U.S. patent application number 09/769676 was filed with the patent office on 2002-10-03 for integrated control of active tire steer and brakes.
This patent application is currently assigned to DELPHI AUTOMOTIVE SYSTEMS. Invention is credited to Bedner, Edward J., Chen, Hsien H., Hac, Aleksander B., Loudon, Steven P..
Application Number | 20020143451 09/769676 |
Document ID | / |
Family ID | 25086197 |
Filed Date | 2002-10-03 |
United States Patent
Application |
20020143451 |
Kind Code |
A1 |
Hac, Aleksander B. ; et
al. |
October 3, 2002 |
INTEGRATED CONTROL OF ACTIVE TIRE STEER AND BRAKES
Abstract
An integrated active steering and braking control system for
providing one or more corrective yaw moments to a vehicle in
response to a plurality of signals indicative of operational and
environmental conditions related to the vehicle is disclosed. The
system comprises a reference model, an estimator, a vehicle level
brake/steer controller, and an actuator controller. The reference
model provides a feedforward front steering angle correction signal
a feedforward rear steering angle correction signal, a desired yaw
rate signal, a desired lateral velocity signal, and a desired side
slip angle signal. The estimator provides an estimated surface
coefficient of adhesion signal, an estimated lateral velocity
signal, and an estimated side slip angle signal. In response to the
signals from the reference model and the estimator, the vehicle
level brake/steer controller provides either a desired speed
differential signal, a desired front steering angle signal and/or a
desired rear steering angle signal. The actuator controller
selectively provides a corrective braking signal to a brake
actuator, a corrective front steering signal to a steering
actuator, and a corrective rear steering signal to the steering
actuator as a function of the desired speed differential signal,
the desired front steering angle signal, and the desired rear
steering angle signal, respectively.
Inventors: |
Hac, Aleksander B.; (Dayton,
OH) ; Chen, Hsien H.; (Troy, MI) ; Bedner,
Edward J.; (Brighton, MI) ; Loudon, Steven P.;
(Howell, MI) |
Correspondence
Address: |
SCOTT A. MCBAIN, DELPHI TECHNOLOGIES, INC.
Legal Staff, Mail Code: 482-204-450
1450 W. Long Lake
P.O. Box 5052
Troy
MI
48098
US
|
Assignee: |
DELPHI AUTOMOTIVE SYSTEMS
|
Family ID: |
25086197 |
Appl. No.: |
09/769676 |
Filed: |
January 25, 2001 |
Current U.S.
Class: |
701/48 ; 701/42;
701/72; 701/91 |
Current CPC
Class: |
B60T 2260/024 20130101;
B62D 6/00 20130101; B60G 2800/24 20130101; B60W 2050/0034 20130101;
B60T 2230/02 20130101; B62D 7/159 20130101; B60T 8/1755 20130101;
B60T 2260/022 20130101; B60G 2800/215 20130101; B60W 30/02
20130101; B60G 2800/922 20130101; B60T 2260/02 20130101 |
Class at
Publication: |
701/48 ; 701/42;
701/72; 701/91 |
International
Class: |
G05D 001/00; G05D
003/00; G06F 007/00; E05F 015/00; G06F 017/00; B60R 022/00 |
Claims
1. An integrated active steering and braking control method for a
vehicle, the vehicle including an axle, a first tire, a second
tire, a steering system, and a braking system, said method
comprising: determining a first corrective yaw moment as a function
of a steering angle of the axle; determining a second corrective
yaw moment as a function of a speed differential between the first
tire and the second tire; providing a corrective steering signal to
the steering system whereby said first corrective yaw moment is
applied to the vehicle; and providing a corrective braking signal
to the braking system whereby said second corrective yaw moment is
applied to the vehicle.
2. The method of claim 1, wherein said corrective steering signal
and said corrective braking signal are concurrently provided
whereby said first corrective yaw moment and said second corrective
yaw moment are concurrently applied to the vehicle.
3. An integrated active steering and braking control method for a
vehicle, the vehicle including an axle, a first tire, and a second
tire, said method comprising: determining a desired speed
differential between the speed of the first tire and the speed of
the second tire; and determining a desired steering angle of the
axle as a function of said desired speed differential.
4. The method of claim 3, further comprising: determining a
corrective braking signal as a function of said desired speed
differential.
5. The method of claim 3, further comprising: determining a
corrective steering signal as a function of said desired steering
angle.
6. The method of claim 3, further comprising: applying a limitation
to said desired steering angle; and determining a corrective
steering signal as a function of said desired steering angle in
view of said limitation.
7. The method of claim 3, further comprising: selectively
determining a corrective braking signal as a function of said
desired speed differential; and determining a corrective steering
signal as a function of said desired steering angle.
8. An integrated active steering and braking control method for a
vehicle, the vehicle including an axle, a first tire, and a second
tire, said method comprising: receiving a plurality of operational
signals indicative of an operational state of the vehicle;
determining a feedforward portion of a corrective front steering
angle signal in response to said plurality of operational signals;
and determining a feedforward portion of a corrective rear steering
angle signal in response to said plurality of operational
signals.
9. The method of claim 8, further comprising: determining a desired
yaw rate in response to said plurality of operational signals;
determining a desired side slip velocity in response to said
plurality of operational signals; and determining a desired side
slip angle in response to said plurality of operational
signals.
10. The method of claim 8, further comprising: estimating a surface
coefficient of adhesion in response to said plurality of
operational signals estimating a side slip velocity in response to
said plurality of operational signals; and estimating a side slip
angle in response to said plurality of operational signals.
11. The method of claim 8, further comprising: determining a
feedback portion of said corrective front steering angle signal in
response to said plurality of operational signals; and determining
a feedback portion of said corrective rear steering angle signal in
response to said plurality of operational signals.
12. An integrated active steering and braking control method for a
vehicle including an axle, a first tire, a second tire, a steering
system, and a braking system, said method comprising: a first
controller operable to determine a first corrective yaw moment as a
function of a steering angle of the axle and to determine a second
corrective yaw moment for the vehicle as a function of a speed
differential between the first tire and the second tire; and a
second controller operable to provide a corrective steering signal
to the steering system whereby said first corrective yaw moment is
applied to the vehicle, and to provide a corrective braking signal
to the braking system whereby said second corrective yaw moment is
applied to the vehicle.
13. The system of claim 12, wherein said second controller is
operable to concurrently provide said corrective steering signal to
the steering system and said corrective braking signal to the
braking system whereby said first corrective yaw moment and said
second corrective yaw moment are concurrently applied to the
vehicle.
14. A vehicle, comprising: an axle; a first tire; a second tire;
and an integrated active steering and braking control system
operable to determine a desired speed differential between a speed
of said first tire and a speed of said second tire and to determine
a desired steering angle of said axle as a function of said desired
speed differential.
15. The vehicle of claim 14, wherein said system is further
operable to determine a corrective braking signal as a function of
said desired speed differential.
16. The vehicle of claim 14, wherein said system is further
operable to determine a corrective steering signal as a function of
said desired steering angle.
17. The vehicle of claim 14, wherein said system is further
operable to apply a limitation to said desired steering angle and
to determine a corrective steering signal as a function of said
desired steering angle in view of said limitation.
18. The vehicle of claim 14, wherein said system is further
operable to selectively determine a corrective braking signal as a
function of said desired speed differential and to determine a
corrective steering signal as a function of said desired steering
angle.
19. An integrated active steering and braking control system for a
vehicle, comprising: a means for determining a feedforward portion
of a corrective front steering angle signal in response to a
plurality of operational signals indicative of an operational state
of the vehicle; and a means for determining a feedforward portion
of a corrective rear steering angle signal in response to said
plurality of operational signals.
20. The system of claim 19, further comprising: a means for
determining a desired yaw rate in response to said plurality of
operational signals; a means for determining a desired side slip
velocity in response to said plurality of operational signals; and
a means for determining a desired side slip angle in response to
said plurality of operational signals.
21. The system of claim 19, further comprising: a means for
estimating a surface coefficient of adhesion in response to said
plurality of operational signals a means for estimating a side slip
velocity in response to said plurality of operational signals; and
a means for estimating a side slip angle in response to said
plurality of operational signals.
22. The system of claim 8, further comprising: a means for
determining a feedback portion of said corrective front steering
angle signal in response to said plurality of operational signals;
and a means for determining a feedback portion of said corrective
rear steering angle signal in response to said plurality of
operational signals.
Description
FIELD OF THE INVENTION
[0001] The present invention generally relates to control systems
for automotive vehicles, and more particularly relates to an
integrated control of an active steering system and a brake system
of an automotive vehicle for improving upon a handling, stability,
and a maneuverability of the automotive vehicle.
BACKGROUND OF THE INVENTION
[0002] Some automotive vehicles known in the art utilize an active
brake control to enhance a directional stability of the vehicle at
or close to a limit of adhesion. Some other automotive vehicles
known in the art utilize a limited active control of a rear tire
steering angle in order to improve a vehicle handling and
maneuverability at low speeds. More recently, automotive vehicles
are utilizing a limited active control of a front tire steering
angle to introduce a steering correction to a steering angle
commanded by a vehicle driver in an effort to improve a vehicle
directional stability. The present invention addresses a need for
an integrated control of vehicle brakes, and a front tire steering
angle and/or a rear tire steering angle.
