US20020143451A1

US20020143451A1 - Integrated control of active tire steer and brakes

Info

Publication number: US20020143451A1
Application number: US09/769,676
Authority: US
Inventors: Aleksander Hac; Hsien Chen; Edward Bedner; Steven Loudon
Original assignee: Delphi Automotive Systems LLC
Current assignee: BWI Co Ltd SA
Priority date: 2001-01-25
Filing date: 2001-01-25
Publication date: 2002-10-03
Anticipated expiration: 2021-01-25
Also published as: US6453226B1

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.

Description

FIELD OF THE INVENTION

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

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

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.

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.

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.

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.

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.

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.

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

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; [0010]
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; [0011]
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; [0012]
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; [0013]
FIG. 2 is a block diagram of one embodiment of a coordinated control system in accordance with the present invention; [0014]
FIG. 3 is a block diagram of one embodiment of a vehicle reference model of FIG. 2 in accordance with the present invention; [0015]
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; [0016]
FIG. 5 is a block diagram of one embodiment of a surface coefficient estimator in accordance with the present invention; [0017]
FIG. 6 is a block diagram of one embodiment of a side slip velocity estimator in accordance with the present invention; [0018]
FIG. 7 is a block diagram of one embodiment of a vehicle level brake/steer controller in accordance with the present invention; and [0019]
FIG. 8 is a graph of a lateral tire force vs. a tire slip angle in accordance with the present invention. [0020]

