CN116552550A

CN116552550A - Vehicle track tracking control system based on parameter uncertainty and yaw stability

Info

Publication number: CN116552550A
Application number: CN202310480148.9A
Authority: CN
Inventors: 袁腾飞; 赵容晨; 谢海锋
Original assignee: Guizhou Education University
Current assignee: Guizhou Education University
Priority date: 2023-04-28
Filing date: 2023-04-28
Publication date: 2023-08-08

Abstract

The invention discloses a vehicle track tracking control system based on parameter uncertainty and yaw stability, which comprises an upper controller and a lower controller, wherein a three-degree-of-freedom vehicle dynamics model comprising transverse movement, yaw movement and longitudinal movement is established, the upper controller comprises a transverse path controller and a longitudinal speed tracking controller, the transverse path controller is used for calculating an expected front wheel corner and an expected rear wheel corner, the longitudinal speed tracking controller is used for calculating an expected acceleration, and the lower controller realizes the output of the upper controller through a steering system and a driving device. The invention combines the commonly used low-cost vehicle-mounted sensor with the mathematical model, thereby estimating and obtaining the yaw rate and the longitudinal speed of the vehicle; after the yaw stability control is applied to the transverse LQR controller, the path tracking precision is greatly improved, the yaw rate and the centroid side deviation angle are greatly reduced, and the riding comfort of a driver is improved to a certain extent.

Description

Vehicle track tracking control system based on parameter uncertainty and yaw stability

Technical Field

The invention relates to the technical field of unmanned vehicle control, in particular to an automatic control system considering vehicle yaw.

Background

The rapid increase of the automobile conservation amount causes a series of social problems, the traffic jam phenomenon is more serious than before, and the travel efficiency of people is reduced. The automatic driving vehicle can safely and efficiently complete the driving task set in advance under the condition of no manual intervention, so that traffic accidents and economic losses caused by misoperation of a driver are reduced. The current automatic vehicle control system or algorithm has the following technical defects:

firstly, for track tracking control, at present, the prior literature mainly aims at single transverse control or longitudinal control, ignores the coupling relation between transverse and longitudinal movement of an automobile, and the transverse and longitudinal directions are mutually influenced and mutually coupled in the process of movement of the automobile;

secondly, the yaw rate and the longitudinal speed of the vehicle change with time during running, and are difficult to be measured by common on-board sensors, and the existing literature mainly regards these parameters as known, which affects the effect of the controller to a certain extent, so that uncertainty of the vehicle state parameters is also a problem to be solved;

finally, when the vehicle runs on a road surface with a low adhesion coefficient (such as an ice-snow road surface), the side-slip phenomenon is caused by the fact that the lateral force of the tire is saturated, so that the accuracy of path tracking is seriously affected, and the problem of the tracking accuracy of the vehicle when the vehicle runs on a good road surface is mainly solved in the prior art, and the problem of stability is ignored.

Disclosure of Invention

The invention aims to solve the technical problems that: aiming at the problem that the existing automatic control system ignores the coupling relation between the transverse movement and the longitudinal movement of the automobile, the track tracking control algorithm considering the uncertainty of the vehicle state parameters and the yaw stability of the automobile is provided.

The technical scheme of the invention is as follows:

a vehicle trajectory tracking control system based on parameter uncertainty and yaw stability, comprising an upper controller and a lower controller, characterized in that: and establishing a three-degree-of-freedom vehicle dynamics model comprising transverse movement, yaw movement and longitudinal movement, wherein the upper-layer controller comprises a transverse path controller and a longitudinal speed tracking controller, the transverse path controller is used for calculating an expected front wheel corner and an expected rear wheel corner, the longitudinal speed tracking controller is used for calculating expected acceleration, and the lower-layer controller realizes the output of the upper-layer controller through a steering system and a driving device.

The upper controller also comprises an extended Kalman observer which is used for estimating the longitudinal vehicle speed and the yaw rate.