SUMMARY OF THE INVENTION
[0003] One form of the present invention is an integrated active
steering and braking control method for a vehicle. First, a first
corrective yaw moment for the vehicle as a function of a steering
angle of an axle of the vehicle is determined, and a second
corrective yaw moment for the vehicle as a function of a speed
differential between a first tire and a second tire of the vehicle
is determined. Second, a corrective steering signal is provided to
a steering system of the vehicle whereby the first corrective yaw
moment is applied to the vehicle, and a corrective braking signal
is provided to a braking system of the vehicle whereby the second
corrective yaw moment is applied to the vehicle.
[0004] A second form of the present invention is also an integrated
active steering and braking control method for a vehicle. First, a
desired speed differential between the speed of the first tire and
the speed of the second tire is determined. Second, a desired
steering angle of the axle as a function of said desired speed
differential is determined.
[0005] A third form of the present invention is also an integrated
active steering and braking control method for a vehicle. First, a
feedforward portion of a corrective front steering angle signal in
response to a plurality of operational signals indicative of an
operational state of the vehicle is determined. Second, a
feedforward portion of a corrective rear steering angle signal in
response to said plurality of operational signals.
[0006] A fourth form of the present invention is also an integrated
active steering and braking control system for a vehicle comprising
a first controller and a second controller. The first controller is
operable to determine a first corrective yaw moment for the vehicle
as a function of a steering angle of an axle of the vehicle, and to
determine a second corrective yaw moment for the vehicle as a
function of a speed differential between a first tire and a second
tire of the vehicle. The second controller is operable to provide a
corrective steering signal to a steering system of the vehicle
whereby the first corrective yaw moment is applied to the vehicle,
and to provide a corrective braking signal to a braking system of
the vehicle whereby the second corrective yaw moment is applied to
the vehicle.
[0007] A fifth form of the present invention is also an integrated
active steering and braking control system for a vehicle. The
system comprises a means for determining a feedforward portion of a
corrective front steering angle signal in response to a plurality
of operational signals indicative of an operational state of the
vehicle. The system further comprises a means for determining a
feedforward portion of a corrective rear steering angle signal in
response to said plurality of operational signals.
[0008] A sixth form of the present invention is a vehicle
comprising an axle, a first tire, a second tire, and an integrated
active steering and braking control system. The system is operable
to determine a desired speed differential between a speed of the
first tire and a speed of the second tire and to determine a
desired steering angle of the axle as a function of the desired
speed differential.
[0009] The foregoing forms, and other forms, features and
advantages of the present invention will become further apparent
from the following detailed description of the presently preferred
embodiments, read in conjunction with the accompanying drawings.
The detailed description and drawings are merely illustrative of
the present invention rather than limiting, the scope of the
present invention being defined by the appended claims and
equivalents thereof.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1A is a vector diagram illustrating a yaw moment of a
vehicle that is generated by a differential braking of a pair of
front tires of the vehicle as known in the art;
[0011] FIG. 1B is a vector diagram illustrating a yaw moment of a
vehicle that is generated by a front tire steering of the vehicle
as known in the art;
[0012] FIG. 1C is a vector diagram illustrating a yaw moment of a
vehicle that is generated by a differential braking of a pair of
rear tires of the vehicle as known in the art;
[0013] FIG. 1D is a vector diagram illustrating a yaw moment of a
vehicle that is generated by a rear tire steering of the vehicle as
known in the art;
[0014] FIG. 2 is a block diagram of one embodiment of a coordinated
control system in accordance with the present invention;
[0015] FIG. 3 is a block diagram of one embodiment of a vehicle
reference model of FIG. 2 in accordance with the present
invention;
[0016] FIG. 4 is a graph illustrating three (3) feedforward gain
curves for an active rear steer as a function of a vehicle speed in
accordance with the present invention;
[0017] FIG. 5 is a block diagram of one embodiment of a surface
coefficient estimator in accordance with the present invention;
[0018] FIG. 6 is a block diagram of one embodiment of a side slip
velocity estimator in accordance with the present invention;
[0019] FIG. 7 is a block diagram of one embodiment of a vehicle
level brake/steer controller in accordance with the present
invention; and
[0020] FIG. 8 is a graph of a lateral tire force vs. a tire slip
angle in accordance with the present invention.
DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS
[0021] Referring to FIGS. 1A-1D, a vehicle 10 including a front
axle 11 having a front left tire 12 and a front right tire 13
coupled thereto, and a rear axle 14 having a rear left tire 15 and
a rear right tire 16 coupled thereto is shown. As known by those
having ordinary skill in the art, a response of vehicle 10 in a yaw
plane is primarily dictated by a combination of longitudinal tire
forces and lateral tire forces being applied to tires 11, 12, 15,
and 16. Good handling of vehicle 10 in the yaw plane requires that
a yaw rate (i.e. a rate of rotation of vehicle 10 about a vertical
axis 17 passing through the center of gravity of vehicle 10) and a
lateral acceleration of vehicle 10 be consistent with driver
intentions, subject to a physical limit imposed by a surface
coefficient of adhesion. Since the vehicle yaw rate is determined
by a yaw moment acting on vehicle 10 (i.e. a moment of forces about
vertical axis 17), a main mechanism to control vehicle yaw response
is by generating a corrective yaw moment. This can be achieved by
applying one or more brakes (not shown) to tires 11, 12, 15, and/or
16; by a change in a steering angle of front axle 11; or by a
change in a steering angle of rear axle 14.
[0022] For example, when vehicle 10 is being driven straight as
illustrated in FIG. 1A, a brake force F.sub.x can be applied to
front right tire 13 to generate corrective yaw moment
.DELTA.M.sub.z1 in a clockwise direction about vertical axis 17.
Corrective yaw moment .DELTA.M.sub.z1 can be computed by the
following equation (1):
.DELTA.M.sub.z1=F.sub.x*(t.sub.w/2) (1)
[0023] where t.sub.w is a track width. In a linear range of tire
operation, brake force F.sub.x can be approximated by the following
equation (2):
F.sub.x=C.sub.x*.lambda.=C.sub.x*(.DELTA.v.sub.lr1/v) (2)
[0024] where C.sub.x is a tire longitudinal stiffness; .lambda. is
a brake slip; .DELTA.v.sub.lr1 is a difference in a linear speed of
tire 12 and a linear speed of tire 13; and v is a vehicle speed of
vehicle 10. Combining equations (1) and (2) yields the following
equation (3):
.DELTA.M.sub.z1=C.sub.x*(t.sub.w/2)*.DELTA.v.sub.lr1/v (3)
[0025] As illustrated in FIG. 1B, tire 12 and tire 13 can also be
controlled to generate corrective yaw moment .DELTA.M.sub.z2 as a
function of incremental front steering angle .DELTA..delta..sub.f.
Corrective yaw moment .DELTA.M.sub.z2 can be computed by the
following equation (4):
.DELTA.M.sub.z2=F.sub.y1*a (4)
[0026] where a is the distance from axis 17 to front axle 11; and
F.sub.y1 is the total lateral force on both tire 12 and tire 13,
which in the linear range of tire operation can be computed by the
following equation (5):
F.sub.y1=2*C.sub.y*.DELTA..delta..sub.f (5)
[0027] where C.sub.y is a cornering stiffness coefficient of both
tire 12 and tire 13. Thus, corrective yaw moment .DELTA.M.sub.z2
can also be computed by the following equation (6):
.DELTA.M.sub.z2=2*C.sub.y*a*.DELTA..delta..sub.f (6)
[0028] Equating yaw moment .DELTA.M.sub.z2 to yaw moment
.DELTA.M.sub.z1 can be accomplished by computing front steering
angle .DELTA..delta..sub.f under the following equation (7) with
the assumption that tire longitudinal stiffness coefficient C.sub.x
and tire lateral stiffness C.sub.y are approximately equal:
.DELTA..delta..sub.f=(C.sub.x*t.sub.w/(4*C.sub.y*a))*(.DELTA.V.sub.lr1/v).-
apprxeq.[t.sub.w/(4*a)]*(.DELTA.V.sub.lr1/v) (7)
[0029] Also by example, when vehicle 10 is being driven straight as
illustrated in FIG. 1C, brake force F.sub.x can be applied to rear
right tire 16 to generate corrective yaw moment .DELTA.M.sub.z3 in
a clockwise direction about vertical axis 17. Corrective yaw moment
.DELTA.M.sub.z3 can be computed by equation (1). In a linear range
of tire operation, brake force F.sub.x can be approximated by the
following equation (8):
F.sub.x=C.sub.x.lambda.*=C.sub.x*(.DELTA.V.sub.lr2/v) (8)
[0030] where C.sub.x is a tire longitudinal stiffness; .lambda. is
a brake slip; .DELTA.V.sub.lr2 is a difference in a linear speed of
tire 15 and a linear speed of tire 16; and v is a vehicle speed of
vehicle 10. Combining equations (1) and (8) yields the following
equation (9):
.DELTA.M.sub.z3=C.sub.x*(t.sub.w/2)*.DELTA.V.sub.lr2/v (9)
[0031] As illustrated in FIG. 1D, tire 15 and tire 16 can also be
controlled to generate corrective yaw moment .DELTA.M.sub.z4 as a
function of incremental rear steering angle .DELTA..delta..sub.r.