DETAILED DESCRIPTION OF THE PRESENTLY PREFERRED EMBODIMENTS

Referring to FIGS. [0021] 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.
For example, when [0022] vehicle 10 is being driven straight as illustrated in FIG. 1A, a brake force F_xcan be applied to front right tire 13 to generate corrective yaw moment ΔM_z1in a clockwise direction about vertical axis 17. Corrective yaw moment ΔM_z1can be computed by the following equation (1):
ΔM _z1 =F _x*(t _w/2) (1)
where t[0023] _wis a track width. In a linear range of tire operation, brake force F_xcan be approximated by the following equation (2):
F _x =C _x *λ=C _x*(Δv_lr1 /v) (2)
where C[0024] _xis a tire longitudinal stiffness; λ is a brake slip; Δv_lr1is 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):
ΔM _z1 =C _x*(t _w/2)*Δv_lr1 /v (3)
As illustrated in FIG. 1B, [0025] tire 12 and tire 13 can also be controlled to generate corrective yaw moment ΔM_z2as a function of incremental front steering angle Δδ_f. Corrective yaw moment ΔM_z2can be computed by the following equation (4):
ΔM _z2 =F _y1 *a (4)
where a is the distance from [0026] axis 17 to front axle 11; and F_y1is 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 _y1=2*C _y*Δδ_f (5)
where C[0027] _yis a cornering stiffness coefficient of both tire 12 and tire 13. Thus, corrective yaw moment ΔM_z2can also be computed by the following equation (6):
ΔM _z2=2*C _y *a*Δδ _f (6)
Equating yaw moment ΔM[0028] _z2to yaw moment ΔM_z1can be accomplished by computing front steering angle Δδ_funder the following equation (7) with the assumption that tire longitudinal stiffness coefficient C_xand tire lateral stiffness C_yare approximately equal:
Δδ_f=(C _x *t _w/(4*C _y *a))*(ΔV _lr1 /v)≈[t _w/(4*a)]*(ΔV _lr1 /v) (7)
Also by example, when [0029] vehicle 10 is being driven straight as illustrated in FIG. 1C, brake force F_xcan be applied to rear right tire 16 to generate corrective yaw moment ΔM_z3in a clockwise direction about vertical axis 17. Corrective yaw moment ΔM_z3can be computed by equation (1). In a linear range of tire operation, brake force F_xcan be approximated by the following equation (8):
F _x =C _x λ*=C _x*(ΔV _lr2 /v) (8)
where C[0030] _xis a tire longitudinal stiffness; λ is a brake slip; ΔV_lr2is 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):
ΔM _z3 =C _x*(t _w/2)*ΔV _lr2 /v (9)
As illustrated in FIG. 1D, [0031] tire 15 and tire 16 can also be controlled to generate corrective yaw moment ΔM_z4as a function of incremental rear steering angle Δδ_r. Corrective yaw moment ΔM_z4can be computed by the following equation (10):
ΔM _z4 =F _y2 *b (10)
where b is the distance from [0032] axis 17 to rear axle 14; and F_y2is 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 _y2=−2*C _y *Δδr (11)
where C[0033] _y1is a cornering stiffness coefficient of both tire 15 and tire 16. Thus, corrective yaw moment ΔM_z4can also be computed by the following equation (12):
ΔM _z4=−2*C _y *a*Δδ _r (12)
Equating yaw moment ΔM[0034] _z4to yaw moment ΔM_z3can be accomplished by computing rear steering angle Δδ_runder the following equation (13) with the assumption that tire longitudinal stiffness coefficient C_xand tire lateral stiffness C_yare approximately equal:
Δδ_r =−[C _x *t _w/(4*C _y *b)]*(Δv _lr2 /v)≈−[t _w/(4*b)]*(Δv _lr2 /v) (13)
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 ΔV[0035] _lr1to generate corrective yaw moment ΔM_z1and/or to generate corrective yaw moment ΔM_z2when vehicle 10 has an active front steering system, and selectively utilizes tire speed differential signal ΔV_lr2to generate corrective yaw moment ΔM_Z3and/or corrective moment ΔM_z4when vehicle 10 has an active rear steering system.
Referring to FIG. 2, an integrated active steering and [0036] 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.
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 [0038] vehicle 10 including, but not limited to, a driver steering wheel angle signal δ_SWA, a front steering wheel angle signal δ_f, a rear steering wheel angle signal δ_r, a vehicle yaw rate signal Ω, a lateral acceleration signal a_y, a wheel speed signal W_S1(from tire 12), a wheel speed signal W_S2(from tire 13), a wheel speed signal W_S3(from tire 15), a wheel speed signs WS_S4(from tire 16), and an estimated vehicle speed signal V_x.
[0039] Reference model 20 inputs driver steering wheel angle signal δ_SWA, lateral acceleration signal a_y, and estimated vehicle speed signal v_xfrom vehicle 10. Alternative to lateral acceleration signal a_y, reference model 20 can input an estimated surface coefficient of adhesion signal μ_efrom estimator 30. In response to the inputted signals, reference model 20 provides signals indicative of a feedforward front steering angle correction signal δ_fdrl, a feedforward rear steering angle correction signal δ_rff, a desired yaw rate signal Ω_dl, a desired lateral velocity signal v_yd, and a desired slip angle signal β_d.