The reference track is generated by a fifth-order polynomial, and parameters of the reference track comprise: road curvature k _r Course angle θ of road _r Reference velocity v _r Transverse coordinate y of reference track _r Longitudinal coordinate x of reference track _r 。

Kinetic differential equation for vehicle dynamics model:

wherein m represents the vehicle mass, l _f And l _r Respectively the front and rear wheelbase of the vehicle, v _x And v _y A velocity component, a, representing the velocity V at the vehicle centroid along the X-axis and the Y-axis, respectively _x Is the longitudinal acceleration of the vehicle;is the yaw angle of the vehicle; />Is the yaw rate of the vehicle; delta _f For the front wheel steering angle C _af And C _ar The cornering stiffness of the front and rear tires, respectively; f (F) _yf And F _yr Representing the lateral forces of the front and rear tires, respectively; i _z Is the moment of inertia of the vehicle about the Z-axis.

Yaw rate of vehicleAnd longitudinal velocity v _x The state equation and the observation equation of (2) are:

in the method, in the process of the invention,is the yaw rate of the vehicle; beta is the centroid slip angle, which represents the angle of the centroid current speed relative to the longitudinal axis of the automobile; a, a _x Is the longitudinal acceleration of the vehicle; a, a _y Is the lateral acceleration of the vehicle; longitudinal vehicle speed and yaw rate are estimated using extended kalman filtering.

The longitudinal speed tracking controller is based on an MPC design, and the lateral path controller includes a tracking error model, an LQR-based lateral controller, and an SMC-based vehicle yaw stability controller.

The tracking error model includes:

the first derivative of heading error is:

in θ _r Is the course angle of the current moment on the target track;

the second derivative of heading error is:

since the road curvature is generally gentle, θ is ignored _r Obtaining a second derivative of the heading error:

the first derivative of the trajectory tracking bias is:

in the method, in the process of the invention,v _x ＝Vcosβ。

the second derivative of the trajectory tracking bias is:

the longitudinal movement of the vehicle may be represented by a first order inertial system:

wherein K is _s =1 denotes the system gain, τ _d Is a time constant, a _des Is the desired acceleration, a is the true acceleration of the car; combined standAnd writing it into a matrix form, a matrix form of the lateral tracking error can be obtained:

in the method, in the process of the invention,

the LQR-based transverse path controller establishes an optimal control performance evaluation function J of the linear quadratic regulator, as shown in the following formula:

wherein X is _k Is a state variable of the system; u (u) _k Is a control variable of the system; q and R are weighting matrices of state error and control quantity, respectively; determination of the weight matrix q=diag [28,4,1 ] by experiment]And r=10, when J is the minimum value, the control amount u is the desired front wheel steering angle.

The SMC-based vehicle yaw stability controller includes: whether the vehicle is unstable or not is judged by a yaw rate-lateral rate phase plane method,

control threshold of yaw rate:in the formula, -alpha _r,lim ≤α _r ≤α _r,lim ；

Vehicle lateral speed v _y Is defined by the threshold value of:

steady state yaw rate:

wherein L= (L) _f +l _r ) Representing the wheelbase of the automobile; k represents a stability factor, which can be represented by the following formula:

reference yaw rate and centroid slip angle:

wherein μ represents a road adhesion coefficient;

the system input is the deviation value of the centroid slip angle and the yaw rate, which can be expressed as:

the slip form surface selects the systematic input error, namely:

and (3) deriving a sliding mode surface:

the index approach rate is adopted:

where ε represents the boundary layer thickness and k represents the approach rate gain matrix.

The simultaneous solving can obtain the output variable as follows:

in the formula, u= [ delta ] _f δ _r ] ^T Selecting the rear wheel angle delta _r Is the final output of the controller.

The invention has the beneficial effects that:

1. after the longitudinal MPC controller is added into the transverse LQR controller, the path tracking precision is greatly improved, and the peak value of the transverse tracking error is reduced by 85%;

2. the vehicle state parameter estimator can combine a commonly used low-cost vehicle-mounted sensor with a mathematical model so as to estimate and obtain the yaw rate and the longitudinal speed of the vehicle, compared with the method of directly measuring the yaw rate and the longitudinal speed by using an expensive sensor, the vehicle-making cost can be greatly reduced by using the estimator, and compared with an inexpensive sensor, the noise and the calibration error can be reduced;

3. after yaw stability control is applied to the transverse LQR controller, the path tracking precision is greatly improved, the yaw rate and the centroid side deviation angle are greatly reduced, and the riding comfort of a driver is improved to a certain extent; after the yaw stability control is applied in the longitudinal and transverse coupling track tracking controllers, the change amplitude of the transverse path deviation is small, but the yaw rate peak value is reduced by more than 60%, and the centroid side deviation angle peak value is reduced by more than 90%.

