main routine is started by a closure of an
ignition switch not shown in the figure and cyclically repeated
therethrough during the operation of the vehicle. Although the
operation of the embodiment device of the present invention is
generally described so as to selectively apply a controlled braking
force to both of the front pair and the rear pair of the wheels,
the device according to the present invention may be so constructed
as to selectively apply a controlled braking force to only the
front pair or the rear pair of the wheels.
[0059] First, in step 50, slip ratios Si of the respective wheels,
which are parameters to be controlled according to the present
invention, are reset to zero for each initial starting.
[0060] In step 100, the signals described with respect to FIG. 1
are read in.
[0061] In step 150, slip angles .beta.i, i.e. .beta.r and .beta.f
of the rear and front wheels (as a pair, for convenience), friction
coefficient .mu. between the tire and the road surface and vertical
load Wi on each of the wheels are calculated as follows:
[0062] First, slip angle .beta. of the vehicle body is calculated
according to a conventional method such that first a lateral slip
acceleration dVy/dt is calculated as a difference between the
lateral acceleration Gy detected by the lateral acceleration sensor
40 and a product of the vehicle speed V detected by the vehicle
speed sensor 42 and the yaw rate .gamma. detected by the yaw rate
sensor 36, such as dVy/dt=Gy-V.gamma., then the lateral slip
acceleration is integrated on time base to obtain a lateral slip
velocity Vy, and then the lateral slip velocity Vy is divided by
longitudinal vehicle speed Vx which may be substituted for by the
vehicle speed V detected by the vehicle speed sensor 42, so as to
provide .beta.=Vy/Vx.
[0063] Then, assuming that the vehicle is an ordinary front steered
vehicle, by denoting the distance between the center of gravity of
the vehicle body and the axis of the rear axle as Lr, the slip
angle .beta.r of the rear wheels is calculated based upon the slip
angle .beta. of the vehicle body, the yaw rate .gamma. and the
vehicle speed V as follows:
.beta.r=.beta.Lr.gamma./V (10)
[0064] When the slip angle .beta.r becomes larger, the magnitude of
the tire slip required to generate a certain desired magnitude of
the longitudinal force becomes correspondingly larger, against the
general desirableness of the running behavior control to be
accomplished by a minimum braking. Therefore, it is desirable that
the value of the slip angle .beta.r of the rear wheels thus
calculated is modified to be within an appropriate range such as
-.beta.rc.ltoreq..beta.r.ltoreq..beta.rc, provided that the rear
wheels are non-steered wheels.
[0065] Next, by denoting the distance between the center of gravity
of the vehicle body and the axis of the front axle as Lf, the slip
angle .beta.f of the front wheels (also as a pair, for convenience)
is calculated based upon steering angle .phi.f converted from turn
angle .phi. of the steering wheel, the slip angle .beta. of the
vehicle body, the yaw rate .gamma. and the vehicle speed V as
follows:
.beta.f=-.phi.f+.beta.+Lf.gamma./V (11)
[0066] Further, friction coefficient .mu. between the tire and the
road surface is calculated based upon the longitudinal and lateral
accelerations Gx and Gy and the gravitational acceleration g as
follows:
.mu.={square root}{square root over (Gx.sup.2+Gy.sup.2)}/g (12)
[0067] Further, vertical load Wi on each of the wheels is
calculated based upon Wsi detected by the static vertical load
sensors 44i, with a modification of a shift of load between the
right and left wheels due to the lateral acceleration Gy and a
shift of load between the front and rear wheels due to the
longitudinal acceleration Gx.
[0068] In step 200, the longitudinal force Ftxi and the lateral
force Ftyi of each of the four wheels are calculated according to
the above-mentioned equations 1 and 2 or 3 and 4 with incorporation
of the equations 5-9, such that the equations 1 and 2 are used when
.xi.i calculated according to the equation 9 is positive (or zero,
for convenience), while the equations 3 and 4 are used when .xi.i
is negative.
