CN109849898B  Vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC  Google Patents
Vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC Download PDFInfo
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 CN109849898B CN109849898B CN201811615282.0A CN201811615282A CN109849898B CN 109849898 B CN109849898 B CN 109849898B CN 201811615282 A CN201811615282 A CN 201811615282A CN 109849898 B CN109849898 B CN 109849898B
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Abstract
The invention discloses a vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC, which comprises the steps of establishing a vehicle twodegreeoffreedom linear model as a prediction model, and calculating by using the prediction model to obtain an ideal yaw angular velocity and an ideal centroid slip angle; detecting by using a sensor to obtain each realtime data, and calculating by using a genetic algorithm hybrid optimization GPC (phase change memory) method aiming at each realtime data to obtain an optimal additional yaw moment; the optimal additional yaw moment is distributed into the driving forces of four wheels of the fourwheel independent driving hub motor electric automobile by adopting a method for regularly distributing the driving forces of the left and right wheels, and the driving forces act on the wheels one by one. Compared with the common generalized prediction algorithm, the algorithm provided by the invention has the advantages that the genetic algorithm is introduced to carry out hybrid optimization in the rolling optimization process of GPC, so that the algorithm has stronger global search capability and global convergence, the required additional yaw moment is subjected to hybrid optimization, and the optimal solution precision is greatly improved.
Description
Technical Field
The invention relates to the field of safe auxiliary driving and intelligent control, in particular to a method for controlling the stability of an electric automobile with fourwheel independent driving hub motors.
Background
The operation stability of the automobile is an important performance influencing the highspeed safe driving of the automobile, when the automobile encounters the interference of external factors (such as lateral wind), road surface separation driving, highspeed emergency obstacle avoidance and the like, the automobile deviates from an ideal vehicle operation characteristic, and in severe cases, a driver loses the control on the automobile and is in a dangerous situation, and a Yaw Stability Control (YSC) system can correct the automobile to the ideal operation characteristic and control the automobile from an unstable area to a stable area. The yaw stability control system has gained wide acceptance in society as an active safety device with great potential for development.
Currently, various research institutions have conducted a great deal of research on yaw stability control, and common methods are optimal control, such as LQR and LQG, but these control methods all need accurate control models, while an automobile is a complex nonlinear system, and the models often need to be simplified in engineering use, so that the accuracy of the models is difficult to guarantee; in addition, when the vehicle is running, parameters and environment have great uncertainty, so that the optimal control obtained according to an ideal model cannot be kept optimal in practice, and sometimes, the quality is even seriously reduced.
Disclosure of Invention
The invention provides a vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC for avoiding the defects in the prior art, and the method is used for performing hybrid optimization on the obtained additional yaw moment and improving the optimal solution precision.
The invention adopts the following technical scheme for solving the technical problems:
the invention discloses a vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC, which is characterized by comprising the following steps of:
step 1: establishing a twodegreeoffreedom linear model of the vehicle as a prediction model, and calculating by using the prediction model to obtain an ideal yaw angular velocity and an ideal centroid slip angle;
step 2: the method comprises the steps that a sensor is used for detecting to obtain each piece of realtime data, the realtime data comprise the steps that a yaw velocity sensor is used for detecting in real time to obtain the actual yaw velocity of a vehicle, a vehicle speed sensor is used for detecting in real time to obtain the actual running velocity of the vehicle, a steering angle sensor is used for detecting in real time to obtain the actual front wheel turning angle of the vehicle, and the optimal additional yaw moment is calculated and obtained by aiming at each piece of realtime data through a genetic algorithm hybrid;
and step 3: and distributing the optimal additional yaw moment into the driving forces of four wheels of the fourwheel independent drive hub motor electric automobile by adopting a regular distribution method of the driving forces of the left and right wheels, and acting on each wheel in a onetoone correspondence manner.