Drawings

FIG. 1 is a system frame diagram of the present invention;

FIG. 2 is a schematic representation of a vehicle dynamics model of the present invention;

fig. 3 is a yaw stability envelope constraint schematic.

Detailed Description

The overall research framework of the present invention is shown in fig. 1. A hierarchical control architecture is proposed for constructing longitudinally and transversely coupled controllers of a track following control system, the overall objective of which is to calculate the desired front wheel steering angle and the desired acceleration, and to achieve this by means of corresponding actuators, eventually following a reference track, wherein the reference track is generated by a fifth order polynomial, as shown in the green part of fig. 1. The hierarchical control structure is composed of an upper controller and a lower controller. The upper-layer controller comprises a transverse path controller and a longitudinal speed tracking controller, and aims to calculate an expected front wheel rotation angle, an expected rear wheel rotation angle and an expected acceleration; the lower controller outputs the upper controller through the steering system and the driving device, and finally the track tracking task is realized. In addition, in order to solve the uncertainty problem of the longitudinal vehicle speed and the yaw rate caused by the longitudinal and transverse coupling relation, and simultaneously reduce the use cost of the vehicle-mounted sensor, an EKF (extended Kalman observer) observer is established to estimate the longitudinal vehicle speed and the yaw rate.

The working principle is as follows:

1. firstly, generating a reference track through a fifth-order polynomial, wherein parameters of the reference track comprise: road curvature k _r Course angle θ of road _r Reference velocity v _r Transverse coordinate y of reference track _r Longitudinal coordinate x of reference track _r 。

2. And secondly, the planned track information is transmitted to an upper controller, wherein the upper controller comprises a transverse controller and a longitudinal controller, and the extended Kalman observer is used as an auxiliary module for acquiring yaw rate and longitudinal speed parameters required by the controller. The following explains the principle of the lateral and longitudinal controllers:

2.1 kinetic model establishment

The dynamics model may reflect dynamics and motion characteristics of the vehicle, and the controller is designed based on a mathematical model of the vehicle, so that a transverse and longitudinal dynamics model of the vehicle needs to be established first. The kinetic model is shown in fig. 2.

The vehicle dynamics model is a three-degree-of-freedom (transverse movement, yaw movement and longitudinal movement) monorail dynamics model, and a force balance equation is established at the center of mass of the vehicle according to Newton's law, so that the following expression is obtained:

by analyzing the three-degree-of-freedom vehicle dynamics model, the front wheel rotation angle delta is assumed _f The smaller lateral force of the tyre is equal to the product of the cornering stiffness and the cornering angle of the tyre, so thatFront wheel slip angle +.>Rear wheel slip angle->Obtaining a kinetic differential equation:

wherein m represents the vehicle mass, l _f And l _r Respectively the front and rear wheelbase of the vehicle, v _x And v _y A velocity component, a, representing the velocity V at the vehicle centroid along the X-axis and the Y-axis, respectively _x Is the longitudinal acceleration of the vehicle;is the yaw angle of the vehicle; />Is the yaw rate of the vehicle; beta is the centroid slip angle, which represents the angle of the centroid current speed relative to the longitudinal axis of the automobile; delta _f Steering angle for front wheel; alpha _f And alpha _r Respectively representing the slip angle of the front tire and the rear tire; c (C) _af And C _ar The cornering stiffness of the front and rear tires, respectively; f (F) _yf And F _yr Representing the lateral forces of the front and rear tires, respectively; i _z Is the rotational inertia of the vehicle about the Z axis;

the first derivative of heading error is:

in θ _r Is the course angle of the current moment on the target track;

the second derivative of heading error is:

due to the first curvature of the roadIs generally gentler, thus ignoring theta _r Obtaining a second derivative of the heading error:

the first derivative of the trajectory tracking bias is:

in the method, in the process of the invention,

the second derivative of the trajectory tracking bias is:

wherein K is _s =1 denotes the system gain, τ _d Is a time constant, a _des Is the desired acceleration, a is the true acceleration of the car;

finally, obtaining a linear time-varying model of the transverse and longitudinal integrated controller:

in the method, in the process of the invention,representing the system state, u _i,t ＝[δ,a _des ] ^T The control input is represented as such,

2.2 State observer design

Two parameters involved in the kinetic model: the vehicle yaw rate and longitudinal speed, which are time-varying and are not readily measured by existing sensors, are estimated using a state observer.