[0069] Further, in this step, partial differentials of Ftxi and
Ftyi against Si are calculated for a later use such as: 4 Ftxi Si
and Ftyi Si
[0070] In step 250, shares Fxi by respective wheels of the
longitudinal force, shares Fyi by respective wheels of the lateral
force and shares Mi by respective wheels of the yaw moment to act
at the vehicle body due to the longitudinal forces Ftxi and the
lateral forces Ftyi of the four wheels are calculated based upon a
mathematical tire model such as defined by equations 1-9 as
follows: 5 [ Fxfr Fyfr ] = T ( f ) [ Ftxfr Ftyfr ] ( 13 ) Mfr = [
Tr 2 Lf ] [ Fxfr Fyfr ] ( 14 ) [ Fxfl Fxfl ] = T ( f ) [ Ftxfl
Ftyfl ] ( 15 ) Mfl = [ - Tr 2 Lf ] [ Fxfl Fyfl ] ( 16 ) [ Fxrr Fyrr
] = T ( r ) [ Ftxrr Ftyrr ] ( 17 ) Mrr = [ Tr 2 - Lr ] [ Fxrr Fyrr
] ( 18 ) [ Fxrl Fyrl ] = T ( r ) [ Ftxrl Ftyrl ] ( 19 ) Mrl = [ -
Tr 2 - Lr ] [ Fxrl Fyrl ] ( 20 )
[0071] wherein 6 T ( f ) = [ cos f - sin f sin f cos f ] ( 21 ) T (
r ) = [ cos r - sin r sin r cos r ] ( 22 )
[0072] Further, in this step, a rate of change of each of Fxi, Fyi
and Mi due to a change of a corresponding Si, i.e. partial
differential of each of Fxi, Fyi and Mi against Si is calculated
based upon the tire model as follows: 7 [ Fxfr Sfr Fyfr Sfr ] = T (
f ) [ Ftxfr Sfr Ftyfr Sfr ] ( 23 ) Mfr Sfr = [ Tr 2 Lf ] [ Fxfr Sfr
Fyfr Sfr ] ( 24 ) [ Fxfl Sfl Fyfl Sfl ] = T ( f ) [ Ftxfl Sfl Ftyfl
Sfl ] ( 25 ) Mfl Sfl = [ - Tr 2 Lf ] [ Fxfl Sfl Fyfl Sfl ] ( 26 ) [
Fxrr Srr Fyrr Srr ] = T ( r ) [ Ftxrr Srr Ftyrr Srr ] ( 27 ) Mrr
Srr = [ Tr 2 - Lr ] [ Fxrr Srr Fyrr Srr ] ( 28 ) [ Fxrl Srl Fyrl
Srl ] = T ( r ) [ Ftxrl Srl Ftyrl Srl ] ( 29 ) Mrl Srl = [ - Tr 2 -
Lr ] [ Fxrl Srl Fyrl Srl ] ( 30 )
[0073] When the front wheels of a four wheeled vehicle are applied
with a braking by a brake-based behavior control device, it is only
a front wheel serving at the outside of a turn that is applied with
a controlled braking when the behavior control is a spin suppress
control, while it is only a front wheel serving at the inside of a
turn that is applied with a controlled braking when the behavior
control is a turn assist control. In any event, it is always only
one of the front wheels at a time that is applied with a behavior
control braking. Therefore, the differences dFx, dFy and dM of
longitudinal force, lateral force and yaw moment, respectively, of
the vehicle body due to the partial differential of the
longitudinal and lateral forces of each wheel are calculated based
upon the three wheels at the most, excluding either one of the
front wheels, as follows: 8 [ dFx dFy dM ] = [ Fxfr Sfr or Fxfl Sfl
Fxrr Srr Fxrl Srl Fyfr Sfr or Fyfl Sfl Fyrr Srr Fyrl Srl Mfr Sfr or
Mfl Sfl Mrr Srr Mrl Srl ] [ dSfr or dSfl dSrr dSrl ] = JdS ( 31
)
[0074] In step 300, Fxi, Fyi and Mi are integrated to provide
longitudinal force Fx, lateral force Fy and yaw moment M of the
vehicle body calculated as a function of the slip ratios Si as
follows: 9 [ Fx Fy M ] = [ Fxfr Fyfr Mfr ] + [ Fxfl Fyfl Mfl ] + [
Fxrr Fyrr Mrr ] + [ Fxrl Fyrl Mrl ] ( 32 )
[0075] In step 350, according to the same process as step 200,
except that the slip ratios Si are all assumed zero, longitudinal
force Ftxiso and lateral force Ftyiso of each of the four wheels
are calculated as a reference tire model conditioned by zero slip,
then shares Fxiso by the respective wheels of the longitudinal
force, shares Fyiso by the respective wheels of the lateral force
and shares Miso by the respective wheels of the yaw moment to act
at the vehicle body due to the longitudinal forces Ftxiso and the
lateral forces Ftyiso of the four wheels are calculated, and then
Fxiso, Fyiso and Miso are integrated to provide longitudinal force
Fxso, lateral force Fyso and yaw moment Mso of the vehicle body
according to the same tire model operating at zero slip, as
follows: 10 [ Fxso Fyso Mso ] = [ Fxfrso Fyfrso Mfrso ] + [ Fxflso
Fyflso Mflso ] + [ Fxrrso Fyrrso Mrrso ] + [ Fxrlso Fyrlso Mrlso ]
( 33 )
[0076] The longitudinal force Fxso, the lateral force Fyso and the
yaw moment Mso of the vehicle body will be herein called a zero
slip longitudinal force, a zero slip lateral force and a zero slip
yaw moment.
