Self-learning collaborative control method for active steering and yaw moment
The present disclosure provides a self-learning collaborative control method for active steering and yaw moment for a motor vehicle, including a first step of constructing fundamental formulas which are stored in a vehicle ECU, and a second step of calculating an active steering angle δ C and a yaw moment M c on line by the vehicle ECU according to following sub-steps during a driving process of the motor vehicle, and controlling a driving state of the motor vehicle according to δ C and M c . The second step includes a first sub-step of collecting raw real-time parameter values, a second sub-step of performing calculation by the identifier and the control target reference model, a third sub-step of calculating δ C and M c . The present disclosure can realize the self-learning collaborative control of active steering and yaw moment without requiring a system control model and correct a driver's steering operation.
1. A self-learning collaborative control method for active steering and yaw moment for a motor vehicle, the motor vehicle having a vehicle ECU connected to a vehicle speed sensor for acquiring a vehicle speed v x , a steering angle sensor for acquiring a steering angle δ f of a driver, a yaw rate sensor for acquiring a yaw rate γ, and a center of mass slip angle sensor for acquiring a center of mass slip angle β;
each sensor being conventionally arranged, wherein the steering angle sensor is arranged on a steering shaft of a steering wheel of the motor vehicle, and the yaw rate sensor and the center of mass slip angle sensor are arranged on the center of mass of the motor vehicle;
a constant K 1 representing an identification gain, a constant Γ representing an online learning gain, time constants τ r and τ β , a vehicle mass m, a distance l f from the center of mass to a front axle, a distance l r from the center of mass to a rear axle, and a constant K 2 representing a control gain being stored in the vehicle ECU; wherein the method comprises:
a first step, constructing fundamental formulas which are stored in the vehicle ECU, comprising an identifier, a control target reference model, and a controller, wherein the fundamental formulas comprises Formulas 1 to 15;
the first step comprises a first sub-step of constructing Formula 1 and Formula 2, and Formula 1 is a parameterized neural network: {dot over (x)}=−ax+ωσ(x)+λu; wherein x=[β, γ] T ∈R 2 is a 2-dimensional column vector in a real number field R, β is the center of mass slip angle in rad, γ is the yaw rate in rad/s, a∈R 2×2 is a 2-by-2 matrix in the real number field R, ω∈R 2×2 is a 2-by-2 matrix in the real number field R, σ(x) is a sigmoidal activation function in the neural network and σ(x)=[σ(x 1 ), σ(x 2 )] T , λ∈R 2×2 is a 2-by-2 matrix in the real number field R, u=[S c , M c ] T ∈R 2 is a 2-dimensional column vector in the real number field R; δ C is an active steering angle in rad; M c is a yaw moment in N·m; and δ C and M c are final calculation results used to control the motor vehicle;
Formula 2 is obtained by rewriting Formula 1: {dot over (x)}=θ T ψ, wherein θ=[a, w, λ] T , ψ=[x,σ(x), u] T ;
the first step comprises a second sub-step of designing the identifier and an online self-learning rate, and constructing Formula 3 and Formula 4;
Formula 3 is the identifier used to implement a system identification: {circumflex over (x)}={circumflex over (θ)}ψ+K 1 e 1 ;