Corrective yaw moment .DELTA.M.sub.z4 can be computed by the
following equation (10):
.DELTA.M.sub.z4=F.sub.y2*b (10)
[0032] where b is the distance from axis 17 to rear axle 14; and
F.sub.y2 is the total lateral force on both tire 15 and tire 16,
which in the linear range of tire operation can be computed by the
following equation (11):
F.sub.y2=-2*C.sub.y*.DELTA..delta.r (11)
[0033] where C.sub.y1 is a cornering stiffness coefficient of both
tire 15 and tire 16. Thus, corrective yaw moment .DELTA.M.sub.z4
can also be computed by the following equation (12):
.DELTA.M.sub.z4=-2*C.sub.y*a*.DELTA..delta..sub.r (12)
[0034] Equating yaw moment .DELTA.M.sub.z4 to yaw moment
.DELTA.M.sub.z3 can be accomplished by computing rear steering
angle .DELTA..delta..sub.r under the following equation (13) with
the assumption that tire longitudinal stiffness coefficient C.sub.x
and tire lateral stiffness C.sub.y are approximately equal:
.DELTA..delta..sub.r=-[C.sub.x*t.sub.w/(4*C.sub.y*b)]*(.DELTA.v.sub.lr2/v)-
.apprxeq.-[t.sub.w/(4*b)]*(.DELTA.v.sub.lr2/v) (13)
[0035] The present invention is an integrated active steering and
braking control method based on equations (7) and (13) that
selectively utilizes tire speed differential signal
.DELTA.V.sub.lr1 to generate corrective yaw moment .DELTA.M.sub.z1
and/or to generate corrective yaw moment .DELTA.M.sub.z2 when
vehicle 10 has an active front steering system, and selectively
utilizes tire speed differential signal .DELTA.V.sub.lr2 to
generate corrective yaw moment .DELTA.M.sub.Z3 and/or corrective
moment .DELTA.M.sub.z4 when vehicle 10 has an active rear steering
system.
[0036] Referring to FIG. 2, an integrated active steering and
braking control system 11 for vehicle 10 in accordance with the
present invention is shown. System 11 comprises a reference model
20, an estimator 30, a vehicle level brake/steer controller 40, and
an actuator controller 50. To implement the principals of the
present invention, reference model 20, estimator 30, vehicle level
brake/steer controller 40, and an actuator controller 50 may
include digital circuitry, analog circuitry, or any combination of
digital circuitry and analog circuitry. Also, reference model 20,
estimator 30, vehicle level brake/steer controller 40, and an
actuator controller 50 may be programmable, a dedicated state
machine, or a hybrid combination of programmable and dedicated
hardware. Additionally, reference model 20, estimator 30, vehicle
level brake/steer controller 40, and an actuator controller 50 may
include any control clocks, interfaces, signal conditioners,
filters, Analog-to-Digital (A/D) converters, Digital-to-Analog
(D/A) converters, communication ports, or other types of operators
as would occur to those having ordinary skill in the art to
implement the principals of the present invention.
[0037] System 11 is incorporated within a processing environment of
vehicle 10. However, for the simplicity in describing the present
invention, system 11 is illustrated and described as being separate
from the processing environment of vehicle 10. Also, for the
simplicity in describing the present invention, system 11 will be
described herein as if vehicle 10 includes both a front active
braking system and a rear active steering system. However, those
having ordinary skill in the art will appreciate an applicability
of system 11 to a vehicle including only a front active braking
system or a rear active steering system.
[0038] As known by those having ordinary skill in the art,
conventional sensors (not shown) provide a plurality of signals
indicative of an operational state of vehicle 10 including, but not
limited to, a driver steering wheel angle signal .delta..sub.SWA, a
front steering wheel angle signal .delta..sub.f, a rear steering
wheel angle signal .delta..sub.r, a vehicle yaw rate signal
.OMEGA., a lateral acceleration signal a.sub.y, a wheel speed
signal W.sub.S1 (from tire 12), a wheel speed signal W.sub.S2 (from
tire 13), a wheel speed signal W.sub.S3 (from tire 15), a wheel
speed signs WS.sub.S4 (from tire 16), and an estimated vehicle
speed signal V.sub.x.
[0039] Reference model 20 inputs driver steering wheel angle signal
.delta..sub.SWA, lateral acceleration signal a.sub.y, and estimated
vehicle speed signal v.sub.x from vehicle 10. Alternative to
lateral acceleration signal a.sub.y, reference model 20 can input
an estimated surface coefficient of adhesion signal .mu..sub.e from
estimator 30. In response to the inputted signals, reference model
20 provides signals indicative of a feedforward front steering
angle correction signal .delta..sub.fdrl, a feedforward rear
steering angle correction signal .delta..sub.rff, a desired yaw
rate signal .OMEGA..sub.dl, a desired lateral velocity signal
v.sub.yd, and a desired slip angle signal .beta..sub.d.
[0040] Estimator 30 inputs front steering wheel angle signal
.delta..sub.f, rear steering wheel angle signal .delta..sub.r,
vehicle yaw rate signal .OMEGA., lateral acceleration signal
a.sub.y, and estimated vehicle speed signal v.sub.x from vehicle
10. Estimator 30 further inputs desired yaw rate signal
.OMEGA..sub.dl from reference model 20. In response to the inputted
signals, estimator 30 provides an estimated surface coefficient of
adhesion signal .mu..sub.e, an estimated lateral velocity signal
V.sub.ye, and an estimated slip angle signal .beta..sub.e.
[0041] Vehicle level brake/steer controller 40 inputs front
steering wheel angle signal .delta..sub.f, rear steering wheel
angle signal .delta..sub.r, vehicle yaw rate signal .OMEGA.,
lateral acceleration signal a.sub.y and estimated vehicle speed
signal v.sub.x from vehicle 10. Controller 40 further inputs
desired yaw rate signal .OMEGA..sub.d, desired lateral velocity
signal v.sub.yd, and desired slip angle signal .beta..sub.e from
reference model 20; and estimated surface coefficient of adhesion
signal lie, estimated lateral velocity signal v.sub.ye, and
estimated slip angle signal .beta..sub.e from estimator 30. In
response to the inputted signals, controller 40 provides a desired
speed differential signal .DELTA.v.sub.lr3t indicating a desired
speed difference between a linear speed of tire 12 and a linear
speed of tire 13 (FIGS. 1A-1D) or a desired speed difference
between a linear speed of tire 15 and a linear speed of tire 16
(FIGS. 1A-1D). Controller 40 further provides a desired front
steering angle signal .delta..sub.ftd1 indicative of a desired
steering angle of front axle 11 (FIGS. 1A-1D), and a desired rear
steering angle signal .delta..sub.rtd1 indicative of a desired
steering angle of rear axle 14 (FIGS. 1A-1D).
[0042] Controller 40 only provides desired speed differential
signal .DELTA.v.sub.lr3t and desired front steering angle
.delta..sub.ftd1 for alternative embodiments of vehicle 10 only
having a front active steering system.
[0043] Actuator controller 50 inputs desired speed differential
signal .DELTA.v.sub.lr3t, desired front steering angle signal
.delta..sub.ftd1, and desired rear steering angle signal
.delta..sub.rtd1 from controller 40. Controller 50 further inputs
front steering wheel angle signal .delta..sub.f, rear steering
wheel angle signal .delta..sub.r, wheel speed signal W.sub.S1,
wheel speed signal W.sub.S2, wheel speed signal W.sub.S3, and wheel
speed signal W.sub.S4 from vehicle 10. In response to the inputted
signals, actuator controller 50 compares desired tire speed
differential signal .DELTA.v.sub.lr3t to either a speed
differential between tire 12 and tire 13 (FIGS. 1A-1D) as indicated
by wheel speed signs WS.sub.S1 and wheel speed signs WS.sub.S2 as
would occur to those having ordinary skill in the art, or a speed
differential between tire 15 and tire 16 (FIGS. 1A-1D) as indicated
by wheel speed signs WS.sub.S3 and wheel speed signs WS.sub.S4 as
would occur to those having ordinary skill in the art. The result
is a corrective braking signal T.sub.b that is provided to a
braking system (not shown) of vehicle 10. In one embodiment of
vehicle 10, a brake actuator of the braking system appropriately
adjusts brake pressure to a corresponding brake in response to
corrective braking signal T.sub.b as would occur to those having
ordinary skill in the art.