The vehicle yaw stability control method based on the genetic algorithm hybrid optimization GPC is also characterized in that:
in the step 1, the ideal yaw rate and the ideal centroid slip angle are obtained by the following calculation:
step 1.1: establishing a twodegreeoffreedom linear model of the vehicle characterized by equation (1) based on two degrees of freedom of lateral motion and yaw motion of the vehicle:
β is the side slip angle of the mass center,is the centroid yaw angular velocity, r is the yaw angular velocity,yaw angular acceleration;
l_{1}is the distance of the center of mass to the front axis,/_{2}Is the distance from the center of mass to the rear axis; k is a radical of_{1}For front wheel cornering stiffness, k_{2}Is rear wheel cornering stiffness;
I_{z}is moment of inertia, m is the mass of the whole vehicle, σ_{f}Is the angle of rotation of the front wheel, v_{d}The vehicle speed, M is the additional yaw moment;
make the front wheel turn angle sigma_{f}Obtaining a transfer function F(s) of a twodegreeoffreedom linear model of the vehicle characterized by equation (2) according to equation (1):
r(s) is the Laplace transform of the yaw rate R,
m(s) is the laplace transform of the additional yaw moment M, s representing the complex variable in the transfer function F(s);
discretizing the transfer function F(s) into a discrete transfer function F (z) characterized by equation (3) using a bilinear transformation:
r (z) is a ztransform of the yaw rate R,
m (z) is the ztransform of the additional yaw moment M, z representing the complex variable in the discrete transfer function F (z);
T_{0}is a sampling period;
n_{0}＝T_{0} ^{2}(a_{11}a_{22}+a_{12}a_{21})2T_{0}(a_{11}+a_{22})+4；n_{1}＝2T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})8；
n_{2}＝T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})+2T_{0}(a_{11}+a_{22})+4；
step 1.2, the ideal centroid side deflection angle beta is calculated_{d}is set to 0, i.e. β_{d}0; calculating the ideal yaw rate r of the vehicle at the k + j moment represented by the formula (4) by utilizing an automobile dynamics theory_{d}(k+j)：
K is a factor of stability,
v_{d}(k + j) is the vehicle speed at time k + j; sigma_{f}(k + j) is the vehicle front wheel steering angle at time k + j;
j is 1,2, … n, n is a prediction period, k +1 represents the time k +1, k +2 represents the next time of k +1, and k + j represents the next time of k + j1; g is the gravity acceleration, l is the vehicle wheelbase, and u is the road adhesion coefficient.
The vehicle yaw stability control method based on the genetic algorithm hybrid optimization GPC is also characterized in that: the step 2 is to obtain the optimal additional yaw moment according to the following processes:
step 2.1: converting a discrete transfer function F (z) characterized by equation (3) to equation (5):
R(z)(n_{0}+n_{1}z^{1}+n_{2}z^{2})＝M(z)(m_{0}+m_{1}z^{1}+m_{2}z^{2}) (5)
step 2.2: according to a GPC control algorithm, introducing a loss map equation into the equation (5) to obtain a predicted value r of the yaw rate at the moment k + j represented by the equation (6)_{e}(k+j)：
r_{e}(k+j)＝F_{j}(z^{1})r(k)+G_{j}(z^{1})ΔM(k+j1) (6)
r (k) is an actual value of yaw rate at the time k detected by the yaw rate sensor;
F_{j}(z^{1}) And G_{j}(z^{1}) Are all polynomials in the chartlet equation;
delta M (k + j1) is the increment of the actual value of the additional yaw moment at the moment k + j1 and the moment k + j2;
according to the GPC principle, given that a prediction period N and a control period N are integers, the vector expression form of the predicted value of the yaw rate is as shown in formula (7):
R＝GΔM+f (7)
in formula (7):
R＝[r_{e}(k+1),r_{e}(k+2),…,r_{e}(k+n)]^{T}；
ΔM＝[ΔM(k),ΔM(k+1),…,ΔM(k+N1)]^{T}；
f＝HΔM(k)+Fr(k)＝[f(k+1),f(k+2),…,f(k+n)]^{T}；
H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) To deplot the polynomials in the equation,
g_{0},g_{1},...g_{n1}is a polynomial G_{j}(z^{1}) Polynomial coefficient of (5);