From the geometrical relationship of FIG. 1, the vehicle front and rear wheel slip angle α _f 、α _r And centroid slip angle β can be expressed as:

by combining the dynamic differential equation described in 2.1, a state equation and an observation equation based on a three-degree-of-freedom nonlinear vehicle model can be obtained, as shown in the following formula:

in the method, in the process of the invention,is the yaw rate of the vehicle; a, a _x Is the longitudinal acceleration of the vehicle; a, a _y Is the lateral acceleration of the vehicle;

since the observer will use a discrete form, the state equation and the observation equation are discretized as shown in the following equation:

discretized state equations and observation equations are written as follows:

wherein x (k) = [ ω, β, v _x ] ^T Is a state variable, u (k) = [ delta ] _f ,a _x ] ^T Is an input variable, a _y Is an observation variable; w (W) _k And V _k Respectively, system noise and measurement noise, which are independent of each other and have zero mean value, W _k The variance is Q _k ，V _k The variance of (2) is R _k 。

For the nonlinear system equation, the longitudinal vehicle speed and the yaw rate are estimated by using the extended Kalman filter, and the state equation and the observation equation are required to be respectively linearized to obtain a jacobian matrix, wherein the jacobian matrix is shown in the following formula:

the extended Kalman filter includes a prediction step that first passes a state variable at time k-1 and an update stepPredicting the state variable +.>The prediction step is performed by the following formula:

prediction error covariance matrix P _k,k-1 Can be calculated by the following formula:

P _k,k-1 ＝FP _k-1 F ^T +Q ^k

in the updating step, kalman gain K is used _l Correcting state variablesThen calculate the state variable +.>The following formula is shown:

in the Kalman gain K _l Can be expressed as K _l ＝P _k,k-1 H ^T (HP _k,k-1 H ^T +R _k ) ^-1 ；

State error covariance matrix P _k Can be calculated by the following formula:

P _k ＝(I-K _l H)P _k,k - ₁

in which Q _k And R is _k Are gaussian white noise with zero mean value and mutually independent;

and a cyclic calculation prediction step and an updating step, wherein estimation results of the longitudinal vehicle speed and the yaw rate are obtained.

2.3 lateral controller design

LQR-based lateral controllers are designed.

Combined standAnd is written in a matrix form,a matrix form of the lateral tracking error can be obtained:

in the method, in the process of the invention,

the above represents a linear time-varying system, LQR is applicable to a discrete time model, and therefore, it is necessary to convert a continuous system into a discrete system, ignoring termsBy using the midpoint euler method and the forward euler method for the above equation and simplifying it, a discretized model of the lateral tracking error can be obtained as follows:

an optimal control performance evaluation function J of the linear quadratic regulator is established, and the optimal control performance evaluation function J is shown as the following formula:

wherein X is _k Is a state variable of the system; u (u) _k Is a control variable of the system; q and R are weighting matrices of state error and control quantity, respectively; determination of the weight matrix q=diag [28,4,1 ] by experiment]And r=10. When J is the minimum value, the control quantity u is the required front wheel steering angle;

taking the discretized transverse tracking error model as a constraint banding performance evaluation function to obtain a Lagrange control problem, wherein the Lagrange control problem is represented by the following formula:

in the method, in the process of the invention,representing a hamiltonian;

solving the Lagrange control problem can obtain a control variable u _k The following formula is shown:

wherein P is _k+1 Representing a solution to the Riccati equation, the Riccati equation can be expressed in the form:

order theThe control variable can be written in the form:

u _k ＝-KX _k

wherein K= [ K ] ₁ ,k ₂ ,k ₃ ,k ₄ ]Representing the gain of the linear quadratic regulator.

2.4 longitudinal controller design

An MPC-based longitudinal speed tracking controller is designed.