[0077] In step 400, a nominal longitudinal force Fxt, a nominal
lateral force Fyt and a nominal yaw moment Mn are calculated based
upon Fxso, Fyso and Mso and a running behavior control input from
an outside running behavior controller. The running behavior
controller herein referred to as the outside controller is already
known in various types, including those for controlling various
turning behaviors of the vehicles while suppressing a driftout or a
spin of the vehicles. It is assumed that the device of the present
invention operates under an input from such an outside running
stability controller, the input being generally a combination of a
longitudinal force Fxm, a lateral force Fym and a yaw moment Mm
applied to vehicle body.
[0078] The longitudinal force Fxm may be considered as a force for
decelerating the vehicle for the purpose of decreasing the
centrifugal force against a drifting out, while the yaw moment Mm
may be considered as a yaw moment generated by a balance between
the braking force applied to the leftside wheel or wheels and the
braking force applied to the rightside wheel or wheels. In fact, no
lateral force will need be considered as a component of such an
input, particularly in connection with the present invention which
operates based upon a selective braking of the wheels. Therefore,
Fym may be constantly set to zero.
[0079] Such a longitudinal force Fxm may be generated by an outside
controller to control a driftout, for example, as follows:
[0080] First, a standard yaw rate .gamma.c of the vehicle body is
calculated based upon the vehicle speed V and the steering angle
.phi., denoting the wheel base of the vehicle as H, assuming an
appropriate factor Kh, as follows:
.gamma.c=V.phi./(1+KhV.sup.2)H (34)
[0081] Then, .gamma.c is modified to be adapted to a transient
performance according to a time constant T and the Laplace operator
s, as follows:
.gamma.t=.gamma.c/(1+Ts) (35)
[0082] Then, a parameter Dv indicating a tendency of the driftout
of the vehicle is calculated as follows:
Dv=(.gamma.t-.gamma.) (36)
[0083] or
Dv=H(.gamma.t-.gamma.)/V (37)
[0084] Then, by judging the turning direction of the vehicle by the
sign of the yaw rate .gamma., the parameter Dv is finalized to Dv
when Dv is positive while the vehicle is making a left turn, or Dv
is negative while the vehicle is making a right turn. The parameter
Dv is made zero when Dv is negative while the vehicle is making a
left turn, or Dv is positive while the vehicle is making a right
turn.
[0085] Then, by looking up a map such as shown in FIG. 10, a factor
Kxm for estimating the force Fxm is read out against the parameter
Dv. Then the longitudinal force Fxm is calculated by the factor
Kxm, mass Qb of the vehicle body and the gravitational acceleration
g as follows:
Fxm=KxmQbg (38)
[0086] By the longitudinal force Fxm being applied to, the vehicle
is decelerated so that a driftout is suppressed.
[0087] On the other hand, also as an example, a spin will be
suppressed such that, based upon the yaw rate .gamma.t calculated
as by equation 35, assuming an appropriate factor Kmm, a slip angle
.beta.t of the vehicle body is calculated with the mass Qb of the
vehicle body and the vehicle speed V, as follows:
.beta.t=KmmQb.gamma.tV (39)
[0088] Then, the yaw moment Mm is calculated by assuming
appropriate factors Km1 and Km2 as follows:
Mm=Km1(.beta.-.beta.t)+Km2(d.beta./dt-d.beta.t/dt) (40)
[0089] By the yaw moment Mm being applied to, the vehicle is
suppressed from spinning.