step 2.3: the optimized performance indicator function J (k) at time k is characterized by equation (8):
in the formula (8), λ is a control weight constant,
and combining the formula (7) and the formula (8), and obtaining the vector representation form of the additional yaw moment increment by using a rolling optimization method according to the formula (9):
ΔM＝(G^{T}G+λI)^{1}G^{T}(R_{D}f) (9)
in the formula: r_{D}＝[r_{d}(k+1),r_{d}(k+2),…,r_{d}(k+n)]^{T}(10)
I is a unit vector; r is_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) is an ideal yaw rate at each sampling time in the prediction period n obtained by calculation using equation (4);
step 2.4: at each sampling moment in the prediction period n, respectively acquiring and obtaining the front wheel rotation angle sigma by using a sensor_{f}And vehicle speed v_{d}The ideal yaw rate r at each sampling instant in the prediction period n is obtained by calculation using equation (4)_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) and obtaining R characterized by formula (10)_{D}(ii) a Then G is obtained by calculation by utilizing the equation of the loss of the pattern_{j}(z^{1})、H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) And F_{j}(z^{1}) A value of (d); finally, the value of the additional yaw moment M (k) at the time k, which is characterized by equation (11), is obtained by calculation using equation (9):
M(k)＝M(k1)+g^{T}(R_{D}f) (11)
in formula (11), g^{T}Is represented by (G)^{T}G+λI)^{1}G^{T}A first row vector of (a);
step 2.5: optimizing the value of the additional yaw moment M (k) through a genetic algorithm to obtain the optimal additional yaw moment value M_{m}(k)。
The vehicle yaw stability control method based on the genetic algorithm hybrid optimization GPC is also characterized in that: the step 3 specifically includes:
the vehicle fourwheel drive torquefourwheel drive force relationship is characterized by equation (12):
F_{1}and T_{1}Left front wheel drive force and drive torque, F_{2}And T_{2}Respectively a right front wheel driving force and a driving torque,
F_{3}and T_{2}Driving force and torque of the left rear wheel, F_{4}And T_{4}Respectively is a right rear wheel driving force and a driving moment;
b is the radius of the wheel;
vehicle fourwheel drive torque and given target drive torque T_{obj}Is characterized by equation (13):
T_{obj}＝T_{1}+T_{2}+T_{3}+T_{4}(13)
setting the optimal additional yaw moment value M_{m}(k) The following rules are assigned:
when M is_{m}(k) When the vehicle is in a neutral steering state, the fourwheel driving force is distributed according to the average distribution principle as shown in the formula (14):
F_{1}＝F_{2}＝F_{3}＝F_{4}(14)
when M is_{m}(k)>At 0, the vehicle is in a left understeer or right oversteer condition, and the redistributed fourwheel drive torque characterized by equation (15) is obtained by combining equation (12) equation (14):
when M is_{m}(k)<At 0, the vehicle is in an understeer or oversteer right state, and the redistributed fourwheel drive torque characterized by equation (16) is obtained by combining equation (12) equation (14):
setting the optimal additional yaw moment value M_{m}(k) Four wheels of electric automobile with hub motor driven by four wheels independentlyThe driving forces of (a) are applied to the respective wheels in a onetoone correspondence.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention introduces the genetic algorithm to carry out the hybrid optimization method in the rolling optimization process of GPC, so that the algorithm has stronger global search capability and global convergence, and carries out the hybrid optimization on the obtained additional yaw moment, thereby greatly improving the accuracy of the optimal solution.
2. The genetic algorithm hybrid optimization GPC of the invention combines multistep prediction and selfadaptation, so that the method is more suitable for uncertain, timevarying, timelag and other process objects.
Drawings
FIG. 1 is a two degree of freedom linear model of a vehicle in the method of the present invention;
FIG. 2 is a control block diagram of genetic algorithm hybrid optimized GPC in the method of the present invention;
FIG. 3 is a control flow diagram of genetic algorithm hybrid optimized GPC in the method of the present invention;
Detailed Description
The vehicle yaw stability control method based on the genetic algorithm hybrid optimization GPC in the embodiment is carried out as follows:
step 1: a twodegreeoffreedom linear model of the vehicle shown in figure 1 is established as a prediction model, and an ideal yaw angular velocity and an ideal centroid slip angle are calculated and obtained by using the prediction model.
In the specific implementation, the ideal yaw angular velocity and the ideal centroid slip angle are obtained by calculation according to the following processes:
step 1.1: establishing a twodegreeoffreedom linear model of the vehicle characterized by equation (1) based on two degrees of freedom of lateral motion and yaw motion of the vehicle:
β is the side slip angle of the mass center,is the sideslip angular velocity of the mass center,r is the yaw rate of the vehicle,yaw angular acceleration;
l_{1}is the distance of the center of mass to the front axis,/_{2}Is the distance from the center of mass to the rear axis; k is a radical of_{1}For front wheel cornering stiffness, k_{2}Is rear wheel cornering stiffness;
I_{z}is moment of inertia, m is the mass of the whole vehicle, σ_{f}Is the angle of rotation of the front wheel, v_{d}The vehicle speed, M is the additional yaw moment;
make the front wheel turn angle sigma_{f}Obtaining a transfer function F(s) of a twodegreeoffreedom linear model of the vehicle characterized by equation (2) according to equation (1):
r(s) is the Laplace transform of the yaw rate R,
m(s) is the laplace transform of the additional yaw moment M, s representing the complex variable in the transfer function F(s);
discretizing the transfer function F(s) into a discrete transfer function F (z) characterized by equation (3) using a bilinear transformation:
r (z) is a ztransform of the yaw rate R,
m (z) is the ztransform of the additional yaw moment M, z representing the complex variable in the discrete transfer function F (z);
T_{0}is a sampling period;
n_{0}＝T_{0} ^{2}(a_{11}a_{22}+a_{12}a_{21})2T_{0}(a_{11}+a_{22})+4；n_{1}＝2T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})8；
n_{2}＝T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})+2T_{0}(a_{11}+a_{22})+4。
step 1.2, in order to ensure the control performance of the system, the ideal mass center slip angle beta is set_{d}is set to 0, i.e. β_{d}0; while the steadystate yawrate response is taken as the ideal yawrate. The ideal yaw rate r of the vehicle at the time k + j represented by the formula (4) is obtained by calculation using the theory of vehicle dynamics by correcting the road adhesion condition in consideration of the restriction thereof_{d}(k+j)：
K is a factor of stability,
v_{d}(k + j) is the vehicle speed at time k + j; sigma_{f}(k + j) is the vehicle front wheel steering angle at time k + j;
j is 1,2, … n, n is a prediction period, k +1 represents the time k +1, k +2 represents the next time of k +1, and k + j represents the next time of k + j1; g is the gravity acceleration, l is the vehicle wheelbase, and u is the road adhesion coefficient.
Step 2: the method comprises the steps that a sensor is used for detecting to obtain each realtime data, including the steps that a yaw velocity sensor is used for detecting in real time to obtain the actual yaw velocity of a vehicle, a vehicle speed sensor is used for detecting in real time to obtain the actual running velocity of the vehicle, and a steering angle sensor is used for detecting in real time to obtain the actual front wheel turning angle of the vehicle; for each realtime data, an optimal additional yaw moment is calculated by using a genetic algorithm hybrid optimization GPC method according to a control block diagram shown in FIG. 2.