Model predictive control is applicable to discrete systems, and the discretized form of the longitudinal dynamics model is shown as follows:

in the method, in the process of the invention,T _s representing a sampling time;

the output equation for the longitudinal control system can be expressed as:

Π _k ＝[1,0]ξ _k

by punishing acceleration or acceleration rate of change to accurately and smoothly track the desired speed, a cost function is established as shown in the following equation:

wherein N is _p Is the prediction time domain; n (N) _c Is the control time domain; pi (II) _p,(k+i|k) Is a predictive value of the control output variable; pi (II) _ref,(k+i|k) Representing a reference control output variable; (k+i|k) denotes predicting the value at the sampling time (k+i) from the information of the sampling time k, where i=1, 2, …, N _p ；Q _L The weight matrix is the weight matrix of the system output quantity and reflects the tracking precision of the control system to the reference speed; r is R _L Is a weight matrix of system control increments.

Model predictive control solves the following equation for each control cycle:

s.t.u _L,min ≤u _L,k+i ≤u _L,max ,i＝0,1,…N _c -1

Δu _L,min ≤Δu _L,k+i ≤Δu _L,max ,i＝0,1,…N _c -1

in the formula DeltaU _min And DeltaU _max Respectively representing a set of minimum and maximum values of the control increment in the control time domain;

after solving to obtain the optimal solution, obtaining a series of input control increments:

and will Deltau _k The first control increment deltau in (1) _L,k As an actual control input increment, a longitudinal control amount is obtained:

u _L,k ＝u _L,k-1 +Δu _L,k

2.5 yaw stability control

SMC-based vehicle yaw stability control is designed.

2.5.1 yaw stability criteria

First, a yaw stability criterion needs to be designed to determine whether the vehicle is out of stability. Whether the vehicle is unstable or not is judged by a yaw rate-lateral rate phase plane method.

And selecting the yaw rate and the transverse speed as main research parameters, and deducing the yaw stability criterion based on the envelope curve by analyzing the maximum yaw rate and the maximum cornering force of the rear wheels when the vehicle runs stably. According to the maximum cornering force constraint of the tire and combining the vehicle dynamics model of 2.1, the control threshold value of the yaw rate can be obtained:

/>

since the vehicle is more critical due to rear axle sideslip when yaw instability occurs, the above is written in the form of:

in the formula, -alpha _r,lim ≤α _r ≤α _r,lim ，

By constraining the rear wheel slip angle-alpha _r,lim ≤α _r ≤α _r,lim Vehicle rear wheel slip angle alpha listed in simultaneous 2.2 _r And the centroid slip angle beta can obtain the transverse speed v of the vehicle _y Is defined by the threshold value of:

the constraints form a closed envelope, as shown in fig. 3, to ensure yaw stability of the vehicle when the vehicle lateral and yaw rates are within the envelope.

FIG. 3 yaw stability envelope constraint schematic

2.5.2 SMC-based yaw stability controller design

Considering the rear wheel steering of the vehicle, a two-degree-of-freedom yaw dynamics model of the vehicle can be obtained according to 2.1 as follows:

for ease of computation, it is written in the form of a state space:

Y＝CX

in the method, in the process of the invention,

the centroid slip angle in the ideal state is zero, and the yaw rate in the ideal state is the steady-state yaw rate. When the automobile reaches steady state, the lateral speed a _y Rate of change of yaw rate of =0And carrying out two-degree-of-freedom yaw dynamics model and simplifying to obtain steady yaw rate:

furthermore, due to the maximum lateral acceleration a that can be reached by the vehicle _y Limited by road adhesion coefficient and movement state, i.e. a _y Mu g or lessThus, the reference yaw rate and the centroid slip angle are obtained: />

Where μ represents the road adhesion coefficient.

the slip form surface selects the systematic input error, namely:

and (3) deriving a sliding mode surface:

the index approach rate is adopted:

The simultaneous solving can obtain the output variable as follows:

in the formula, u= [ delta ] _f δ _r ] ^T SelectingRear wheel steering angle delta _r Is the final output of the controller.

Further, in order to eliminate buffeting, the following form of saturation function is used instead of sgn (S):

according to the second method of Lyapunov in modern control theory, a positive scalar function V is defined ifNegative, then the system is asymptotically stable. Definition of lyapunov function as v=ss ^T And 2, deriving the Lyapunov function according to a formula of the simultaneous index approach rate to obtain:

as can be seen from the above, when S>At the time of 0, the temperature of the liquid,when S is<At 0, the +>When s=0, the number of the slots is,thus (S)>This holds true, thus proving that the designed system is stable.