[0044] Actuator controller 50 compares desired front steering angle
signal .delta..sub.ftd1 and front steering wheel angle signal
.delta..sub.f as would occur to those with ordinary skill in the
art, and compares desired rear steering angle signal
.delta..sub.rtd1 and rear steering wheel angle signal .delta..sub.r
as would occur to those with ordinary skill in the art to thereby
provide a corrective front steering signal T.sub.fs and a
corrective rear steering signal T.sub.rs to a steering system (not
shown) of vehicle 10. In one embodiment of vehicle 10, a front
steering actuator of the steering system adjusts a position of a
steering rack for axle 11 (FIGS. 1A-1D) in response to corrective
front steering signal T.sub.fs and a rear steering actuator of the
steering system adjusts a position of a steering rack for axle 14
(FIGS. 1A-1D) in response to corrective rear steering signal
T.sub.rs.
[0045] Referring to FIG. 3, one embodiment of reference model 20 in
accordance with the present invention is shown. A block 21 converts
steering wheel angle signal .delta..sub.SWA into a corresponding
angle of front tires signal .delta..sub.fdr as computed by the
following equation (14):
.delta..sub.fdr=.delta..sub.SWA* K.sub.f(v.sub.x) (14)
[0046] where K.sub.f(v.sub.x) is a ratio between the angle of
rotation of a steering wheel of vehicle 10 (FIGS. 1A-1D) and front
wheels 12 and 13 (FIGS. 1A-1D). In the case of active front steer,
front ratio K.sub.f(v.sub.x) may be speed dependent, for example
decreasing with speed to promote maneuverability at low speeds and
stability at high speeds.
[0047] A block 22 determines a feedforward part of a steering angle
correction by limiting a magnitude of front tire steering angle
.delta..sub.fdr to a reasonable level. A desired value of lateral
acceleration is computed from the following equation (15):
a.sub.yd=(v.sub.x.sup.2*.delta..sub.fdr)/(L+K.sub.u* v.sub.x.sup.2)
(15)
[0048] where L is a vehicle tirebase and K.sub.u is an understeer
coefficient. It follows from equation (15) that in order to limit a
magnitude of this acceleration to a reasonable level a.sub.ydmax
(an example value of a.sub.ydmax is 12 m/s.sup.2), a magnitude of
steering angle .delta..sub.fdr has to be limited in accordance with
the following equation (16):
[.delta..sub.fmax]=[a.sub.ydmax]*(L+K.sub.u*v.sub.x.sup.2)/v.sub.x.sup.2
(16)
[0049] This limiting can be interpreted as adding a feedforward
term to the steering angle .delta..sub.fff, as given by the
following equation (17): 1 fff = { 0 if fdr f max ( v x ) [ f max (
v x ) - fdr * sign ( fdr ) if fdr > f max ( v x ) ( 17 )
[0050] After the limitation, front steering angle .delta..sub.fdrl
desired by the driver is computed from the following equation
(18):
.delta..sub.fdrl=.delta..sub.fdr+.delta..sub.fff (18)
[0051] When vehicle 10 is equipped with a traditional steering
mechanism, the ratio K.sub.f does not depend on speed of vehicle 10
and the limitation of the steering angle cannot be performed, (i.e.
.delta..sub.fdrl=.delta..sub.fdr).
[0052] A block 23 determines a feedforward part of the rear tire
steering angle .delta..sub.rff as computed from the following
equation (19):
.delta..sub.rff=.delta..sub.fdr* K.sub.rff(v.sub.x) (19)
[0053] where K.sub.rff(V.sub.x) is a speed dependant gain that must
be selected to achieve an improved maneuverability (to reduce
radius of curvature and/or driver steering effort) at low speeds,
an improved stability at high speeds and a reduction of vehicle
side slip velocity (or side slip angle). One possible choice is
requiring that the side slip velocity be equal to zero in a steady
state maneuver. Side slip velocity v.sub.yss is computed by the
following equation (20):
v.sub.yss=[(v.sub.x*.delta..sub.fdrl)/(L+K.sub.u*
v.sub.x.sup.2)]*{b-M*a*v-
.sub.x.sup.2/(C.sub.r*L)+K.sub.rff(v.sub.x)*[a+M*b*v.sub.x.sup.2/(C.sub.f*-
L)]} (20)
[0054] where M is mass of vehicle 10, a and b are a distances of
vertical axis 17 to front axle 11 and rear axle 14 (FIGS. 1A-1D),
respectively, and C.sub.f and C.sub.r are the cornering stiffness
coefficients of front tires 12 and 13, and rear tires 15 and 16
(FIGS. 1A-1D), respectively. In order to make side slip velocity
v.sub.yss equal zero, a feedforward gain K.sub.rff'(v.sub.x) is
computed by the following equation (21):
K.sub.rff'(v.sub.x)=-[b-M*a*v.sub.x.sup.2/(C.sub.r*L)]/[a+M*b*v.sub.x.sup.-
2/(C.sub.r*L)] (21)
[0055] Feedforward gain K.sub.rff'(v.sub.x) is illustrated in FIG.
4 as curve 1. Gain K.sub.rff'(v.sub.x) is negative for small speeds
and positive for large speeds and it changes sign at a velocity
v.sub.xc given by the following equation (22):
v.sub.xc=[C.sub.r*L*b/(M*a)].sup.1/2 (22)
[0056] Thus, the sign of the rear tire steering angle
.delta..sub.rff is opposite to that of the front steering angle
.delta..sub.fdrl (out of phase steering) at low speeds, which
improves maneuverability. At high speeds, rear tires 15 and 16 are
steered in phase with the front tires 12 and 13, which improves
stability of vehicle 10. In practice, feedforward gain
K.sub.rff'(v.sub.x) given by equation (21) would require too large
rear tire steering angle .delta..sub.rff, which is typically
limited to several degrees. Also, yaw rate .OMEGA. of vehicle 10
during cornering maneuvers would be very limited at high
velocities, thus compromising subjective handling feel. To rectify
these problems, feedforward gain K.sub.rff'(v.sub.x) can be
multiplied by a factor .eta., which is less than 1 in accordance
with the following equation (23):
K.sub.rff"(v.sub.x)=-.eta.*[b-M*a*v.sub.x.sup.2/(C.sub.r*L)]/[a+M*b*v.sub.-
x.sup.2/(C.sub.f*L)] (23)
[0057] with a reasonable value of .eta.=0.4 (the optimal value for
a given application depends on the range of steering angle for rear
tires 15 and 16). Gain K.sub.rff"(v.sub.x) given by equation (23)
is represented by curve 2 in FIG. 4.
[0058] According to equation (22), a velocity v.sub.xc at which
gain K.sub.rff changes sign depends on cornering stiffness C.sub.r
of rear tires 15 and 16. On slippery surfaces, the value of the
cornering stiffness C.sub.r, and the characteristic velocity
v.sub.xc (at which gain K.sub.rff crosses zero) will be reduced. If
the gain determined by equation (23) with the nominal values of
cornering stiffness coefficient C.sub.r that correspond to a dry
surface are used, vehicle 10 will exhibit a tendency to oversteer
during driving on slippery surfaces at the velocities just below
v.sub.xc. This is due to out of phase steering increasing a rate of
rotation of vehicle 10. To rectify this problem and make the
behavior of vehicle 10 acceptable over the entire range of
surfaces, the feedforward gain K.sub.rff is chosen to be 0 for
speed between approximately 0.4*v.sub.xc and v.sub.xc, as
illustrated by curve 3 in FIG. 4.
[0059] A block 24 determines a steady state desired values of yaw
rate .OMEGA..sub.dss and side slip velocity v.sub.ydss. These
values can be computed from look up tables, which are obtained from
vehicle testing performed on dry surface. During tests, the
feedforward portion of the rear tire steering angle .delta..sub.rff
must be active and vehicle 10 must be in approximately steady state
cornering conditions. Thus, the desired values at a given speed and
front steering angle .delta..sub.f represent the values which
vehicle 10 achieves on dry surface in steady state cornering with
the feedforward portion of the rear tire steer being active.
Another way of obtaining the desired values is by using analytical
models. For example, the steady state values of yaw rate
.OMEGA..sub.dss and side slip velocity v.sub.ydss can be computed
from the following equations (24) and (25):
.OMEGA..sub.dss=[1-K.sub.rff(v.sub.x)]*v.sub.x*.delta..sub.fdrl/[L+K.sub.u-
*v.sub.x.sup.2] (24)
v.sub.ydss=[(v.sub.x*.delta..sub.fdrl)/(L+K.sub.u*
v.sub.x.sup.2)]*{b-M*a*-
v.sub.x.sup.2/(C.sub.r*L)+K.sub.rff(v.sub.x)*[a+M*b*v.sub.x.sup.2/(C.sub.f-
*L)]} (25)
[0060] In the equations (24) and (25), an understeer coefficient
K.sub.u depends on the magnitude of lateral acceleration a.sub.y.