In the specific implementation, the optimal additional yaw moment is obtained according to the following processes:
step 2.1: converting a discrete transfer function F (z) characterized by equation (3) to equation (5):
R(z)(n_{0}+n_{1}z^{1}+n_{2}z^{2})＝M(z)(m_{0}+m_{1}z^{1}+m_{2}z^{2}) (5)
step 2.2: according to a GPC control algorithm, introducing a loss map equation into the equation (5) to obtain a predicted value r of the yaw rate at the moment k + j represented by the equation (6)_{e}(k+j)：
r_{e}(k+j)＝F_{j}(z^{1})r(k)+G_{j}(z^{1})ΔM(k+j1) (6)
r (k) is an actual value of yaw rate at the time k detected by the yaw rate sensor;
F_{j}(z^{1}) And G_{j}(z^{1}) Are all polynomials in the chartlet equation;
delta M (k + j1) is the increment of the actual value of the additional yaw moment at the moment k + j1 and the moment k + j2;
the expression of the charpy in this embodiment is as shown in formulas (61) and (62)
E_{j}(z^{1})(n_{0}+n_{1}z^{1}+n_{2}z^{2})Δ+z^{j}F_{j}(z^{1})＝1 (61)
E_{j}(z^{1})(m_{0}+m_{1}z^{1}+m_{2}z^{2})＝G_{j}(z^{1})+z^{j}H_{j}(z^{1}) (62)
In the formula:
E_{j}(z^{1})＝1+e_{1}z^{1}+...+e_{j1}z^{(j1)}，E_{j}(z^{1}) Is a polynomial of e_{1}...e_{j}Is E_{j}(z^{1}) A polynomial coefficient of (d);
F_{j}(z^{1})＝f_{0} ^{j}+f_{1} ^{j}z^{1}+f_{2} ^{j}z^{2}，F_{j}(z^{1}) Is a polynomial of f_{0}，f_{1}，f_{2}Is F_{j}(z^{1}) A polynomial coefficient of (d);
G_{j}(z^{1})＝g_{0}+g_{1}z^{1}+...+g_{j1}z^{(j1)}，G_{j}(z^{1}) Is a polynomial of g_{0}...g_{j1}Is G_{j}(z^{1}) A polynomial coefficient of (d);
H_{j}(z^{1})＝h_{0} ^{j}+h_{1} ^{j}z^{1}，H_{j}(z^{1}) Is a polynomial of h_{0}，h_{1}Is H_{j}(z^{1}) A polynomial coefficient of (d);
Δ＝1z^{1}is a difference operator;
according to the GPC principle, given that a prediction period N and a control period N are integers, the vector expression form of the predicted value of the yaw rate is as shown in formula (7):
R＝GΔM+f (7)
in formula (7):
R＝[r_{e}(k+1),r_{e}(k+2),…,r_{e}(k+n)]^{T}；
ΔM＝[ΔM(k),ΔM(k+1),…,ΔM(k+N1)]^{T}；
f＝HΔM(k)+Fr(k)＝[f(k+1),f(k+2),…,f(k+n)]^{T}；
H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) To deplot the polynomials in the equation,
g_{0},g_{1},...g_{n1}is a polynomial G_{j}(z^{1}) Polynomial coefficient of (5);
step 2.3: since the ideal centroid slip angle is 0, only the following of the yaw velocity is considered, the actual value of the yaw velocity is measured by the yaw velocity sensor, the optimization performance index at the time k is a quadratic objective function containing the error of the actual value of the yaw velocity to the expected value and an additional yaw moment weighting term, and the optimization performance index function J (k) at the time k is characterized by the equation (8):
in the formula (8), λ is a control weight constant,
and combining the formula (7) and the formula (8), and obtaining the vector representation form of the additional yaw moment increment by using a rolling optimization method according to the formula (9):
ΔM＝(G^{T}G+λI)^{1}G^{T}(R_{D}f) (9)
in the formula: r_{D}＝[r_{d}(k+1),r_{d}(k+2),…,r_{d}(k+n)]^{T}(10)
I is a unit vector; r is_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) is an ideal yaw rate at each sampling time in the prediction period n obtained by calculation using equation (4);
step 2.4: at each sampling moment in the prediction period n, respectively acquiring and obtaining the front wheel rotation angle sigma by using a sensor_{f}And vehicle speed v_{d}The ideal yaw rate r at each sampling instant in the prediction period n is obtained by calculation using equation (4)_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) and obtaining R characterized by formula (10)_{D}(ii) a Then G is obtained by calculation by utilizing the equation of the loss of the pattern_{j}(z^{1})、H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) And F_{j}(z^{1}) A value of (d); finally, the value of the additional yaw moment M (k) at the time k, which is characterized by equation (11), is obtained by calculation using equation (9):
M(k)＝M(k1)+g^{T}(R_{D}f) (11)
in the formula g^{T}Is represented by (G)^{T}G+λI)^{1}G^{T}A first row vector of (a);
step 2.5: optimizing the value of the additional yaw moment M (k) through a genetic algorithm, including population initialization, selection, intersection and mutation operations to obtain the optimal additional yaw moment value M_{m}(k) (ii) a Genetic algorithm mixtureThe control flow for cooptimized GPC is shown in fig. 3.