[0040] Estimator 30 inputs front steering wheel angle signal δ_f, rear steering wheel angle signal δ_r, vehicle yaw rate signal Ω, lateral acceleration signal a_y, and estimated vehicle speed signal v_xfrom vehicle 10. Estimator 30 further inputs desired yaw rate signal Ω_dlfrom reference model 20. In response to the inputted signals, estimator 30 provides an estimated surface coefficient of adhesion signal μ_e, an estimated lateral velocity signal V_ye, and an estimated slip angle signal β_e.
Vehicle level brake/[0041] steer controller 40 inputs front steering wheel angle signal δ_f, rear steering wheel angle signal δ_r, vehicle yaw rate signal Ω, lateral acceleration signal a_yand estimated vehicle speed signal v_xfrom vehicle 10. Controller 40 further inputs desired yaw rate signal Ω_d, desired lateral velocity signal v_yd, and desired slip angle signal β_efrom reference model 20; and estimated surface coefficient of adhesion signal lie, estimated lateral velocity signal v_ye, and estimated slip angle signal β_efrom estimator 30. In response to the inputted signals, controller 40 provides a desired speed differential signal Δv_lr3tindicating 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 δ_ftd1indicative of a desired steering angle of front axle 11 (FIGS. 1A-1D), and a desired rear steering angle signal δ_rtd1indicative of a desired steering angle of rear axle 14 (FIGS. 1A-1D).
[0042] Controller 40 only provides desired speed differential signal Δv_lr3tand desired front steering angle δ_ftd1for alternative embodiments of vehicle 10 only having a front active steering system.
[0043] Actuator controller 50 inputs desired speed differential signal Δv_lr3t, desired front steering angle signal δ_ftd1, and desired rear steering angle signal δ_rtd1from controller 40. Controller 50 further inputs front steering wheel angle signal δ_f, rear steering wheel angle signal δ_r, wheel speed signal W_S1, wheel speed signal W_S2, wheel speed signal W_S3, and wheel speed signal W_S4from vehicle 10. In response to the inputted signals, actuator controller 50 compares desired tire speed differential signal Δv_lr3tto either a speed differential between tire 12 and tire 13 (FIGS. 1A-1D) as indicated by wheel speed signs WS_S1and wheel speed signs WS_S2as 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_S3and wheel speed signs WS_S4as would occur to those having ordinary skill in the art. The result is a corrective braking signal T_bthat 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_bas would occur to those having ordinary skill in the art.
[0044] Actuator controller 50 compares desired front steering angle signal δ_ftd1and front steering wheel angle signal δ_fas would occur to those with ordinary skill in the art, and compares desired rear steering angle signal δ_rtd1and rear steering wheel angle signal δ_ras would occur to those with ordinary skill in the art to thereby provide a corrective front steering signal T_fsand a corrective rear steering signal T_rsto 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_fsand 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_rs.
Referring to FIG. 3, one embodiment of [0045] reference model 20 in accordance with the present invention is shown. A block 21 converts steering wheel angle signal δ_SWAinto a corresponding angle of front tires signal δ_fdras computed by the following equation (14):
δ_fdr=δ_SWA * K _f(v _x) (14)
where K[0046] _f(v_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_f(v_x) may be speed dependent, for example decreasing with speed to promote maneuverability at low speeds and stability at high speeds.
A [0047] block 22 determines a feedforward part of a steering angle correction by limiting a magnitude of front tire steering angle δ_fdrto a reasonable level. A desired value of lateral acceleration is computed from the following equation (15):
a _yd=(v _x ²*δ_fdr)/(L+K _u * v _x ²) (15)
where L is a vehicle tirebase and K[0048] _uis an understeer coefficient. It follows from equation (15) that in order to limit a magnitude of this acceleration to a reasonable level a_ydmax(an example value of a_ydmaxis 12 m/s²), a magnitude of steering angle δ_fdrhas to be limited in accordance with the following equation (16):
[δ_fmax]=[a_ydmax]*(L+K _u *v _x ²)/v _x ² (16)
This limiting can be interpreted as adding a feedforward term to the steering angle δ[0049] _fff, as given by the following equation (17): $\begin{matrix} δ_{fff} = {\begin{matrix} 0 & if \langle δ_{fdr} \rangle \leq δ_{f \max} (v_{x}) \\ [δ_{f \max} (v_{x}) - \langle δ_{fdr} \rangle * sign (δ_{fdr}) & if \langle δ_{fdr} \rangle > δ_{f \max} (v_{x}) \end{matrix} & (17) \end{matrix}$
After the limitation, front steering angle δ[0050] _fdrldesired by the driver is computed from the following equation (18):
δ_fdrl=δ_fdr+δ_fff (18)
When [0051] vehicle 10 is equipped with a traditional steering mechanism, the ratio K_fdoes not depend on speed of vehicle 10 and the limitation of the steering angle cannot be performed, (i.e. δ_fdrl=δ_fdr).
A [0052] block 23 determines a feedforward part of the rear tire steering angle δ_rffas computed from the following equation (19):
δ_rff=δ_fdr * K _rff(v _x) (19)
where K[0053] _rff(V_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_yssis computed by the following equation (20):
v _yss=[(v _x*δ_fdrl)/(L+K _u * v _x ²)]*{b−M*a*v _x ²/(C _r *L)+K _rff(v _x)*[a+M*b*v _x ²/(C _f *L)]} (20)
where M is mass of [0054] 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_fand C_rare 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_yssequal zero, a feedforward gain K_rff′(v_x) is computed by the following equation (21):
K _rff′(v _x)=−[b−M*a*v _x ²/(C _r *L)]/[a+M*b*v _x ²/(C _r *L)] (21)
Feedforward gain K[0055] _rff′(v_x) is illustrated in FIG. 4 as curve 1. Gain K_rff′(v_x) is negative for small speeds and positive for large speeds and it changes sign at a velocity v_xcgiven by the following equation (22):
v _xc =[C _r *L*b/(M*a)]^½ (22)
Thus, the sign of the rear tire steering angle δ[0056] _rffis opposite to that of the front steering angle δ_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_rff′(v_x) given by equation (21) would require too large rear tire steering angle δ_rff, which is typically limited to several degrees. Also, yaw rate Ω 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_rff′(v _x) can be multiplied by a factor η, which is less than 1 in accordance with the following equation (23):
K _rff″(v _x)=−η*[b−M*a*v _x ²/(C _r *L)]/[a+M*b*v _x ²/(C _f *L)] (23)
with a reasonable value of η=0.4 (the optimal value for a given application depends on the range of steering angle for [0057] rear tires 15 and 16). Gain K_rff″(v_x) given by equation (23) is represented by curve 2 in FIG. 4.
According to equation (22), a velocity v[0058] _xcat which gain K_rffchanges sign depends on cornering stiffness C_rof rear tires 15 and 16. On slippery surfaces, the value of the cornering stiffness C_r, and the characteristic velocity v_xc(at which gain K_rffcrosses zero) will be reduced. If the gain determined by equation (23) with the nominal values of cornering stiffness coefficient C_rthat 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_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_rffis chosen to be 0 for speed between approximately 0.4*v_xcand v_xc, as illustrated by curve 3 in FIG. 4.
A [0059] block 24 determines a steady state desired values of yaw rate Ω_dssand side slip velocity v_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 δ_rffmust 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 δ_frepresent 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 Ω_dssand side slip velocity v_ydsscan be computed from the following equations (24) and (25):
Ω_dss=[1−K _rff(v _x)]*v _x*δ_fdrl /[L+K _u *v _x ²] (24)
v _ydss=[(v _x*δ_fdrl)/(L+K _u * v _x ²)]*{b−M*a*v _x ²/(C _r *L)+K _rff(v _x)*[a+M*b*v _x ²/(C _f *L)]} (25)
In the equations (24) and (25), an understeer coefficient K[0060] _udepends on the magnitude of lateral acceleration a_y. When vehicle 10 is without active rear tire steer, feedforward gain K_rff=0. Since yaw rate Ω and side slip velocity v_yare 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 Ω can be computed from the following equation (26):
Ω_dmax =g/v _x (26)
where g is acceleration of gravity. The limited value of a desired yaw rate Ω[0061] _dsslcan be computed from the following equation (27): $\begin{matrix} Ω_{dssl} = {\begin{matrix} Ω_{dss} & if \langle Ω_{dss} \rangle \leq g / v_{x} \\ (g / v_{x}) * sign (Ω_{dss}) & if \langle Ω_{dss} \rangle > g / v_{x} \end{matrix} & (27) \end{matrix}$
The limited value of lateral velocity v[0062] _ydsslcan be computed from the following equation (28):
v _ydssl=[Ω_dss/(1−K _rff)]*{b−M*a*v _x ²/(C _r *L)+K _rff *[a+M*b*v _x ²/(C_f *L)]} (28)
A [0063] block 25 receives steady state yaw rate Ω_dssland lateral velocity V_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 δ_fdrland desired yaw rate Ω_dand between front steering angle δ_fdrland desired lateral velocity v_ydcan be computed by the following equations (29) and (30):
G _Ω(s)=Ω_d(s)/δ_fdrl(s)=(C _f /M)*[s−z _Ω(v _x)]/[s²+2*ζ(v _x)*ω_n(v _x)*s+ω_n ²(v_x)] (29)
G _vy(s)=v _yd(s)/δ_fdrl(s)=(a*C _f /I _zz)*[s−z _vy(v _x)]/[s²+2*ζ(v _x )*ω _n(v _x)*s+ω _n ²(v _x)] (30)
In equations (29) and (30), s is the Laplace operand, I[0064] _zzis the moment of inertia of vehicle 10 about axis 17, z_Ω(v_x) and z_vy(v_x) are zeros of the corresponding transfer functions, ζ(v_x) is the damping coefficient, and ω_n(v_x) is the undamped natural frequency.
When [0065] vehicle 10 has active rear tire steer, the zeros of the transfer functions depend on feedforward gain K_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 _Ω(s)=(Ω_dss/δ_fss)*G _Ω′(s) (31)
G _vy(s)=(v _yss/δ_fss)*G _vy′(s) (32)
Where [0066]
G _ω′(s)=[−ω_n ²(v _x)/z_ω(v _x) ]*[s−z _ω(v _x)]/[s²+2*ζ(v _x)*ω_n(v _x)*s+ω _n ²(v _x)] (33)
G _vy′(s)=[−ω_n ²(v _x)/z _vy(v _x)]*[s−z _vy(v _x)]/[s ²+2*ζ(v _x)*ω_n(v _x)*s+ω _n ²(v _x)] (34)
Thus, the dynamic values of the desired yaw rate Ω[0067] _dand lateral velocity v_ydcan 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_Ω′(s) and G_vy′(s).
In a [0068] block 26, the values of desired yaw rate Ω_dand side slip velocity v_ydare 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 _f(s)=a _f(v _x)/[s+a _f(v _x)] (35)
in which a filter parameter a[0069] _f(v_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.
The desired values of yaw rate Ω[0070] _dand lateral velocity v_ydobtained 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 μ_Lor a magnitude of lateral acceleration a_y. In the first case, a limited value of desired yaw rate Ω_dlis computed from the 20 following equation (36): $\begin{matrix} Ω_{dl} = {\begin{matrix} Ω_{d} & if \langle Ω_{d} \rangle \leq μ_{L} * g / v_{x} \\ (μ_{L} * g / v_{x}) * sign (Ω_{d}) & if \langle Ω_{d} \rangle > μ_{L} * g / v_{x} \end{matrix} & (36) \end{matrix}$
If the magnitude of lateral acceleration a[0071] _yis used by block 27, the limited desired yaw rate Ω_dlis computed from the following equation (37): $\begin{matrix} Ω_{dl} = {\begin{matrix} Ω_{d} & if \langle Ω_{d} \rangle \leq (\langle a_{y} \rangle + Δ a_{y}) / v_{x} \\ [(\langle a_{y} \rangle + Δ a_{y}) / v_{x}] * sign (Ω_{d}) & if \langle Ω_{d} \rangle > (\langle a_{y} \rangle + Δ a_{y}) / v_{x} \end{matrix} & (37) \end{matrix}$
where Δa[0072] _yis a constant positive value, for example 2 m/s². The magnitude of desired lateral velocity V_ydis limited by the value obtained from equation (26) with the desired yaw rate at steady state Ω_dssreplaced by the limited desired yaw rate Ω_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):
β_d=Arctan(v _yd /v _x) (38)
Referring to FIG. 5, an embodiment of estimator [0074] 30 (FIG. 2) for estimating surface coefficient of adhesion μ_eis shown. A block 31 performs preliminary calculations. First, it is recognized that the most robust signal available is yaw rate Ω, and an entry and an exit conditions are dependent mainly on a yaw rate error, i.e. a difference between the desired yaw rate Ω_dland measured yaw rate Ω, and to a lesser extent on measured lateral acceleration a_y(entry condition only). Thus, a yaw rate error is calculated and filtered, and lateral acceleration a_yis filtered.
Second, when vehicle [0075] 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_yfiltto a maximum lateral acceleration a_ymaxthat vehicle 10 can sustain on dry pavement as shown in the following equation (39):
μ_L_temp=|a _yfilt‘|/a _ymax (39)
where μ[0076] _L_temp is a temporary estimate of surface coefficient of adhesion in the lateral direction, and a_yfiltis 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.
A [0077] 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 μ_Lfrom measured lateral acceleration a_y. This estimate is calculated by identifying one of the following three conditions.
First, entry conditions are tested during a stage S[0078] 1. 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 μ_Lequal to temporary estimate of surface coefficient of adhesion μ_L_temp as calculated by equation (37).
Second, exit conditions are tested during a stage S[0079] 3. 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 μ_Lto a default value of 1.
Third, when neither the entry conditions nor the exit conditions are met, a stage S[0080] 5 holds coefficient of adhesion μ_Lunchanged from a previous value (i.e. holding conditions). The only exception is when the magnitude of measured lateral acceleration a_yexceeds the maximum value predicted using currently held estimate. In this case, stage S5 calculates coefficient of adhesion μ_Las if vehicle 10 was in an entry condition.
The entry conditions are met during stage S[0081] 1 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 Ω_dand the measured yaw rate Ω being greater than a threshold as computed in the following equation (40):
|Ω_d−Ω|_filt >Yaw _— Threshold1 (40)
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): [0082]
|Ω_d−Ω|_filt >Yaw _— Threshold2 for Te seconds (41)
where Yaw_Threshold2 depends on the magnitude of desired yaw rate Ω[0083] _dor measured yaw rate Ω. For example, Yaw_Threshold2=4 deg/s +5*|Ω_d|=0.07 rad/s+0.09*1|Ω_d|, where Ω_dis 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 Ω_dor measured yaw rate Ω.
The second condition is the signs of the filtered lateral acceleration a[0084] _yfiltland the weighted sum of yaw rate Ω and the derivative of yaw rate are the same in accordance with the following mathematical expression (42):
a _yfilt1*(Ω+Yaw _— Der _— Mult*dΩ/dt)>Sign _— Comp (42)
where Ω is the measured yaw rate and dΩ/dt is its derivative. The magnitude of the filtered lateral acceleration a[0085] _yfiltis limited from equation (43): $\begin{matrix} a_{yfiltl} = {\begin{matrix} a_{yfiltl} & if \langle a_{yfilt} \rangle \geq a_{y \min} \\ a_{y \min} * sign (Ω_{d}) & if \langle a_{yfilt} \rangle < a_{y \min} \end{matrix} & (43) \end{matrix}$
where a[0086] _yminis a constant with a typical value of 0.2 M/s². Thus if a_yfiltis very small in magnitude, it is replaced by the a_yminwith a sign the same as the desired yaw rate Ω_d. This limit is needed to improve estimation on very slick surfaces (e.g. ice) when the magnitude of lateral acceleration a_yis comparable to the effect of noise, so that the sign of a_yfiltcannot be established.
The recommended values in equation (42) for the constant Yaw_Der_Mult is 0.5 and for Sign_Comp is 0.035 (if Ω is in rad/s and dΩ/dt in rad/s[0087] ²).
In order to allow lateral acceleration a[0088] _yto fully build up at the beginning of maneuver and after each change in sign, before it can be used for estimation of surface coefficient μ_L, a condition is used that requires both the desired yaw rate Ω_dland lateral acceleration a_yto 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 Ω_dand lateral acceleration a_yhave had the same signs, a timer is introduced. In accordance with an equation (44), the timer becomes zero when the desired yaw rate Ω_dand lateral acceleration a_yhave opposite signs and counts the time that elapses from the moment the signs become and remain the same. $\begin{matrix} timer = {\begin{matrix} 0 when Ω_{d} * a_{yfiltl} < Ay_sign_comp \\ timer + loop_time otherwise \end{matrix} & (44) \end{matrix}$
where Ω[0089] _dis the desired yaw rate in [rad/s] and Ay_sign_comp is a constant with a typical value of 0.2 m/s³.
The third condition is either (1) the signs of the desired yaw rate Ω[0090] _dand measured lateral acceleration a_yare the same and they have been the same for some time in accordance with following equation (45):
timer>hold_time (45)
The hold_time in equation (42) can be 0.25 s, or (2) the magnitude of a derivative of lateral acceleration da[0091] _y/dt is less than a threshold in accordance with the following mathematical equation (46):
|da _y /dt|<Ay _— Der _— Thresh (46)
A recommended value of the threshold, Ay_Der_Thresh=2.5 m/s[0092] ³. The derivative da_y/dt is obtained by passing filtered lateral acceleration a_yfilthrough a high pass filter with a transfer function a_f*s/(s+a_f) with a typical value of a_f=6 rad/s.
The exit conditions are met during stage S[0093] 3 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):
|Ω_d−Ω|_filt ≦Yaw _— Threshold3 (47)
with a typical value of Yaw_Threshold3=0.10 rad/s. [0094]
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): [0095]
(|Ω_d−Ω|_filt)_filt <Yaw _— Treshold4 (48)
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[0096] _f/(s+a_f) with a_f=1.8 rad/s). The thresholds Yaw_Threshold3 and Yaw_Thereshold4 may depend on the magnitude of desired yaw rate Ω_dor the measured yaw rate Ω.
A [0097] block 33 corrects surface estimate μ_Lfor 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_yis not directly proportional to the surface coefficient of adhesion μ_LTo account for this effect, the surface estimate μ_L_temp computed from equation (37), is corrected using the following equation (49):
μ_L=μ_L_temp*(c ₁ +C ₂*μ_L_temp) (49)
where c[0098] ₁<1 and c₂=1−c₁, so that on dry surface μ_L=μ_L_temp=1, while on slippery surfaces μ_L<μ_L_temp. Example values are c₁=0.85 and C₂=0.15.
A [0099] block 34 limits surface estimate μ_Lfrom below by a value μ_Lmin(a typical value 0.07) and may be limited from above by μ_Lmax(a typical value 1.2). Surface estimate μ_lcan 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.
A [0100] block 35 estimates total surface coefficient of adhesion μ_eusing the following equation (50): $\begin{matrix} µ_{e} = {\begin{matrix} μ_{Lfilt} & when \langle a_{xe} \rangle \leq Ax_Dz \\ {{(μ_{Lfilt})}^{2} + {[(\langle a_{xe} \rangle - Ax_DZ) / a_{x \max}]}^{2}}^{1 / 2} & when \langle a_{xe} \rangle > Ax_Dz \end{matrix} & (50) \end{matrix}$
where Ax_Dz is the dead-zone applied to the estimated longitudinal acceleration (a typical value is 2m/s2) and a[0101] _xmaxis a maximum longitudinal deceleration which vehicle 10 can achieve on dry surface (a typical value is 9 m/s²). 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 μ_emin(typical value is 0.2) and from above by μ_emax(1.0).
The (unfiltered) estimate of surface coefficient in lateral direction, μ[0102] _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.
Referring to FIG. 6, an embodiment of estimator [0103] 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 δ_f, rear steering wheel angle signal δ_r, yaw rate signal Ω, estimated vehicle speed signal v_x, and the estimated lateral surface coefficient of adhesion μ_Lis shown. The slip angle estimation implements an iterative nonlinear closed loop observer to determine the estimated vehicle lateral velocity v_yeand slip angle β_e.
A [0104] 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):
α_fe =[v _ye(k−1)+a*Ω]/v _x−δ_f (51a)
α_re =[v _ye(k−1)−b*Ω]/v _x−δ_r (51b)
where v[0105] _ye(k−1) is the estimated lateral velocity from the previous iteration of the observer, and α_feand α_reare the estimated front and rear axle side slip angles, respectively. The steering angles δ_fand δ_rare the actual (measured) steering angles of front tires 12 and 13, and rear tires 15 and 16, respectively, including the corrective terms.
A [0106] block 37 of the observer estimates lateral forces F_yfeof the front axle 11 according to one of two functions as illustrated in the following equation (52): $\begin{matrix} F_{yfe} = {\begin{matrix} - C_{f} * α_{fe} * (1 - (b_{cf} * (\langle α_{fe} \rangle / μ_{L}))), & if \langle α_{fe} \rangle < μ_{L} * α_{f^{*}} \\ - N_{f^{*}} * (\langle α_{fe} \rangle / α_{fe}) * [μ_{L} + s_{f} * (\langle α_{fe} \rangle / α_{f^{*}} - μ_{L})] & if \langle α_{fe} \rangle \geq μ_{L} * α_{f^{*}} \end{matrix} & (52) \end{matrix}$
where s[0107] _fis a small non-negative number (the slope of the F_yf−α_fcurve at the limit of adhesion), e.g., s_f=0.05, and where α_f*is defined by the following equation (53):
α_f*=1/(2*b _cf,) (53)
where b[0108] _cfis defined by the following equation (54):
b _cf =C _f/(4*N _f), (54)
where N[0109] _fis defined by the following equation (55):
N _f* =M*b*(a _ymax+Δ_a)/(a+b) (55)
where a[0110] _ymaxis the maximum lateral acceleration that vehicle 10 can sustain on a dry surface in m/s²and Δ_ais a positive constant, e.g., Δ_a=0.5 m/s². M is the nominal value of the total vehicle mass.
The observer similarly estimates lateral forces F[0111] _yreof the rear axle 14 according to the following equation (56): $\begin{matrix} F_{yre} = {\begin{matrix} - C_{r} * α_{re} * (1 - b_{cr} * \langle α_{re} \rangle), & if \langle α_{re} \rangle < μ_{L} * α_{r^{*}} \\ - N_{r^{*}} * (\langle α_{re} \rangle / α_{re}) * [μ_{L} + s_{r} * (\langle α_{re} \rangle / α_{r^{*}} - μ_{L})] & if \langle α_{re} \rangle \geq μ_{L} * α_{r^{*}} \end{matrix} & (56) \end{matrix}$
where s[0112] _ris a small non-negative number, e.g., s_r=0.05 and where α_r*is defined by the following equation (57):
α_r*=1/(2*b _cr,) (57)
where b[0113] _cris defined by the following equation (58):
b _cr =C _r/(4*N _r*), (58)
where N[0114] _r*is defined by the following equation (59):
N _r* =M*a*(a _ymax+Δ_a)/(a+b). (59)
A [0115] 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)+Δt*{−(1+g ₂)*v _x*Ω+((1+g ₃)/M−a*g ₁ /I _zz) *F_yfe+[(1+g ₃)/M+b*g ₁ /I _zz ]*F _yre+(g ₂ −g ₃)*a _y −g ₄ *ΔA _yf} (60)
where ΔA[0116] _yis defined by the following equation (61):
ΔA _y =a _y−(F _yfe +F _yre)/M, (61)
and ΔA[0117] _yfis ΔA_ypassed through a first order digital low pass filter, for example, with a cut off frequency of 1 rad/s.
A [0118] block 39 of the observer uses state variable q(k) to determine estimates of lateral velocity v_yeand slip angle β_eusing equations (62) and (63):
v _ye(k)=[q(k)+g ₁*•_a]/(1+g ₂) (62)
β_e=Arctan[v _ye(k)/v _x]. (63)
The gains g[0119] ₁, g₂, g₃and g₄are 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_yeand the estimated slip angle β_eare the main outputs of the observer.
Referring to FIG. 7, one embodiment of [0120] 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 Δv_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 Δδ_fand front steering angle signal δ_fdr1(FIG. 2) to form the total front steering angle signal δ_ftdand in terms of a summation of rear steer angle correction signal Δδ_rand rear steering angle signal δ_rff(FIG. 2) to form the total desired rear steer angle signal δ_rtd. The magnitudes of total desired rear steer angle signal δ_rtdand the total desired front steering angle signal δ_ftdmay be subsequently limited to desired rear steering angle signal δ_rtd1and desired front steering angle signal δ_ftd1, respectively.
A [0121] block 41 calculates desired speed differential signal Δv_lr3, front steer angle correction signal Δδ_fand rear steer angle correction signal Δδ_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 Ω_d−Ω is the difference between the desired yaw rate signal Ω_dand measured yaw rate signal Ω. Similarly, the side slip velocity error is the difference between the desired side slip velocity signal v_ydand the estimated side slip velocity signal v_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_x, estimated surface coefficient of adhesion signal μ_e, and on the magnitude of the estimated vehicle slip angle error. Thus, for the delta velocity signal Δv_lr3, the control law equation (64) may be written as follows: $\begin{matrix} Δ v_{lr3} = k_{Ω p} (v_{x}, μ_{e}) * (Ω_{d} - Ω) + k_{Ω d} (v_{x}, μ_{e}) * d (Ω_{d} - Ω) / dt + k_{vyp} (v_{x}, μ_{e}, \langle β_{d} - β_{e} \rangle) * (v_{yd} - v_{ye}) + k_{vyd} (v_{x}, μ_{e}, \langle β_{d} - β_{e} \rangle) * d (v_{yd} - v_{ye}) / dt & (64) \end{matrix}$
where k[0122] _Ωp(v_x,μ_e) and k_Ωd(v_x,μ_e) are the proportional and derivative yaw rate gains, while k_vyp(v_x,μ_e, |β_d−β_e|) and k_vyd(V_x, μ_e, |μ_d−μ_e|) 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_Ωp(v_x,μ_e) and derivative yaw rate gain k_Ωd(v_x, μ_e) increase nearly proportionally with vehicle speed v_xand decrease as the estimated surface coefficient of adhesion μ_eincreases. The lateral velocity gains, k_vyp(v_x,μ_e, |β_d−β_e|) and k_vyd(v_x,μ_e, |β_d−β_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.
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. [0123]