[0090] In any event, receiving a control input in the form of
longitudinal force Fxm and/or yaw moment Mm from an outside running
behavior controller, [Fxso, Fyso, Mso] are modified by [Fxm, 0, Mm]
to produce nominal Fxn, Fyn and Mn as follows: 11 [ Fxn Fyn Mn ] =
[ Fxm 0 Mm ] + [ Fxso Fyso Mso ] ( 41 )
[0091] In step 450, differences of the nominal Fxt, Fyt and Mn from
the actual Fx, Fy and M are calculated as follow: 12 = [ Fx Fy M ]
= [ Fxn - Fx Fyn - Fy Mn - M ] ( 42 )
[0092] The control conducted by the device according to the present
invention is to approach the thus calculated [.delta.Fx, .delta.Fy,
.delta.M] to [dFx, dFy, dM] based upon the differentiation of the
mathematical tire model by the slip ratio at each of the wheels
through a cyclic convergent calculation of the difference in the
slip ratio. Of course, it is very difficult to mathematically solve
such a set of simultaneous equations as .delta.Fx=dFx,
.delta.Fy=dFy and .delta.M=dM. Therefore, it is contemplated to
minimize the value of L such as defined below:
L=E.sup.TWfE+.delta.S.sup.TWds.delta.S+(S+.delta.S).sup.TWs(S+.delta.S)
(43)
[0093] wherein 13 E = [ Fx - dFx Fy - dFy M - dM ] ( 44 )
[0094] (E.sup.T=[.delta.Fx-dFx, .delta.Fy-dFy, .delta.M-dM] The
same with others.) 14 Wf = [ W Fx 0 0 0 W Fy 0 0 0 W M ] ( 45 ) S =
[ Sfr or Sfl Srr Srl ] ( 46 ) Wds = [ Wdsfr or Wdsrl 0 0 0 Wdsrr 0
0 0 Wdsrl ] ( 47 ) S = [ Sfr or Sfl Srr Srl ] ( 48 ) Ws = [ Wsfr or
Wsrl 0 0 0 Wsrr 0 0 0 Wsrl ] ( 49 )
[0095] In equation 43, the first term on the right side is a sum of
weighted squares of the differences .delta.Fx-dFx, .delta.Fy-dFy
and .delta.M-dM. As a first approach, if this term is minimized, it
is duly expected that the vehicle is controlled to follow the
control by the outside controller at an optimum operating condition
of the brake means that they are actuated generally at a necessary
minimum.
[0096] In this connection, the second term on the right side of
equation 43 is provided to restrict the width of change of
.delta.S, so that the calculations do not diverge. The third term
on the right side of equation 43 is provided to restrict the
absolute value of the slip ratio S, so that a uniform distribution
of the slip ratio to the respective wheels is ensured.
[0097] In step 500, .delta.Sfr and .delta.Sfl of .delta.Si are
processed for a modification of the weighting factor Wdsfr or Wdsfl
of the front right wheel or the front left wheel such as shown by a
flowchart of FIG. 3. The purpose of the processing according to the
flowchart of FIG. 3 is as follows:
[0098] When the slip ratio Sfr, for example, increases, the
longitudinal force Fxfr increases toward rearward, while the
lateral force Fyfr decreases, both monotonously in any event, as
shown in FIG. 11A. On the other hand, assuming that the vehicle is
now making a right turn, when the front right wheel is braked for
assisting the turn, the vehicle body is first applied with a yaw
moment for a right turn about the front right wheel, thus
effectively applying a turn assisting yaw moment to the vehicle
body. In this case, the turn assist yaw moment generated around the
front right wheel first increases along with increase of the
braking force, but soon the lateral tire grip force available at
the front right wheel starts to decrease due to the limited radius
of the friction circle, so that the front right wheel starts to
slip toward outside of the turn, thereby canceling the turn assist
yaw moment first generated. Therefore, the yaw moment Mfr available
for the vehicle body according to Sfr first increases but soon
reaches a peak point P and then decreases as shown in FIG. 1B. (It
is the general practice that the yaw moment is made positive when
it turns the vehicle body counter-clockwise as viewed from above,
and negative for the direction opposite thereto.) Therefore, if the
slip ratio Sfr is controlled around the peak point P, the running
behavior control becomes unstable. The processing according to the
flowchart of FIG. 3 is to avoid such a problem.
[0099] Referring to FIG. 3, in step 552, the factors Wdsfr and
Wdsfl are normally set to 1 for convenience.