And step 3: the optimal additional yaw moment is distributed into the driving forces of four wheels of the fourwheel independent driving hub motor electric automobile by adopting a method for regularly distributing the driving forces of the left and right wheels, and the driving forces act on the wheels one by one.
The method specifically comprises the following steps:
the vehicle fourwheel drive torquefourwheel drive force relationship is characterized by equation (12):
F_{1}and T_{1}Left front wheel drive force and drive torque, F_{2}And T_{2}Respectively a right front wheel driving force and a driving torque,
F_{3}and T_{2}Driving force and torque of the left rear wheel, F_{4}And T_{4}Respectively is a right rear wheel driving force and a driving moment;
b is the radius of the wheel;
vehicle fourwheel drive torque and given target drive torque T_{obj}Is characterized by equation (13):
T_{obj}＝T_{1}+T_{2}+T_{3}+T_{4}(13)
setting the optimal additional yaw moment value M_{m}(k) The following rules are assigned:
set positive to the left in the direction of travel of the vehicle, i.e. corresponding to a positive additional yaw moment M_{m}(k) Then negative to the right, corresponding to a negative additional yaw moment M_{m}(k) (ii) a The steering wheel angle is set to be positive to the left and negative to the right. The vehicle fourwheel drive torque is directly provided by the fourwheel drive motor output torque.
When M is_{m}(k) When the vehicle is in a neutral steering state, the fourwheel driving force is distributed according to the average distribution principle as shown in the formula (14):
F_{1}＝F_{2}＝F_{3}＝F_{4}(14)
when M is_{m}(k)>At 0, the vehicle is in a left understeer or right oversteer condition, i.e.: when the steering wheel turns left, the vehicle is in a left understeer state; or the steering wheel angle to the right, the vehicle is in a righthand oversteer condition, in which the lefthand wheel drive torque is appropriately decreased and the righthand wheel drive torque is increased, i.e., the lefthand wheel is decreased by 1/4 of the additional yaw moment and the righthand wheel is increased by 1/4 of the additional yaw moment, and the redistributed fourwheel drive torque represented by equation (15) is obtained by combining equation (12) equation (14):
when M is_{m}(k)<At 0, the vehicle is in an understeer or oversteer right state, i.e.: when the steering wheel turns to the left, the vehicle is in a left oversteer state; or the steering wheel angle to the right, the vehicle is in an understeer right state, when the left wheel drive torque is appropriately increased and the right wheel drive torque is decreased, i.e., the left wheel is increased by 1/4 of the additional yaw moment and the right wheel is decreased by 1/4 of the additional yaw moment, the redistributed fourwheel drive torque represented by equation (16) is obtained by combining equation (12) equation (14):
will optimize the additional yaw moment value M_{m}(k) The driving force of four wheels of the electric automobile with the fourwheel independent driving hub motor is distributed and acts on each wheel in a onetoone correspondence mode.