wherein e 1 =x−{circumflex over (x)} represents an identification error, {circumflex over (x)} represents an identification state, {circumflex over (θ)}=[{circumflex over (α)},ŵ,{circumflex over (λ)}] T represents an identification parameter, K 1 >0 is a constant obtained by trial and error and stored in the vehicle ECU, representing the identification gain; {circumflex over (θ)} is an identification result of Formula 3 and is provided to Formula 7;
Formula 4 is the online self-learning rate: {dot over ({circumflex over (θ)})}=Γψe 1 wherein Γ is a constant obtained by trial and error and is stored in the vehicle ECU, Γ>0, and Γ represents the online learning gain;
the first step comprises a third sub-step of constructing the control target reference model expressed by Formula 5 to generate a target tracking signal;
Formula 5 is: {dot over (x)} r =A r x r +E r δ f ; wherein x r is a reference state, and x r =[β r γ r ] T , β r is a target center of mass slip angle, γ r is a target yaw rate, and β r and γ r are calculation results of Formula 5 and serve as the target tracking signals;
A
r
=
[
-
1
τ
β
0
0
-
1
τ
r
]
,
,
wherein:
τ
β
=
a
1
2
a
2
1
-
a
1
1
a
2
2
a
1
2
(
a
2
1
f
1
-
a
1
1
f
2
)
,
τ
γ
=
a
1
2
a
2
1
-
a
1
1
a
2
2
a
2
2
(
a
2
1
f
1
-
a
1
1
f
2
)
·
k
γ
,
k
γ
=
a
2
1
f
1
-
a
1
1
f
2
a
1
1
a
2
2
-
a
1
2
a
2
1
a
1
1
=
C
f
+
C
r
mv
x
,
a
1
2
=
C
f
l
f
-
C
r
l
r
m
v
x
2
-
1
,
a
2
1
=
C
f
l
f
-
C
r
l
r
I
z
,
a
2
2
=
C
f
l
f
2
+
C
r
l
r
2
I
z
v
x
,
f
1
=
-
C
f
m
v
x
,
f
2
=
-
C
f
l
f
I
z
;
I Z is a vertical rotational inertia of the motor vehicle in kg·m 2 , which is determined by a vehicle manufacturer and stored in the vehicle ECU;
E
r
=
[
1
-
m
l
f
2
(
l
f
+
l
r
)
l
r
c
r
v
x
2
1
+
m
(
l
f
+
l
r
)
(
l
f
2
c
r
-
l
r
2
c
f
)
v
x
2
×
l
r
(
l
f
+
l
r
)
v
x
l
f
+
l
r
1
+
m
(
l
f
+
l
r
)
(
l
f
2
c
r
-
l
r
2
c
f
)
v
x
2
]
m is the vehicle mass in kg; I f is the distance from the center of mass to the front axle in meters; l r is the distance from the center of mass to the rear axle in meters, v x is the vehicle speed obtained by the vehicle speed sensor in m/s; C f is a front wheel cornering stiffness in N/rad; C r is a rear wheel cornering stiffness in N/rad;
the first step comprises a fourth sub-step of constructing the controller expressed by Formula 6 based on an approximate dynamic programming theory to achieve a self-learning collaborative control for active steering and yaw moment:
Formula 6 is the controller: u=u 1 +u 2 ; wherein u 1 is configured to ensure that a controlled steady-state error converges to zero, and u 1 is expressed by Formula 7: u 1 =λ ⊕ [({dot over (x)}−αx−wσ(x)−K 2 e 2 ]; wherein λ ⊕ represents a generalized inverse of λ,
e
2
=
x
-
x
r
=
[
β
-
β
r
γ
-
γ
r
]
=
[
e
β
e
r
]
represents a tracking error, x r is obtained from Formula 5, K 2 is obtained by trial and error and is stored as the constant representing the control gain in the vehicle ECU, and K 2 >0;
Formula 6 is configured to ensure an optimal control performance based on the approximate dynamic programming theory, and is obtained through Formulas 8 to 15;
Formula 8 is an evaluation function V:
V
(
e
2
)
=
min
u
2
∫
0
∞
[
e
2
T
(
τ
)
Q
e
2
(
τ
)
+
u
2
T
(
τ
)
P
u
2
(
τ
)
]
d
τ
;
wherein Q∈R 2×2 is a 2-by-2 diagonal matrix in the real number field R representing a weight for optimizing and controlling the tracking error e 2 in the evaluation function, which is obtained through trial and error and is stored in the vehicle ECU; P∈R 2×2 is a 2-by-2 diagonal matrix in the real number field R representing a weight for optimizing and controlling u 2 in the evaluation function, which is obtained through trial and error and is stored in the vehicle ECU;
Formula 9 is a Hamiltonian function: H(e 2 , u 2 , ∇V(e 2 ))=(∇V(e 2 )) T (−K 2 e 2 +{circumflex over (λ)}u 2 )+e 2 T Qe 2 +u 2 T Pu 2 ; wherein
∇
V
(
e
2
)
=
∂
V
(
e
2
)
e
2
represents a partial derivative of V with respect to e 2 , and an optimal evaluation function V is approximated with the neural network in Formula 10;
Formula 10 is: V(e 2 )=W v T σ(e 2 ); wherein W v is an ideal weight vector, and σ(e 2 ) is the sigmoidal activation function in the neural network;
Formula 11 is derived from Formula 10:
∇
V
(
e
2
)
=
∂
V
(
e
2
)
e
2
=
(
∇
σ
(
e
2
)
)
T
W
V
+
∇
ε
;
a Hamiltonian function, that is, Formula 12 is obtained by substituting Formula 11 into Formula 9: H(e 2 , u 2 , ∇V(e 2 ))=W V T ∇σ(e 2 )(−K 2 e2+{circumflex over (λ)}u 2 )+e 2 T Qe 2 +u 2 T Pu 2 ;
Formula 13 is obtained by making a left side of Formula (12) equal to zero: M=W V T N; wherein M=−e 2 T Qe 2 −u 2 T Pu 2 , and N=∇σ(e 2 )(−K 2 e 2 +{circumflex over (λ)}u 2 );
Formula 14 is obtained through a principle of least squares method: W v =(N T N) −1 N T M; and
Formula 15 is obtained by solving Formula (12): u 2 =−½P −1 {circumflex over (λ)} T (∇σ(e 2 )) T W V ; and
a second step, during a driving process of the motor vehicle, calculating values of the active steering angle δ C and the yaw moment M c online by the vehicle ECU according to the following sub-steps, and controlling an operating state of the motor vehicle according to the calculation results of δ C and M c .
2. The method according to claim 1 , wherein the second step comprises a first sub-step of collecting raw real-time parameter values, comprising a value of the steering angle δ f measured by the steering angle sensor when the driver is steering the wheel, a value of the vehicle speed v x from the vehicle speed sensor, a value of the center of mass slip angle β from the center of mass slip angle sensor, and a value of the yaw rate γ from the yaw rate sensor.
3. The method according to claim 2 , wherein the second step comprises a second sub-step of performing calculation by the identifier and the control target reference model, comprising:
providing the value of the center of mass slip angle β and the value of the yaw rate γ to the identifier expressed by Formula 3 by the vehicle ECU, and performing a calculation to obtain {circumflex over (θ)} as a basis for calculating a value of u 1 in Formula 6;
providing {circumflex over (θ)} to Formula 7 to calculate the value of u 1 required by Formula 6; and
providing the value of the steering angle δ f and the value of the vehicle speed v x to the control target reference model expressed by Formula 5 by the vehicle ECU, and performing a calculation to obtain a value of the target center of mass slip angle β r and a value of the target yaw rate γ r as basis for calculating e 2 required for u 1 and u 2 in Formula 6.
4. The method according to claim 3 , wherein the second step comprises a third sub-step of providing β r , γ r and {circumflex over (θ)} to the controller expressed by Formula 6 by the vehicle ECU, and performing a calculation to obtain the active steering angle δ C and the yaw moment M c through Formulas 6 to 15;
controlling, by the vehicle ECU, a rotation of a steering wheel of the motor vehicle according to the active steering angle δ C obtained in real time, and controlling a braking action of a baker of the motor vehicle according to the yaw moment M c obtained in real time;
repeating the second step to achieve an online model-free self-learning collaborative control for active steering and yaw moment.