When vehicle 10 is without active rear tire steer, feedforward gain
K.sub.rff=0. Since yaw rate .OMEGA. and side slip velocity v.sub.y
are overestimated at large steering angles by equations (24) and
(25), the desired values obtained from equations (24) and (25) must
be limited. A reasonable maximum value for a magnitude of yaw rate
.OMEGA. can be computed from the following equation (26):
.OMEGA..sub.dmax=g/v.sub.x (26)
[0061] where g is acceleration of gravity. The limited value of a
desired yaw rate .OMEGA..sub.dssl can be computed from the
following equation (27): 2 dssl = { dss if dss g / v x ( g / v x )
* sign ( dss ) if dss > g / v x ( 27 )
[0062] The limited value of lateral velocity v.sub.ydssl can be
computed from the following equation (28):
v.sub.ydssl=[.OMEGA..sub.dss/(1-K.sub.rff)]*{b-M*a*v.sub.x.sup.2/(C.sub.r*-
L)+K.sub.rff*[a+M*b*v.sub.x.sup.2/(C.sub.f*L)]} (28)
[0063] A block 25 receives steady state yaw rate .OMEGA..sub.dssl
and lateral velocity V.sub.ydss. Block 25 represents a desired
dynamics of vehicle 10 and the delay in the generation of tire
lateral forces. In the linear range of handling, the transfer
functions between front steering angle .delta..sub.fdrl and desired
yaw rate .OMEGA..sub.d and between front steering angle
.delta..sub.fdrl and desired lateral velocity v.sub.yd can be
computed by the following equations (29) and (30):
G.sub..OMEGA.(s)=.OMEGA..sub.d(s)/.delta..sub.fdrl(s)=(C.sub.f/M)*[s-z.sub-
..OMEGA.(v.sub.x)]/[s.sup.2+2*.zeta.(v.sub.x)*.omega..sub.n(v.sub.x)*s+.om-
ega..sub.n.sup.2(v.sub.x)] (29)
G.sub.vy(s)=v.sub.yd(s)/.delta..sub.fdrl(s)=(a*C.sub.f/I.sub.zz)*[s-z.sub.-
vy(v.sub.x)]/[s.sup.2+2*.zeta.(v.sub.x)*.omega..sub.n(v.sub.x)*s+.omega..s-
ub.n.sup.2(v.sub.x)] (30)
[0064] In equations (29) and (30), s is the Laplace operand,
I.sub.zz is the moment of inertia of vehicle 10 about axis 17,
z.sub..OMEGA.(v.sub.x) and z.sub.vy(v.sub.x) are zeros of the
corresponding transfer functions, .zeta.(v.sub.x) is the damping
coefficient, and .omega..sub.n(v.sub.x) is the undamped natural
frequency.
[0065] When vehicle 10 has active rear tire steer, the zeros of the
transfer functions depend on feedforward gain K.sub.rff. Each one
of the above transfer functions can be represented as a product of
a steady-state value (corresponding to s=0) and a term representing
the dynamics can be computed by the following equations (31) and
(32):
G.sub..OMEGA.(s)=(.OMEGA..sub.dss/.delta..sub.fss)*G.sub..OMEGA.'(s)
(31)
G.sub.vy(s)=(v.sub.yss/.delta..sub.fss)*G.sub.vy'(s) (32)
[0066] Where
G.sub..omega.'(s)=[-.omega..sub.n.sup.2(v.sub.x)/z.sub..omega.(v.sub.x)
]*[s-z.sub..omega.(v.sub.x)]/[s.sup.2+2*.zeta.(v.sub.x)*.omega..sub.n(v.s-
ub.x)*s+.omega..sub.n.sup.2(v.sub.x)] (33)
G.sub.vy'(s)=[-.omega..sub.n.sup.2(v.sub.x)/z.sub.vy(v.sub.x)]*[s-z.sub.vy-
(v.sub.x)]/[s.sup.2+2*.zeta.(v.sub.x)*.omega..sub.n(v.sub.x)*s+.omega..sub-
.n.sup.2(v.sub.x)] (34)
[0067] Thus, the dynamic values of the desired yaw rate
.OMEGA..sub.d and lateral velocity v.sub.yd can by obtained by
passing the steady state values through the differential (or
difference) equations (with parameters dependent on speed)
representing the dynamics of the transfer functions
G.sub..OMEGA.'(s) and G.sub.vy'(s).
[0068] In a block 26, the values of desired yaw rate .OMEGA..sub.d
and side slip velocity v.sub.yd are subsequently passed through
first order filters representing a delay in generating tire forces
due to tire relaxation length. Block 26 can be represented as a
transfer function in accordance with the following equation
(35):
G.sub.f(s)=a.sub.f(v.sub.x)/[s+a.sub.f(v.sub.x)] (35)
[0069] in which a filter parameter a.sub.f(v.sub.x) is speed
dependent. In the case of vehicle 10 having active rear tire steer,
one of the control objectives is to achieve quick response of
vehicle 10 to steering inputs. Thus, in this case, the dynamics of
vehicle 10 as represented by the transfer functions (31) and (32)
can be ignored, since vehicle 10 can respond faster to steering
inputs with active rear steer than a conventional vehicle.
[0070] The desired values of yaw rate .OMEGA..sub.d and lateral
velocity v.sub.yd obtained as outputs of block 26 may be
subsequently limited in magnitude by a block 27 depending on the
surface conditions. A block 27 can utilize either an explicit
estimate of surface coefficient of adhesion in lateral direction
.mu..sub.L or a magnitude of lateral acceleration a.sub.y. In the
first case, a limited value of desired yaw rate .OMEGA..sub.dl is
computed from the 20 following equation (36): 3 dl = { d if d L * g
/ v x ( L * g / v x ) * sign ( d ) if d > L * g / v x ( 36 )
[0071] If the magnitude of lateral acceleration a.sub.y is used by
block 27, the limited desired yaw rate .OMEGA..sub.dl is computed
from the following equation (37): 4 dl = { d if d ( a y + a y ) / v
x [ ( a y + a y ) / v x ] * sign ( d ) if d > ( a y + a y ) / v
x ( 37 )
[0072] where .DELTA.a.sub.y is a constant positive value, for
example 2 m/s.sup.2. The magnitude of desired lateral velocity
V.sub.yd is limited by the value obtained from equation (26) with
the desired yaw rate at steady state .OMEGA..sub.dss replaced by
the limited desired yaw rate .OMEGA..sub.dl.
[0073] Block 27 also outputs a desired side slip angle pd that can
be computed as an arctangent function of the ratio of desired
lateral velocity to longitudinal velocity in accordance with the
following equation (38):
.beta..sub.d=Arctan(v.sub.yd/v.sub.x) (38)
[0074] Referring to FIG. 5, an embodiment of estimator 30 (FIG. 2)
for estimating surface coefficient of adhesion .mu..sub.e is shown.
A block 31 performs preliminary calculations. First, it is
recognized that the most robust signal available is yaw rate
.OMEGA., and an entry and an exit conditions are dependent mainly
on a yaw rate error, i.e. a difference between the desired yaw rate
.OMEGA..sub.dl and measured yaw rate .OMEGA., and to a lesser
extent on measured lateral acceleration a.sub.y (entry condition
only). Thus, a yaw rate error is calculated and filtered, and
lateral acceleration a.sub.y is filtered.
[0075] Second, when vehicle 10 (FIGS. 1A-1D) reaches the limit of
adhesion in a steady turn, a surface coefficient of adhesion can be
determined as a ratio of the magnitude of a filtered lateral
acceleration a.sub.yfilt to a maximum lateral acceleration
a.sub.ymax that vehicle 10 can sustain on dry pavement as shown in
the following equation (39):
.mu..sub.L_temp=.vertline.a.sub.yfilt`.vertline./a.sub.ymax
(39)
[0076] where .mu..sub.L_temp is a temporary estimate of surface
coefficient of adhesion in the lateral direction, and a.sub.yfilt
is filtered lateral acceleration, which is also corrected for the
effects of measured gravity components resulting from vehicle body
roll and bank angle of the road.
[0077] A block 32 is designed to recognize situations when vehicle
10 operates at or close to the limit of adhesion and estimates a
lateral surface coefficient of adhesion .mu..sub.L from measured
lateral acceleration a.sub.y. This estimate is calculated by
identifying one of the following three conditions.
[0078] First, entry conditions are tested during a stage S1. Entry
conditions are when vehicle 10 is handling at the limit of adhesion
and is not in a quick transient maneuver. Under entry conditions,
stage S2 sets coefficient of adhesion .mu..sub.L equal to temporary
estimate of surface coefficient of adhesion .mu..sub.L_temp as
calculated by equation (37).
[0079] Second, exit conditions are tested during a stage S3. Exit
conditions indicate vehicle 10 is well below the limit of adhesion
(within the linear range of handling behavior). Under exit
conditions, a stage S4 resets coefficient of adhesion .mu..sub.L to
a default value of 1.
[0080] Third, when neither the entry conditions nor the exit
conditions are met, a stage S5 holds coefficient of adhesion
.mu..sub.L unchanged from a previous value (i.e. holding
conditions). The only exception is when the magnitude of measured
lateral acceleration a.sub.y exceeds the maximum value predicted
using currently held estimate. In this case, stage S5 calculates
coefficient of adhesion .mu..sub.L as if vehicle 10 was in an entry
condition.