Claims (2)
1. A vehicle yaw stability control method based on genetic algorithm hybrid optimization GPC is characterized by comprising the following steps:
step 1: establishing a twodegreeoffreedom linear model of the vehicle as a prediction model, and calculating by using the prediction model according to the following process to obtain an ideal yaw angular velocity and an ideal centroid slip angle;
step 1.1: establishing a twodegreeoffreedom linear model of the vehicle characterized by equation (1) based on two degrees of freedom of lateral motion and yaw motion of the vehicle:
β is the side slip angle of the mass center,is the centroid yaw angular velocity, r is the yaw angular velocity,yaw angular acceleration;
l_{1}is the distance of the center of mass to the front axis,/_{2}Is the distance from the center of mass to the rear axis; k is a radical of_{1}For front wheel cornering stiffness, k_{2}Is rear wheel cornering stiffness;
I_{z}is moment of inertia, m is the mass of the whole vehicle, σ_{f}Is the angle of rotation of the front wheel, v_{d}The vehicle speed, M is the additional yaw moment;
make the front wheel turn angle sigma_{f}Obtaining a transfer function F(s) of a twodegreeoffreedom linear model of the vehicle characterized by equation (2) according to equation (1):
r(s) is the Laplace transform of the yaw rate R,
m(s) is the laplace transform of the additional yaw moment M, s representing the complex variable in the transfer function F(s);
discretizing the transfer function F(s) into a discrete transfer function F (z) characterized by equation (3) using a bilinear transformation:
r (z) is a ztransform of the yaw rate R,
m (z) is the ztransform of the additional yaw moment M, z representing the complex variable in the discrete transfer function F (z);
T_{0}is a sampling period;
n_{0}＝T_{0} ^{2}(a_{11}a_{22}+a_{12}a_{21})2T_{0}(a_{11}+a_{22})+4；n_{1}＝2T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})8；
n_{2}＝T_{0} ^{2}(a_{11}a_{22}a_{12}a_{21})+2T_{0}(a_{11}+a_{22})+4；
step 1.2, the ideal centroid side deflection angle beta is calculated_{d}is set to 0, i.e. β_{d}0; calculating the ideal yaw rate r of the vehicle at the k + j moment represented by the formula (4) by utilizing an automobile dynamics theory_{d}(k+j)：
K is a factor of stability,
v_{d}(k + j) is the vehicle speed at time k + j; sigma_{f}(k + j) is the vehicle front wheel steering angle at time k + j;
j is 1,2, … n, n is a prediction period, k +1 represents the time k +1, k +2 represents the next time of k +1, and k + j represents the next time of k + j1; g is the gravity acceleration, l is the vehicle wheelbase, and u is the road surface adhesion coefficient;
step 2: the method comprises the following steps of utilizing a sensor to detect and obtain each realtime data, wherein the realtime data comprises the steps of utilizing a yaw velocity sensor to detect and obtain the actual yaw velocity of a vehicle in real time, utilizing a vehicle speed sensor to detect and obtain the actual running velocity of the vehicle in real time, utilizing a steering angle sensor to detect and obtain the actual front wheel turning angle of the vehicle in real time, and aiming at each realtime data, utilizing a genetic algorithm to optimize a GPC method to calculate and obtain the optimal additional yaw moment according to the following processes:
step 2.1: converting a discrete transfer function F (z) characterized by equation (3) to equation (5):
R(z)(n_{0}+n_{1}z^{1}+n_{2}z^{2})＝M(z)(m_{0}+m_{1}z^{1}+m_{2}z^{2}) (5)
step 2.2: according to a GPC control algorithm, introducing a loss map equation into the equation (5) to obtain a predicted value r of the yaw rate at the moment k + j represented by the equation (6)_{e}(k+j)：
r_{e}(k+j)＝F_{j}(z^{1})r(k)+G_{j}(z^{1})ΔM(k+j1) (6)
r (k) is an actual value of yaw rate at the time k detected by the yaw rate sensor;
F_{j}(z^{1}) And G_{j}(z^{1}) Are all polynomials in the chartlet equation;
delta M (k + j1) is the increment of the actual value of the additional yaw moment at the moment k + j1 and the moment k + j2;