As discussed earlier, differential speed signal Δv[0124] _lr3determined for the brake controller can be converted into equivalent steering angle correction signal Δδ_rfor rear axle 14 and front steering angle correction signal Δδ_ffor axle 12. Thus the feedback portions of the front or rear steering angles can be computed from equations (65) and (66):
Δδ_r =g _f(v _x, μ_e)*Δv _lr3 (65)
Δδ_f =g _r(v _x, μ_e)*Δv _lr3 (66)
where the gains can vary with speed and the estimated surface coefficient of adhesion. [0125]
[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 δ_f, control signal Δv_lr3and lateral acceleration signal a_yare 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 δ_fis in different direction from control signal Δv_lr3; or front steering angle signal δ_fand control signal Δv_lr3are in the same direction, but lateral acceleration signal a_yis 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 δ_fand control signal Δv_lr3have opposite signs (oversteer). In this case vehicle state is considered oversteer (i.e. oversteer overrides understeer if both are true).
The situation when [0128] vehicle 10 is plowing is identified when the magnitude of the desired yaw rate Ω_dis significantly larger than the magnitude of measured yaw rate Ω over a pre-defined period of time, and the measured yaw rate Ω is small. This can happen only on very slippery road surface. In this situation, we do not demand that front steering angle signal δ_f, control signal Δv_lr3and lateral acceleration signal a_yhave the same signs, in order to declare understeer, since lateral acceleration signal a_ymay be very small in magnitude.
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 [0129] front tires 12 and 13 (FIGS. 1A-1D) or rear tires 15 and 16 (FIGS. 1A-1D), then the control command Δv_lr3is 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 Δv_lr3is always applied to tire 12 and/or tire 13. The actual commanded differential speed signal Δv_lr3is 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 Ω, and the track width t_w. Thus, the target tire slip difference can be computed from equation (67):
Δv _lr3t =Δv _lr3 +t _w*Ω (67)
When the driver is not braking, the velocity difference between [0130] 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.
A [0131] block 43 tests entry and exits conditions for applying the brake command Δv_lr3tto vehicle 10. The brake command Δv_lr3tis 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_xmust be above a certain entry speed v_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_x, front steering angle signal δ_fand 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):
|Ω_d −Ω+k _e *d(Ω_d−Ω)/dt |>Ω _thresh(v_x, δ_f , steer_flag) (68)
where k[0132] _eis a constant and Ω_thresh(v_x, δ_f, steer_flag) is a threshold, which depends on the vehicle speed signal v_x, front steering angle signal δ_fand 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.
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. [0133]
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 [0134] block 44 determines total commanded targeted control valves. First, rear steering angle δ_rtdis computed as the sum of the feedforward part δ_rffand the feedback part Δδ_rin accordance with the following equation (69):
δ_rtd=δ_rff+Δδ_r (69)
If [0135] 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 α_rmax(μ_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 α_rmaxleads 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): $\begin{matrix} δ_{rtdl} = {\begin{matrix} (v_{ye} - b * Ω) / v_{x} - α_{r \max} & if δ_{rtd} < (v_{ye} - b * Ω) / v_{x} - α_{r \max} \\ (v_{ye} - b * Ω) / v_{x} + α_{r \max} & if δ_{rtd} > (v_{ye} - b * Ω) / v_{x} + α_{r \max} \\ δ_{rtd} & otherwise \end{matrix} & (70) \end{matrix}$
Similarly, the commanded front steer angle correction, Δδ[0136] _ftdconsists of the feedforward part δ_fffand the feedback part Δδ_fin accordance with following equation (71):
Δδ_ftd=δ_fff+Δδ_f (71)
The total desired steering angle δ[0137] _ftdis the sum of the steering angle correction and the angle commanded by the driver δ_fdras computed from the following equation (72):
δ_ftd=δ_fdr+Δδ_ftd (72)
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 δ[0138] _ftdis limited to by the following equation (73): $\begin{matrix} δ_{ftd1} = {\begin{matrix} (v_{ye} + a * Ω) / v_{x} - α_{f \max} & if δ_{ftd} < (v_{ye} + a * Ω) / v_{x} - α_{f \max} \\ (v_{ye} + a * Ω) / v_{x} + α_{f \max} & if δ_{ftd} > (v_{ye} + a * Ω) / v_{x} - α_{f \max} \\ δ_{ftd} & otherwise \end{matrix} & (73) \end{matrix}$
where α[0139] _fmax(μ_e) is a front tires slip angle corresponding to maximum lateral force. It is a function of the estimated surface coefficient of adhesion μ_e.
Thus, during normal vehicle operation, [0140] 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.
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. [0141]

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

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.