[0081] The entry conditions are met during stage S1 when the
following three (3) conditions are simultaneously satisfied. The
first condition is either (1) the magnitude of the yaw rate error,
that is the difference between the desired yaw rate .OMEGA..sub.d
and the measured yaw rate .OMEGA. being greater than a threshold as
computed in the following equation (40):
.vertline..OMEGA..sub.d-.OMEGA..vertline..sub.filt>Yaw.sub.--Threshold1
(40)
[0082] where the typical value of Yaw_Thershold1 is 0.123 rad/s=7
deg/s); or (2) the magnitude of yaw rate error being greater than a
lower threshold Yaw_Threshold2 for some time Te as computed in the
following equation (41):
.vertline..OMEGA..sub.d-.OMEGA..vertline..sub.filt>Yaw.sub.--Threshold2
for Te seconds (41)
[0083] where Yaw_Threshold2 depends on the magnitude of desired yaw
rate .OMEGA..sub.d or measured yaw rate .OMEGA.. For example,
Yaw_Threshold2=4 deg/s +5*.vertline..OMEGA..sub.d.vertline.=0.07
rad/s+0.09*1.vertline..OM- EGA..sub.d.vertline., where
.OMEGA..sub.d is the desired yaw rate in [rad/s]. A typical value
of the time period Te for which this condition must be satisfied is
0.3 sec. The threshold Yaw_Threshold1 used in equation (40) may
also depend on the magnitude of desired yaw rate .OMEGA..sub.d or
measured yaw rate .OMEGA..
[0084] The second condition is the signs of the filtered lateral
acceleration a.sub.yfiltl and the weighted sum of yaw rate .OMEGA.
and the derivative of yaw rate are the same in accordance with the
following mathematical expression (42):
a.sub.yfilt1*(.OMEGA.+Yaw.sub.--Der.sub.--Mult*d.OMEGA./dt)>Sign.sub.---
Comp (42)
[0085] where .OMEGA. is the measured yaw rate and d.OMEGA./dt is
its derivative. The magnitude of the filtered lateral acceleration
a.sub.yfilt is limited from equation (43): 5 a yfiltl = { a yfiltl
if a yfilt a y min a y min * sign ( d ) if a yfilt < a y min (
43 )
[0086] where a.sub.ymin is a constant with a typical value of 0.2
M/s.sup.2. Thus if a.sub.yfilt is very small in magnitude, it is
replaced by the a.sub.ymin with a sign the same as the desired yaw
rate .OMEGA..sub.d. This limit is needed to improve estimation on
very slick surfaces (e.g. ice) when the magnitude of lateral
acceleration a.sub.y is comparable to the effect of noise, so that
the sign of a.sub.yfilt cannot be established.
[0087] The recommended values in equation (42) for the constant
Yaw_Der_Mult is 0.5 and for Sign_Comp is 0.035 (if .OMEGA. is in
rad/s and d.OMEGA./dt in rad/s.sup.2).
[0088] In order to allow lateral acceleration a.sub.y to fully
build up at the beginning of maneuver and after each change in
sign, before it can be used for estimation of surface coefficient
.mu..sub.L, a condition is used that requires both the desired yaw
rate .OMEGA..sub.dl and lateral acceleration a.sub.y to have the
same signs for a specific time period (necessary for the
acceleration to build up). In order to keep track of how long the
desired yaw rate .OMEGA..sub.d and lateral acceleration a.sub.y
have had the same signs, a timer is introduced. In accordance with
an equation (44), the timer becomes zero when the desired yaw rate
.OMEGA..sub.d and lateral acceleration a.sub.y have opposite signs
and counts the time that elapses from the moment the signs become
and remain the same. 6 timer = { 0 when d * a yfiltl < Ay_sign
_comp timer + loop_time otherwise ( 44 )
[0089] where .OMEGA..sub.d is the desired yaw rate in [rad/s] and
Ay_sign_comp is a constant with a typical value of 0.2
m/s.sup.3.
[0090] The third condition is either (1) the signs of the desired
yaw rate .OMEGA..sub.d and measured lateral acceleration a.sub.y
are the same and they have been the same for some time in
accordance with following equation (45):
timer>hold_time (45)
[0091] The hold_time in equation (42) can be 0.25 s, or (2) the
magnitude of a derivative of lateral acceleration da.sub.y/dt is
less than a threshold in accordance with the following mathematical
equation (46):
.vertline.da.sub.y/dt.vertline.<Ay.sub.--Der.sub.--Thresh
(46)
[0092] A recommended value of the threshold, Ay_Der_Thresh=2.5
m/s.sup.3. The derivative da.sub.y/dt is obtained by passing
filtered lateral acceleration a.sub.yfil through a high pass filter
with a transfer function a.sub.f*s/(s+a.sub.f) with a typical value
of a.sub.f=6 rad/s.
[0093] The exit conditions are met during stage S3 when the
following two (2) conditions are simultaneously satisfied. The
first condition is the magnitude of yaw rate error filtered is less
than or equal to a threshold as illustrated in the following
equation (47):
.vertline..OMEGA..sub.d-.OMEGA..vertline..sub.filt.ltoreq.Yaw.sub.--Thresh-
old3 (47)
[0094] with a typical value of Yaw_Threshold3=0.10 rad/s.
[0095] The second condition is a low-pass filtered version of the
magnitude of the yaw rate error is less than or equal to a
threshold as illustrated in the following equation (48):
(.vertline..OMEGA..sub.d-.OMEGA..vertline..sub.filt).sub.filt<Yaw.sub.--
-Treshold4 (48)
[0096] where the value of Yaw_Threshold4=0.06 rad/s is recommended
and the filter is a first order filter with a cutoff frequency of
1.8 rad/s, e.g. a filter with a transfer function
a.sub.f/(s+a.sub.f) with a.sub.f=1.8 rad/s). The thresholds
Yaw_Threshold3 and Yaw_Thereshold4 may depend on the magnitude of
desired yaw rate .OMEGA..sub.d or the measured yaw rate
.OMEGA..
[0097] A block 33 corrects surface estimate .mu..sub.L for load
transfer. Because of the effects of load transfer to the outside
tires during cornering, which is smaller on slippery surfaces than
on dry roads, lateral acceleration a.sub.y is not directly
proportional to the surface coefficient of adhesion .mu..sub.L To
account for this effect, the surface estimate .mu..sub.L_temp
computed from equation (37), is corrected using the following
equation (49):
.mu..sub.L=.mu..sub.L_temp*(c.sub.1+C.sub.2*.mu..sub.L_temp)
(49)
[0098] where c.sub.1<1 and c.sub.2=1-c.sub.1, so that on dry
surface .mu..sub.L=.mu..sub.L_temp=1, while on slippery surfaces
.mu..sub.L<.mu..sub.L_temp. Example values are c.sub.1=0.85 and
C.sub.2=0.15.
[0099] A block 34 limits surface estimate .mu..sub.L from below by
a value .mu..sub.Lmin (a typical value 0.07) and may be limited
from above by .mu..sub.Lmax (a typical value 1.2). Surface estimate
.mu..sub.l can be passed through a slew filter, which limits the
rate of change of the estimate to a specified value, for example
2/sec, or a low pass filter.
[0100] A block 35 estimates total surface coefficient of adhesion
.mu..sub.e using the following equation (50): 7 e = { Lfilt when a
xe Ax_Dz { ( Lfilt ) 2 + [ ( a xe - Ax_DZ ) / a x max ] 2 } 1 / 2
when a xe > Ax_Dz ( 50 )
[0101] where Ax_Dz is the dead-zone applied to the estimated
longitudinal acceleration (a typical value is 2m/s2) and a.sub.xmax
is a maximum longitudinal deceleration which vehicle 10 can achieve
on dry surface (a typical value is 9 m/s.sup.2). The square root
function in the above expression can be replaced by a simplified
linear equation or by a look-up table. The estimate is finally
limited from below by .mu..sub.emin (typical value is 0.2) and from
above by .mu..sub.emax (1.0).
[0102] The (unfiltered) estimate of surface coefficient in lateral
direction, .mu..sub.L, was found to be good for estimation of
vehicle side slip angle. However, for control purposes, the
estimate of the surface coefficient in lateral direction may be too
low in some situations (for example during heavy braking on slick
surfaces) and may cause unnecessary tight control of slip angle.
Therefore, for the purpose of control the estimated surface
coefficient is increased when the magnitude of the estimated
vehicle longitudinal acceleration exceeds certain value. Note that
separate thresholds on yaw rate error for the entry and exit
conditions are used, with the thresholds on the exit conditions
being a little tighter.
[0103] Referring to FIG. 6, an embodiment of estimator 30 (FIG. 2)
for estimating the actual lateral velocity and slip angle of
vehicle 10 (FIGS. 1A-1D) as a function of front steering wheel
angle signal .delta..sub.f, rear steering wheel angle signal
.delta..sub.r, yaw rate signal .OMEGA., estimated vehicle speed
signal v.sub.x, and the estimated lateral surface coefficient of
adhesion .mu..sub.L is shown. The slip angle estimation implements
an iterative nonlinear closed loop observer to determine the
estimated vehicle lateral velocity v.sub.ye and slip angle
.beta..sub.e.