according to the GPC principle, given that a prediction period N and a control period N are integers, the vector expression form of the predicted value of the yaw rate is as shown in formula (7):
R＝GΔM+f (7)
in formula (7):
R＝[r_{e}(k+1),r_{e}(k+2),…,r_{e}(k+n)]^{T}；
ΔM＝[ΔM(k),ΔM(k+1),…,ΔM(k+N1)]^{T}；
f＝HΔM(k)+Fr(k)＝[f(k+1),f(k+2),…,f(k+n)]^{T}；
H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) To deplot the polynomials in the equation,
g_{0},g_{1},...g_{n1}is a polynomial G_{j}(z^{1}) Polynomial coefficient of (5);
step 2.3: the optimized performance indicator function J (k) at time k is characterized by equation (8):
in the formula (8), λ is a control weight constant,
and combining the formula (7) and the formula (8), and obtaining the vector representation form of the additional yaw moment increment by using a rolling optimization method according to the formula (9):
ΔM＝(G^{T}G+λI)^{1}G^{T}(R_{D}f) (9)
in the formula: r_{D}＝[r_{d}(k+1),r_{d}(k+2),…,r_{d}(k+n)]^{T}(10)
I is a unit vector; r is_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) is an ideal yaw rate at each sampling time in the prediction period n obtained by calculation using equation (4);
step 2.4: at each sampling moment in the prediction period n, respectively acquiring and obtaining the front wheel rotation angle sigma by using a sensor_{f}And vehicle speed v_{d}The ideal yaw rate r at each sampling instant in the prediction period n is obtained by calculation using equation (4)_{d}(k+1),r_{d}(k+2),...,r_{d}(k + n) and obtaining R characterized by formula (10)_{D}(ii) a Then G is obtained by calculation by utilizing the equation of the loss of the pattern_{j}(z^{1})、H_{1}(z^{1}),H_{2}(z^{1})...H_{n}(z^{1}) And F_{j}(z^{1}) A value of (d); finally, the value of the additional yaw moment M (k) at the time k, which is characterized by equation (11), is obtained by calculation using equation (9):
M(k)＝M(k1)+g^{T}(R_{D}f) (11)
in formula (11), g^{T}Is represented by (G)^{T}G+λI)^{1}G^{T}A first row vector of (a);
step 2.5: optimizing the value of the additional yaw moment M (k) through a genetic algorithm to obtain the optimal additional yaw moment value M_{m}(k)；
And step 3: and distributing the optimal additional yaw moment into the driving forces of four wheels of the fourwheel independent drive hub motor electric automobile by adopting a regular distribution method of the driving forces of the left and right wheels, and acting on each wheel in a onetoone correspondence manner.
2. The method for vehicle yaw stability control based on hybrid optimized GPC of genetic algorithms according to claim 1, characterized in that: the step 3 specifically includes:
the vehicle fourwheel drive torquefourwheel drive force relationship is characterized by equation (12):
F_{1}and T_{1}Left front wheel drive force and drive torque, F_{2}And T_{2}Respectively a right front wheel driving force and a driving torque,
F_{3}and T_{2}Driving force and torque of the left rear wheel, F_{4}And T_{4}Respectively is a right rear wheel driving force and a driving moment;
b is the radius of the wheel;
vehicle fourwheel drive torque and given target drive torque T_{obj}Is characterized by equation (13):
T_{obj}＝T_{1}+T_{2}+T_{3}+T_{4}(13)
setting the optimal additional yaw moment value M_{m}(k) The following rules are assigned:
when M is_{m}(k) When the vehicle is in a neutral steering state, the fourwheel driving force is distributed according to the average distribution principle as shown in the formula (14):
F_{1}＝F_{2}＝F_{3}＝F_{4}(14)
when M is_{m}(k)>At 0, the vehicle is in a left understeer or right oversteer condition, and the redistributed fourwheel drive torque characterized by equation (15) is obtained by combining equation (12) equation (14):
when M is_{m}(k)<At 0, the vehicle is in an understeer or oversteer right state, and the redistributed fourwheel drive torque characterized by equation (16) is obtained by combining equation (12) equation (14):
setting the optimal additional yaw moment value M_{m}(k) The driving force of four wheels of the electric automobile with the fourwheel independent driving hub motor is distributed and acts on each wheel in a onetoone correspondence mode.
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