[0100] In step 554, it is judged if the slip angle .beta.f of the
front wheels is positive. (It is the general practice that the slip
angle of a wheel is made positive when it is oriented leftward from
the direction of rotation thereof, and negative for the direction
opposite thereto.) When the answer is yes, the control proceeds to
step 556, and it is judged if the nominal yaw moment Mn is
negative. Therefore, the yes of the judgment of step 556 means that
the vehicle is making a right turn, while the control exerts a
clockwise yaw moment to the vehicle body. Under such a condition,
if the front right wheel is braked much, there would occur that the
yaw moment Mfr is controlled around the peak point P of FIG. 11B,
thereby causing a fluctuation of the control. In order to avoid
such a problem, in step 558, as an embodiment, the weighting factor
Wdsfr for .delta.Sfr is set to 5, i.e. five times as much as
compared with those for the other wheels, so that the value of
.delta.Sfr is suppressed low to be apart from the peak point P.
[0101] Similarly, when the answer of step 554 is no, and the answer
of step 560 is yes, the weighting factor Wdsfl is set to 5.
[0102] In step 550, in order to obtain a difference in slip ratio
at each of the three wheels which minimizes the value of L,
equation 43 is partially differentiated by each .delta.S as
follows:
{fraction
(.differential.L/.differential..delta.S)}=2Wds.delta.S+2Ws(S+.de-
lta.S)-2J.sup.TWfJE (50)
[0103] 15 L S = [ L Sfr or L Sfl L Srr L Srl ] ( 51 ) E = - J S (
52 ) E S = ( - J S ) S ( 53 ) = - J ( 54 ) 16 Making L S = 0 in
equation 50 ,
Wds.delta.S+Ws(S+.delta.S)-J.sup.TWf(.DELTA.-J.delta.S)=0 (55)
[0104] By rearranging equation 55 with respect to .delta.S, there
is provided an equation which minimizes the value of L of equation
43 as follows:
.delta.S=(Wds+Ws+J.sup.TWfJ).sup.-1(-WsS+J.sup.TWf.DELTA.) (56)
[0105] In step 600, the slip ratios Si are modified by
corresponding .delta.Si calculated.
[0106] In step 650, the slip ratio Si is modified for a precaution
of a spin which might be induced by the controlled braking of the
rear wheels. When a vehicle is controlled by the running behavior
control device of the present invention with one or both of the
rear wheels being braked at a controlled slip ratio Srr and/or Srl
to assist a turn running of the vehicle, it can occur that the
turning of the vehicle overshoots. In such a case, it is desirable
that the rear wheel braking is released as quick as possible,
because otherwise a spin might be induced by a delay in releasing
the rear wheel braking.
[0107] In view of this, in the flowchart of FIG. 4 forming a
subroutine of the main routine of FIG. 2, in step 652, it is judged
if the nominal yaw moment Mn is negative and the slip ratio .beta.r
is positive and further the yaw rate .gamma. is positive. During a
normal right turn of a vehicle, generally there is a first stage in
which Mn<0, .beta.r>0 and .gamma.<0, then a second stage
in which Mn< 0, .beta.r>0 and .gamma.=0, and then a third
stage in which at least .gamma.>0. In step 652 it is detected
that the conditions turned over from the second stage to the third
stage.
[0108] Similarly, in step 654 it is detected that the same turnover
occurred during a left turn of the vehicle.
[0109] When the above turnover was detected in step 652 during a
right turn or in step 654 during a left turn, the control proceeds
to step 656, and the slip ratios Srr and Srl are immediately
returned to zero.
[0110] In step 700, the hydraulic circuit 22 is operated according
to a control signal bearing the instructions with regard to the
slip ratios Si to be realized at the respective wheels.
[0111] Thus, the calculations through the main routine of FIG. 2
are repeated at a cycle time such as tens of microseconds as long
as the vehicle is operated with the ignition switch being turned
on, while the calculations continually converging to each different
state according to continual variations of the running conditions
of the vehicle, realizing the condition that the braking for the
running behavior control is executed at a minimum necessity to
follow the tire model which executes no braking.
[0112] Although the present invention has been described in detail
with respect to a preferred embodiment thereof and some partial
modifications thereof, it will be apparent for those skilled in the
art that other various modifications are possible with respect to
the shown embodiment within the scope of the present invention.
* * * * *