[0104] A block 36 of the observer estimates the side slip angles of
front axle 11 and rear axle 14 using the following equations (51a)
and (51b):
.alpha..sub.fe=[v.sub.ye(k-1)+a*.OMEGA.]/v.sub.x-.delta..sub.f
(51a)
.alpha..sub.re=[v.sub.ye(k-1)-b*.OMEGA.]/v.sub.x-.delta..sub.r
(51b)
[0105] where v.sub.ye(k-1) is the estimated lateral velocity from
the previous iteration of the observer, and .alpha..sub.fe and
.alpha..sub.re are the estimated front and rear axle side slip
angles, respectively. The steering angles .delta..sub.f and
.delta..sub.r are the actual (measured) steering angles of front
tires 12 and 13, and rear tires 15 and 16, respectively, including
the corrective terms.
[0106] A block 37 of the observer estimates lateral forces
F.sub.yfe of the front axle 11 according to one of two functions as
illustrated in the following equation (52): 8 F yfe = { - C f * fe
* ( 1 - ( b cf * ( fe / L ) ) ) , if fe < L * f * - N f * * ( fe
/ fe ) * [ L + s f * ( fe / f * - L ) ] if fe L * f * ( 52 )
[0107] where s.sub.f is a small non-negative number (the slope of
the F.sub.yf-.alpha..sub.f curve at the limit of adhesion), e.g.,
s.sub.f=0.05, and where .alpha..sub.f* is defined by the following
equation (53):
.alpha..sub.f*=1/(2*b.sub.cf,) (53)
[0108] where b.sub.cf is defined by the following equation
(54):
b.sub.cf=C.sub.f/(4*N.sub.f), (54)
[0109] where N.sub.f is defined by the following equation (55):
N.sub.f*=M*b*(a.sub.ymax+.DELTA..sub.a)/(a+b) (55)
[0110] where a.sub.ymax is the maximum lateral acceleration that
vehicle 10 can sustain on a dry surface in m/s.sup.2 and
.DELTA..sub.a is a positive constant, e.g., .DELTA..sub.a=0.5
m/s.sup.2. M is the nominal value of the total vehicle mass.
[0111] The observer similarly estimates lateral forces F.sub.yre of
the rear axle 14 according to the following equation (56): 9 F yre
= { - C r * re * ( 1 - b cr * re ) , if re < L * r * - N r * * (
re / re ) * [ L + s r * ( re / r * - L ) ] if re L * r * ( 56 )
[0112] where s.sub.r is a small non-negative number, e.g.,
s.sub.r=0.05 and where .alpha..sub.r* is defined by the following
equation (57):
.alpha..sub.r*=1/(2*b.sub.cr,) (57)
[0113] where b.sub.cr is defined by the following equation
(58):
b.sub.cr=C.sub.r/(4*N.sub.r*), (58)
[0114] where N.sub.r* is defined by the following equation
(59):
N.sub.r*=M*a*(a.sub.ymax+.DELTA..sub.a)/(a+b). (59)
[0115] A block 38 of the observer then estimates a state variable
q(k) related to lateral velocity according to the following
equation (60):
q(k)=q(k-1)+.DELTA.t*{-(1+g.sub.2)*v.sub.x*.OMEGA.+((1+g.sub.3)/M-a*g.sub.-
1/I.sub.zz)
*F.sub.yfe+[(1+g.sub.3)/M+b*g.sub.1/I.sub.zz]*F.sub.yre+(g.sub-
.2-g.sub.3)*a.sub.y-g.sub.4*.DELTA.A.sub.yf} (60)
[0116] where .DELTA.A.sub.y is defined by the following equation
(61):
.DELTA.A.sub.y=a.sub.y-(F.sub.yfe+F.sub.yre)/M, (61)
[0117] and .DELTA.A.sub.yf is .DELTA.A.sub.y passed through a first
order digital low pass filter, for example, with a cut off
frequency of 1 rad/s.
[0118] A block 39 of the observer uses state variable q(k) to
determine estimates of lateral velocity v.sub.ye and slip angle
.beta..sub.e using equations (62) and (63):
v.sub.ye(k)=[q(k)+g.sub.1*.cndot..sub.a]/(1+g.sub.2) (62)
.beta..sub.e=Arctan[v.sub.ye(k)/v.sub.x]. (63)
[0119] The gains g.sub.1, g.sub.2, g.sub.3 and g.sub.4 are tuning
parameters preset by a system designer, typically through
experimentation on a test vehicle, and may vary from implementation
to implementation. The estimated lateral velocity v.sub.ye and the
estimated slip angle .beta..sub.e are the main outputs of the
observer.
[0120] Referring to FIG. 7, one embodiment of controller 40 in
accordance with the present invention is shown. In controller 40,
an overall corrective yaw moment is determined and expressed in
terms of a desired speed differential signal .DELTA.v.sub.lr3t
(which is achieved by differential braking) between either front
tire 12 and front tire 13 (FIGS. 1A-1D), or rear tire 15 and rear
tire 16 (FIGS. 1A-1D). The corrective yaw moment is also expressed
in terms of a summation of front steer angle correction signal
.DELTA..delta..sub.f and front steering angle signal
.delta..sub.fdr1 (FIG. 2) to form the total front steering angle
signal .delta..sub.ftd and in terms of a summation of rear steer
angle correction signal .DELTA..delta..sub.r and rear steering
angle signal .delta..sub.rff (FIG. 2) to form the total desired
rear steer angle signal .delta..sub.rtd. The magnitudes of total
desired rear steer angle signal .delta..sub.rtd and the total
desired front steering angle signal .delta..sub.ftd may be
subsequently limited to desired rear steering angle signal
.delta..sub.rtd1 and desired front steering angle signal
.delta..sub.ftd1, respectively.
[0121] A block 41 calculates desired speed differential signal
.DELTA.v.sub.lr3, front steer angle correction signal
.DELTA..delta..sub.f and rear steer angle correction signal
.DELTA..delta..sub.r. The corrective yaw moment is obtained by a
feedback control operating on the yaw rate error and the side slip
velocity (or side slip angle) error. The yaw rate error
.OMEGA..sub.d-.OMEGA. is the difference between the desired yaw
rate signal .OMEGA..sub.d and measured yaw rate signal .OMEGA..
Similarly, the side slip velocity error is the difference between
the desired side slip velocity signal v.sub.yd and the estimated
side slip velocity signal v.sub.ye. The control law is essentially
a PD (proportional and derivative) feedback control law, in which
the control gains depend on vehicle speed signal v.sub.x, estimated
surface coefficient of adhesion signal .mu..sub.e, and on the
magnitude of the estimated vehicle slip angle error. Thus, for the
delta velocity signal .DELTA.v.sub.lr3, the control law equation
(64) may be written as follows: 10 v lr3 = k p ( v x , e ) * ( d -
) + k d ( v x , e ) * d ( d - ) / dt + k vyp ( v x , e , d - e ) *
( v yd - v ye ) + k vyd ( v x , e , d - e ) * d ( v yd - v ye ) /
dt ( 64 )
[0122] where k.sub..OMEGA.p(v.sub.x,.mu..sub.e) and
k.sub..OMEGA.d(v.sub.x,.mu..sub.e) are the proportional and
derivative yaw rate gains, while k.sub.vyp(v.sub.x,.mu..sub.e,
.vertline..beta..sub.d-.beta..sub.e.vertline.) and
k.sub.vyd(V.sub.x, .mu..sub.e,
.vertline..mu..sub.d-.mu..sub.e.vertline.) are the proportional and
derivative lateral velocity gains. The magnitudes of the gains for
each velocity and surface coefficient are tuned through vehicle
testing and are implemented as look up tables. Typically, the
proportional yaw rate gain k.sub..OMEGA.p(v.sub.x,.mu..sub.e) and
derivative yaw rate gain k.sub..OMEGA.d(v.sub.x, .mu..sub.e)
increase nearly proportionally with vehicle speed v.sub.x and
decrease as the estimated surface coefficient of adhesion
.mu..sub.e increases. The lateral velocity gains,
k.sub.vyp(v.sub.x,.mu..sub.e,
.vertline..beta..sub.d-.beta..sub.e.vertline.) and
k.sub.vyd(v.sub.x,.mu..sub.e,
.vertline..beta..sub.d-.beta..sub.e.vertlin- e.), increase with
vehicle speed and increase quite rapidly on slippery surfaces. This
is done to provide a proper balance between yaw control and side
slip control. On dry surfaces, the yaw rate feedback control
usually dominates to achieve responsive handling, while on slippery
surface the control of side slip increases to achieve better
stability. In addition, the slip angle gains may depend on the
magnitude of side slip angle error, with the gain generally
increasing as the side slip angle error increases. For example, the
gain may be zero or close to zero when the magnitude of side slip
angle error is below a threshold, and increases as the side slip
angle error increases in magnitude.
[0123] There exist several modifications of the control law, which
may be considered the special cases of the control law (64). First,
the desired side slip velocity and side slip angle may be set to
zero. In this case, the last two terms in equation (64) are
proportional and derivative terms with respect to side slip
velocity, rather than side slip errors. In this case, the desired
side slip velocity does not need to be computed, which simplifies
the algorithm. This simplification is justified, because at higher
speeds the desired side slip angles are small, especially for
active rear steer vehicles. Further simplification may be achieved
by deleting the third term in the control law (64), involving the
side slip velocity. In this case, the control law includes P
(proportional) and D (derivative) yaw rate terms, but only a
derivative lateral velocity term. In that manner, the estimation of
vehicle side slip velocity is avoided and the algorithm is further
simplified. The control gains may depend on whether vehicle is in
oversteer or understeer condition.
[0124] As discussed earlier, differential speed signal
.DELTA.v.sub.lr3 determined for the brake controller can be
converted into equivalent steering angle correction signal
.DELTA..delta..sub.r for rear axle 14 and front steering angle
correction signal .DELTA..delta..sub.f for axle 12. Thus the
feedback portions of the front or rear steering angles can be
computed from equations (65) and (66):
.DELTA..delta..sub.r=g.sub.f(v.sub.x, .mu..sub.e)*.DELTA.v.sub.lr3
(65)
.DELTA..delta..sub.f=g.sub.r(v.sub.x, .mu..sub.e)*.DELTA.v.sub.lr3
(66)
[0125] where the gains can vary with speed and the estimated
surface coefficient of adhesion.
[0126] Block 42 determines a vehicle steer flag, which determines
whether vehicle 10 is in understeer (flag=1) or oversteer (flag=0).
The following is an example of steer flag determination.
[0127] Vehicle 10 is in understeer if either front steering angle
signal .delta..sub.f, control signal .DELTA.v.sub.lr3 and lateral
acceleration signal a.sub.y are all in the same direction or when
vehicle 10 is plowing on a slippery surface. Vehicle 10 is in
oversteer if either front steering angle signal .delta..sub.f is in
different direction from control signal .DELTA.v.sub.lr3; or front
steering angle signal .delta..sub.f and control signal
.DELTA.v.sub.lr3 are in the same direction, but lateral
acceleration signal a.sub.y is in opposite direction. If neither
oversteer nor understeer conditions are satisfied, previous steer
definition is held. It is theoretically possible that vehicle 10 is
plowing (understeer) and front steering angle signal .delta..sub.f
and control signal .DELTA.v.sub.lr3 have opposite signs
(oversteer). In this case vehicle state is considered oversteer
(i.e. oversteer overrides understeer if both are true).
[0128] The situation when vehicle 10 is plowing is identified when
the magnitude of the desired yaw rate .OMEGA..sub.d is
significantly larger than the magnitude of measured yaw rate
.OMEGA. over a pre-defined period of time, and the measured yaw
rate .OMEGA. is small. This can happen only on very slippery road
surface. In this situation, we do not demand that front steering
angle signal .delta..sub.f, control signal .DELTA.v.sub.lr3 and
lateral acceleration signal a.sub.y have the same signs, in order
to declare understeer, since lateral acceleration signal a.sub.y
may be very small in magnitude.
[0129] The over/understeer flag is used to further influence the
control actions. If the brake control system is a four channel
system, i.e. it can actively apply brakes to either front tires 12
and 13 (FIGS. 1A-1D) or rear tires 15 and 16 (FIGS. 1A-1D), then
the control command .DELTA.v.sub.lr3 is applied to tire 12 and/or
tire 13 when vehicle 10 is in oversteer and to tire 15 and./or tire
16 when vehicle 10 is in understeer. For a two channel system, the
control command .DELTA.v.sub.lr3 is always applied to tire 12
and/or tire 13. The actual commanded differential speed signal
.DELTA.v.sub.lr3 is corrected for the difference in tire
velocities, resulting from kinematics of turn. During cornering
maneuvers, free rolling tires have a speed difference equal to the
product of vehicle yaw rate .OMEGA., and the track width t.sub.w.
Thus, the target tire slip difference can be computed from equation
(67):
.DELTA.v.sub.lr3t=.DELTA.v.sub.lr3+t.sub.w*.OMEGA. (67)
[0130] When the driver is not braking, the velocity difference
between front tires 12 and 13 is achieved by braking of one or both
front tires 12 and 13, and the velocity difference between rear
tires 15 and 16 is achieved by braking of one or both front tires
15 and 16. When driver is braking, the braking force may also be
reduced on the opposite side, if braking of the desired tire
reached a saturation point without achieving the desired speed
difference.
[0131] A block 43 tests entry and exits conditions for applying the
brake command .DELTA.v.sub.lr3t to vehicle 10. The brake command
.DELTA.v.sub.lr3t is applied only if entry conditions for the
active brake control are established and only until the exit
conditions for active brake control satisfied. First, the estimated
vehicle speed signal v.sub.x must be above a certain entry speed
v.sub.min, which is rather low, for example 5 mph. If this
condition is satisfied, then the brake system becomes active when
the magnitude of yaw rate error exceeds a threshold value, which
depends on vehicle speed signal v.sub.x, front steering angle
signal .delta..sub.f and over or understeer flag. The yaw rate
error consists of a proportional and a derivative terms. Thus the
entry condition can be computed from the following equation
(68):
.vertline..OMEGA..sub.d-.OMEGA.+k.sub.e*d(.OMEGA..sub.d-.OMEGA.)/dt
.vertline.>.OMEGA..sub.thresh(v.sub.x, .delta..sub.f,
steer_flag) (68)
[0132] where k.sub.e is a constant and .OMEGA..sub.thresh(v.sub.x,
.delta..sub.f, steer_flag) is a threshold, which depends on the
vehicle speed signal v.sub.x, front steering angle signal
.delta..sub.f and steer flag. It is larger in understeer condition
than in oversteer. The entry conditions for the brake system are
significantly relaxed, or even the system may not be allow to
enter, when vehicle 10 is being braked in ABS mode. In this case,
the directional control is provided by steering only, until the
errors in yaw following are quite large. In the case of braking on
split mu surface (a surface with significantly different
coefficients of adhesion under left and right tires) the entire
correction of the yaw motion is provided by steering alone. This is
done in order to avoid compromising the stopping distance.
[0133] An exit condition is established if the magnitude of the yaw
rate error, as defined above, is below a predetermined yaw rate
error threshold (which is lower than the entry threshold) for a
specified period of time or when vehicle speed drops below a
certain value.
[0134] When entry conditions are not met, the active brake control
system is disabled. During this time vehicle dynamic behavior is
controlled through active steer control, front or rear, which do
not have entry conditions. A block 44 determines total commanded
targeted control valves. First, rear steering angle .delta..sub.rtd
is computed as the sum of the feedforward part .delta..sub.rff and
the feedback part .DELTA..delta..sub.r in accordance with the
following equation (69):
.delta..sub.rtd=.delta..sub.rff+.DELTA..delta..sub.r (69)
[0135] If vehicle 10 is in oversteer, the commanded rear steer
angle is limited in order to limit the side slip angle of the rear
tires to a maximum value .alpha..sub.rmax(.mu..sub.e), which
depends on the estimated surface coefficient of adhesion (it
decreases when the surface estimate decreases). Typical shapes of
the curves relating lateral force to the tire slip angle for two
different surfaces are shown in FIG. 8. Increasing slip angle
beyond .alpha..sub.rmax leads to decline in the magnitude of
lateral force on most surfaces. The purpose is to avoid increasing
slip angle beyond that corresponding to the peak lateral force.
This yields the following equation (70): 11 rtdl = { ( v ye - b * )
/ v x - r max if rtd < ( v ye - b * ) / v x - r max ( v ye - b *
) / v x + r max if rtd > ( v ye - b * ) / v x + r max rtd
otherwise ( 70 )
[0136] Similarly, the commanded front steer angle correction,
.DELTA..delta..sub.ftd consists of the feedforward part
.delta..sub.fff and the feedback part .DELTA..delta..sub.f in
accordance with following equation (71):
.DELTA..delta..sub.ftd=.delta..sub.fff+.DELTA..delta..sub.f
(71)
[0137] The total desired steering angle .delta..sub.ftd is the sum
of the steering angle correction and the angle commanded by the
driver .delta..sub.fdr as computed from the following equation
(72):
.delta..sub.ftd=.delta..sub.fdr+.DELTA..delta..sub.ftd (72)
[0138] This steering may subsequently be a subject of the following
limitation. If vehicle is in an understeer condition, then the
total front tire steering angle .delta..sub.ftd is limited to by
the following equation (73): 12 ftd1 = { ( v ye + a * ) / v x - f
max if ftd < ( v ye + a * ) / v x - f max ( v ye + a * ) / v x +
f max if ftd > ( v ye + a * ) / v x - f max ftd otherwise ( 73
)
[0139] where .alpha..sub.fmax(.mu..sub.e) is a front tires slip
angle corresponding to maximum lateral force. It is a function of
the estimated surface coefficient of adhesion .mu..sub.e.
[0140] Thus, during normal vehicle operation, vehicle 10 is
controlled through steering inputs only, which are quite effective
in controlling vehicle yaw motion in and close to the linear range
of handling behavior. Only if the actual response of vehicle 10
significantly deviates from the desired response, the active brake
control is activated in addition to the steering control.
[0141] While the embodiments of the present invention disclosed
herein are presently considered to be preferred, various changes
and modifications can be made without departing from the spirit and
scope of the invention. The scope of the invention is indicated in
the appended claims, and all changes that come within the meaning
and range of equivalents are intended to be embraced therein.
* * * * *