It should be noted that the foregoing examples are limited to further illustrating and understanding the technical solutions of the present invention, and should not be construed as further limiting the technical solutions of the present invention, but rather the invention that is not obvious to the person skilled in the art but is provided with substantial features and significant improvements still falls within the scope of protection of the present invention.

Claims

1. A vehicle trajectory tracking control system based on parameter uncertainty and yaw stability, comprising an upper controller and a lower controller, characterized in that: and establishing a three-degree-of-freedom vehicle dynamics model comprising transverse movement, yaw movement and longitudinal movement, wherein the upper-layer controller comprises a transverse path controller and a longitudinal speed tracking controller, the transverse path controller is used for calculating an expected front wheel corner and an expected rear wheel corner, the longitudinal speed tracking controller is used for calculating expected acceleration, and the lower-layer controller realizes the output of the upper-layer controller through a steering system and a driving device.

2. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 1, wherein: the upper controller also comprises an extended Kalman observer which is used for estimating the longitudinal vehicle speed and the yaw rate.

3. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 2, wherein: the reference track is generated by a fifth-order polynomial, and parameters of the reference track comprise: road curvature k _r Course angle θ of road _r Reference velocity v _r Transverse coordinate y of reference track _r Longitudinal coordinate x of reference track _r 。

4. A vehicle trajectory tracking control system based on parameter uncertainty and yaw stability as claimed in claim 3, characterized by the dynamics differential equation of the vehicle dynamics model:

wherein m represents the vehicle mass, l _f And l _r Respectively the front and rear wheelbase of the vehicle, v _x And v _y A velocity component, a, representing the velocity V at the vehicle centroid along the X-axis and the Y-axis, respectively _x Is the longitudinal acceleration of the vehicle;is the yaw angle of the vehicle; />Is the yaw rate of the vehicle; beta is the centroid slip angle, which represents the angle of the centroid current speed relative to the longitudinal axis of the automobile; delta _f Steering angle for front wheel; alpha _f And alpha _r Respectively representing the slip angle of the front tire and the rear tire; c (C) _af And C _ar The cornering stiffness of the front and rear tires, respectively; f (F) _yf And F _yr Representing the lateral forces of the front and rear tires, respectively; i _z Is the rotational inertia of the vehicle about the Z axis; .

5. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 4, wherein: yaw rate of vehicleAnd longitudinal velocity v _x The state equation and the observation equation of (2) are:

in the method, in the process of the invention,is the yaw rate of the vehicle; a, a _x Is the longitudinal acceleration of the vehicle; a, a _y Is the lateral acceleration of the vehicle; using extended kalmanThe filtering estimates the longitudinal vehicle speed and yaw rate.

6. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 5, wherein: the longitudinal speed tracking controller is based on an MPC design, and the lateral path controller includes a tracking error model, an LQR-based lateral controller, and an SMC-based vehicle yaw stability controller.

7. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 6, wherein the tracking error model comprises:

the first derivative of heading error is:

in θ _r Is the course angle of the current moment on the target track;

the second derivative of heading error is:

the first derivative of the trajectory tracking bias is:

in the method, in the process of the invention,v _x ＝Vcosβ。

the second derivative of the trajectory tracking bias is:

in the method, in the process of the invention,

8. the vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 7, wherein the LQR-based lateral path controller:

9. The vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 7, wherein the SMC-based vehicle yaw stability controller comprises: whether the vehicle is unstable or not is judged by a yaw rate-lateral rate phase plane method,

Vehicle lateral speed v _y Is defined by the threshold value of:

10. the vehicle trajectory tracking control system based on parameter uncertainty and yaw stability of claim 9, wherein:

steady state yaw rate:

wherein L= (L) _f +l _r ) Representing the wheelbase of a motor vehicleThe method comprises the steps of carrying out a first treatment on the surface of the K represents a stability factor, which can be represented by the following formula:

reference yaw rate and centroid slip angle:

wherein μ represents a road adhesion coefficient;

the slip form surface selects the systematic input error, namely:

and (3) deriving a sliding mode surface:

the index approach rate is adopted:

The simultaneous solving can obtain the output variable as follows: