Electric vehicle chassis cooperative control method considering lateral stability and roll stability

Abstract

The invention belongs to the technical field of automatic driving automobiles, and particularly relates to an electric automobile chassis cooperative control method considering lateral stability and roll stability. Comprising the following steps: step 1, constructing a multi-cell body linear parameter variable model based on a longitudinal vehicle speed auxiliary parameter and a tire cornering stiffness correction coefficient; step 2, on the basis of the multi-cell-body linear parameter variable vehicle model, designing an electric vehicle chassis cooperative controller by applying an online optimization solution robust model predictive control method; thirdly, according to the additional yaw moment and the anti-roll moment output by the chassis cooperative controller, optimal distribution of the additional yaw moment is achieved by solving the problem of minimization of the attachment utilization rate of four-wheel tires, and distribution of the anti-roll moment of the front active suspension and the anti-roll moment of the rear active suspension is adjusted according to the difference value of the actual yaw velocity and the reference quantity. According to the invention, a good solution can be provided for cooperative control of the intelligent automobile chassis in the future.

Description

Technical Field

[0001] The present invention belongs to the technical field of autonomous vehicles, and specifically provides a cooperative control method for an electric vehicle chassis taking into account lateral and roll stability. Background Art

[0002] The innovative development of electric vehicles has effectively alleviated major challenges such as energy depletion and environmental pollution, and has become a hot topic in global automotive research. Without differential braking or interference with driver steering, electric vehicles and by-wire chassis, such as intelligent suspensions, form active safety systems that effectively improve vehicle stability, comfort, and maneuverability. However, when a vehicle performs extreme maneuvers such as tight turns on low-adhesion surfaces, the vertical load transfer caused by lateral acceleration affects roll stability. Furthermore, the lateral force of the tires tends to saturate, leading to a decrease in vehicle lateral stability. In practice, active vehicle safety systems designed to ensure lateral and roll stability may fail to function promptly due to differences or conflicts in control objectives, thereby reducing the vehicle's overall safety performance. Therefore, it is necessary to develop a collaborative chassis control method that considers lateral and roll stability to improve the vehicle's overall performance.

[0003] Advanced control theories such as sliding mode control, linear quadratic regulator control, and robust H∞ control have been applied to chassis cooperative control design. It is worth noting that these methods often fail to fully consider physical constraints such as actuator saturation and tire friction limits during controller design, resulting in the inability to effectively execute the generated desired control objectives. In contrast, model predictive control (MPC) exhibits excellent performance in handling multi-objective and multi-constraint problems and has therefore garnered widespread attention in chassis cooperative control. To simplify controller design, existing MPC methods often assume uniform longitudinal motion when constructing dynamic models, ignoring the uncertainties of tire cornering stiffness under large lateral acceleration excitation and external random input disturbances. This results in a decline in the robust safety performance of chassis cooperative control strategies under extreme driver maneuvers. Summary of the Invention

[0004] To solve the above problems, the present invention provides an electric vehicle chassis cooperative control method that takes into account lateral and roll stability. The method can construct the external random input disturbances existing in vehicle motion as explicit constraints of a bounded set. Combined with the linear parameter variable modeling method, it can effectively deal with disturbance problems such as tire lateral stiffness uncertainty and dynamic changes in longitudinal vehicle speed in chassis cooperative control, and can provide a better solution for future intelligent vehicle chassis cooperative control.

[0005] The technical solution of the present invention is described as follows in conjunction with the accompanying drawings:

[0006] A method for cooperatively controlling the chassis of an electric vehicle considering lateral and roll stability comprises the following steps:

[0007] Step 1: Construct a polyhedral linear parameter variable model based on the longitudinal vehicle speed auxiliary parameter and the tire cornering stiffness correction coefficient;

[0008] Step 2: Based on the polyhedral linear parameter variable vehicle model, a robust model predictive control method with online optimization is used to design an electric vehicle chassis cooperative controller;

[0009] Step 3: Based on the additional yaw moment and anti-roll moment output by the chassis cooperative controller, the additional yaw moment is optimally distributed by solving the problem of minimizing the adhesion utilization of the four-wheel tires, and the anti-roll moment distribution of the front and rear active suspensions is adjusted according to the difference between the actual yaw angular velocity and the reference value.

[0010] Furthermore, the specific method of step one is as follows:

[0011] 11) Lateral, yaw, and roll motions are expressed as:

[0012]

[0013] Where m is the vehicle mass; F y is the tire lateral force, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; δ f is the front wheel angle input; v y and v x are the lateral and longitudinal vehicle speeds respectively; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; φ r is the disturbance vector given by the road inclination angle; r is the yaw rate; φ is the roll angle; is the roll angular velocity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ for roll damping;

[0014] 12) The approximate linear tire model is expressed as:

[0015] F yf =k f C f α f , (2)

[0016] F yr =k r Cr α r . (3)

[0017] Where, F yf and F yr are the lateral forces of the front and rear wheels respectively; k f and k r are the front and rear wheel cornering stiffness correction coefficients respectively; and C r are the linear cornering stiffness of the front and rear wheels respectively; α f and α r are the front and rear wheel slip angles, respectively;

[0018] 13) Design a longitudinal speed auxiliary parameter ρ∈[-1,1] that satisfies:

[0019]

[0020] Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds;

[0021] 14) Apply Taylor approximation method to convert the other two longitudinal speed related parameters v x and 1 / v x 2 Expressed as:

[0022]

[0023] Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds;

[0024] 15) The established linear parameter variable vehicle model is converted into a polyhedral form composed of a finite number of vertices convex combination. The characteristics of the convex set are used to design only the controller at the vertex, and only one coefficient matrix discretization operation is required in the entire control process. Since the linear parameter variable vehicle model has three bounded time-varying parameters ρ, k f 、k r , so there are 2 3 polytope vertices; the convex combination coefficient λ of the corresponding vertices l (l=1,2,…,L) is:

[0025]

[0026] Where λl is the convex combination coefficient of the polyhedral vertex, subscript l=1,2,…,L, the number of convex combinations L=8; ​​ρ is the longitudinal speed auxiliary parameter; k f and k r are the front wheel and rear wheel cornering stiffness correction coefficients respectively; l is the vertex of the polyhedron; is the polyhedral vertex with the opposite extreme value of the corresponding coefficient, which is specifically expressed as:

[0027] o1=[ρ min ,k fmin ,k rmin ],o2=[ρ min ,k fmin ,k rmax ],

[0028] o3=[ρ min ,k fmax ,k rmin ],o4=[ρ min ,k fmax ,k rmax ],

[0029] o5=[ρ max ,k fmin ,k rmin ],o6=[ρ max ,k fmin ,k rmax ],

[0030] o7=[ρ max ,k fmax ,k rmin ],o8=]ρ max ,k fmax ,k rmax ]. (8)

[0031]

[0032] 16) Set the vehicle's center of mass sideslip angle, yaw rate, roll angle, and roll rate as system state variables The additional yaw moment and anti-roll moment are the control input variables u=M z M φ ] T , the front wheel steering angle and road tilt disturbance vector are disturbance variables ω=[δ f φ r ] T , the polyhedral form of the state space equation of the vehicle dynamics system is expressed as:

[0033]

[0034] Where x is the system state variable; is the derivative of the system state variable; u is the control input variable; ω is the disturbance variable; λ l is the convex combination coefficient of the corresponding vertex; l are the vertices of the polyhedron; the number of convex combinations L = 8; A, B, and D are the state matrix, input matrix, and external perturbation matrix, respectively, expressed as follows:

[0035]

[0036]

[0037] Where, I eq =I x +mh 2 ; v x is the minimum longitudinal speed, is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; k f and k r are the correction coefficients of the front and rear wheel cornering stiffness respectively; C f and C r are the linear cornering stiffness of the front and rear wheels respectively; m is the vehicle mass; v x is the longitudinal speed; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ For roll damping.

[0038] Furthermore, the specific method of step 2 is as follows:

[0039] 21) Set the ideal lateral speed v yd =0, and the ideal yaw rate r d It is expressed as follows:

[0040]

[0041] Among them, r d is the ideal yaw rate; L d is the distance from the front axle to the rear axle; K u is the stability coefficient determined by the vehicle mass; v x is the longitudinal speed; δ f is the front wheel turning angle;

[0042] 22) Apply the forward Euler method to discretize the continuous state space equations at the vertices of the polyhedron, which can be expressed as:

[0043] x(k+1)=A d x(k)+B d u(k)+D d ω(k), (12)

[0044] Where A d 、B d 、D d are discrete state matrix, discrete input matrix, and discrete external disturbance matrix respectively; A d =A·T+I,B d =B·T,D d =D·T, where T is the sampling time interval, I is the unit matrix of the corresponding order; x(k+1) is the system state variable at time k+1; x(k) is the system state variable at time k; u(k) is the control input variable at time k; ω(k) is the disturbance variable at time k;

[0045] 23) Set the reference value x of the state variable r (k)=[0 r d (k) 0 0] T ; Define the feedback gain matrix F and design the feedback control law as follows:

[0046] u(k+i|k)=F(k)(x(k+i)-x r (k+i)). (13)

[0047] Where u(k+i|k) is the control input variable at the i-th prediction moment; F(k) is the feedback gain matrix at time k; x(k+i) is the system state variable at the i-th prediction moment; x r (k+i) is the reference system state variable at the i-th prediction moment;

[0048] 24) Apply the min-max method to minimize the upper bound of the cost function in the worst case caused by the changing system model and external random input disturbances; define a multi-objective cost function in the infinite time domain and describe the optimization problem as:

[0049]

[0050] Where, J ∞ (k) is the cost function in the infinite time domain; x(k+i|k) is the system state variable at the i-th prediction moment; x r(k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices, and the coefficient matrix is ​​a convex set

[0051] 25) Define the symmetric positive definite Lyapunov matrix P, and the quadratic Lyapunov function of the system is:

[0052]

[0053] Where V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; P(k) is the Lyapunov matrix at time k;

[0054] According to the stability theorem, it is assumed that the quadratic function is monotonically decreasing and satisfies the following robust inequality constraints:

[0055]

[0056] Where V(k+i+1|k) is the Lyapunov function at the i+1th prediction moment; V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices;

[0057] For a stable system, x(∞|k)=x r (∞|k) and V(∞|k)=0, and accumulating inequality (16) from i=0 to i→∞, we get:

[0058]

[0059] Where, J ∞ (k) is the cost function in infinite time domain; A d 、D d are the discrete state matrix and the discrete external disturbance matrix respectively; Ω is the convex set of the coefficient matrix; V(k|k) is the Lyapunov function at time k;

[0060] Assume that there exists a scalar γ>0, and the upper bound of the Lyapunov function V(k|k) satisfies:

[0061] V(k|k)≤γ, (18)

[0062] 26) In order to satisfy the condition that the function V(k|k) has an upper bound, it is necessary to restrict the initial state x(k)-x r (k) In the corresponding elliptical domain, that is, Define Q(k) = γP(k) -1 , based on Schur's complement lemma, the initial state condition is converted into the following matrix positive definiteness condition:

[0063]

[0064] Where x(k) is the system state variable at time k; x r (k) is the reference system state variable at time k; Q(k) is the transformation matrix calculated from the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P;

[0065] In order to ensure the robust stability condition (16) of the closed-loop system, the corresponding constraints need to be set as follows:

[0066]

[0067] 27) Introducing an asymmetric positive definite relaxation matrix G(k), the following conditions must be met:

[0068] G(k) T Q(k) -1 G(k)≥G(k) T +G(k)-Q(k), (21)

[0069] The matrix is ​​expressed as a convex combination, that is, According to the previous definition, we can get F j =Y j Q -1 , the robust stability condition is simplified to the following form:

[0070]

[0071] Where G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Q and R are given positive definite weighting matrices; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; I is the unit matrix of the corresponding order; γ is the upper bound of the Lyapunov function;

[0072] 28) Referring to the quadratic boundedness theorem and applying Schur's complement lemma, this is equivalent to:

[0073]

[0074] Where τ is a predefined scalar and τ∈(0,1); G is an asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j ; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; P ω is an external perturbation bounded matrix and satisfies

[0075] Set the magnitude constraint to |u n (k+i|k)|≤U nmax ,n=1,2; where U nmax is the limit value of the corresponding component of the given control input; according to the Cauchy inequality:

[0076]

[0077] Where U nmax is the limit value of the corresponding component of the given control input; I is the unit matrix of the corresponding order; G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j The transformation matrix calculated by and matrix Q;

[0078] 29) The constraints of the optimization problem include robust stability conditions (22), initial state conditions (19), recursive feasibility conditions (23), and physical constraints (24). By satisfying the positive definiteness constraints of the above matrices, the robust stability and recursive feasibility of the closed-loop system can be guaranteed. Finally, the online optimization problem of robust model predictive control can be summarized as:

[0079]

[0080] Where γ(k) is the upper bound of the Lyapunov function at time k;

[0081] Since the system has recursive feasibility, the optimization problem can be solved online. Set the system prediction time domain to N, and the specific steps of the solution algorithm are as follows:

[0082] (1) Initialization time k;

[0083] (2) Predict x(i)-x in N steps r (i), i=1,2,…N, satisfying x(i+1)-x r (i+1)=e -0.3i+0.3 (x(i)-x r (i));

[0084] (3) Solve the optimization problem formulas respectively and add the constraints G(i)≥G(i-1), Q(i)≥Q(i-1), γ(i)≤γ(i-1);

[0085] (4) Update matrices G(k) and Q(k);

[0086] (5) Calculate the system control input u(k) = F(k)(k(x)-x r (k));

[0087] (6) Update the time to k+1 and go to step (1).

[0088] Furthermore, the specific method of step three is as follows:

[0089] 31) The optimal objective function is defined as the minimization problem of the four-wheel tire adhesion utilization rate, which is specifically expressed as:

[0090]

[0091] Where J is the optimal objective function; F xij is the longitudinal force of the four wheels in the vehicle body coordinate system; ε ij is the weighting coefficient corresponding to the four wheels; F zij is the vertical load of the four tires, the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; μ is the road adhesion coefficient;

[0092] 32) Define the quadratic programming equality constraints as follows:

[0093]

[0094] Where M z is the desired additional yaw moment; F xij is the longitudinal force of the four wheels, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; l f is the distance from the vehicle's center of mass to the front axle; δ f is the front wheel turning angle; B t is the wheelbase;

[0095] 33) According to the difference between the actual yaw rate and the reference value rr dAdjust the torque distribution of the front and rear active suspensions; assume that the actuating forces generated by the active suspension actuators on the left and right sides are equal in magnitude and opposite in direction, and then adjust the actuating forces F output by the active suspension actuators at the four wheels. aij Expressed as:

[0096]

[0097] Where, the force F of the active suspension at the four wheels is aij , the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; r is the actual yaw angular velocity; r d is the ideal yaw rate; M φ is the desired anti-roll moment; d f and d r They are the distances between the left and right mounting points of the front and rear axle suspensions respectively.

[0098] The beneficial effects of the present invention are:

[0099] 1) Based on the longitudinal speed auxiliary parameter and the tire cornering stiffness correction coefficient, this invention constructs a vehicle system model with variable linear parameters, effectively compensating for vehicle dynamics modeling errors. The linear variable parameter vehicle model is converted into a polyhedron consisting of a finite number of convex sets of vertices. The properties of convex sets allow controllers to be designed only at the vertices, thus simplifying the controller design process.

[0100] 2) This paper applies a robust model predictive control method with online optimization to design a cooperative controller for the chassis of an electric vehicle that considers lateral and roll stability. Based on the Schur's complement lemma, multiple sets of matrix inequality conditions are derived. Under the premise of considering actuator saturation constraints, the robust stability and recursive feasibility of the proposed controller are strictly guaranteed under the influence of external random input disturbances.

[0101] 3) The present invention achieves the distribution of additional yaw moment by solving a quadratic programming problem with the goal of minimizing tire adhesion utilization, and adjusts the anti-roll moment distribution of the front and rear active suspension of the vehicle according to the difference between the actual yaw angular velocity and the reference value, and optimizes the distribution of the output torque calculated by the chassis cooperative controller into tire torque and active suspension force. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0103] Figure 1 A diagram of the coordinated control architecture of the electric vehicle chassis considering lateral and roll stability;

[0104] Figure 2a A schematic diagram of a three-degree-of-freedom vehicle dynamics model from one angle;

[0105] Figure 2b A schematic diagram of the three-degree-of-freedom vehicle dynamics model from another angle;

[0106] Figure 3 Schematic diagram of the front wheel cornering stiffness correction coefficient;

[0107] Figure 4 Schematic diagram of the rear wheel cornering stiffness correction coefficient;

[0108] Figure 5 Schematic diagram of reference trajectory for serpentine working condition;

[0109] Figure 6a Schematic diagram of the change trend of the vehicle's center of mass sideslip angle under serpentine working conditions;

[0110] Figure 6b Schematic diagram of the changing trend of yaw angular velocity under serpentine working conditions;

[0111] Figure 6c Schematic diagram of the changing trend of the roll angle under serpentine working conditions;

[0112] Figure 6d Schematic diagram of the changing trend of roll angular velocity under serpentine working conditions;

[0113] Figure 7a Schematic diagram of the additional yaw moment output by the controller;

[0114] Figure 7b Schematic diagram of the anti-roll moment output by the controller;

[0115] Figure 7c Schematic diagram of tire torque calculated by the controller;

[0116] Figure 7d Schematic diagram of the active suspension forces calculated for the controller. DETAILED DESCRIPTION

[0117] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.

[0118] Example 1

[0119] See Figure 1, this embodiment provides a method for cooperatively controlling the chassis of an electric vehicle considering lateral and roll stability, comprising the following steps:

[0120] Step 1: Construct a polyhedral linear parameter variable model based on the longitudinal vehicle speed auxiliary parameter and the tire cornering stiffness correction coefficient, as follows:

[0121] 11) Build Figure 2a-2b The three-degree-of-freedom vehicle dynamics model shown, lateral, yaw, and roll motion can be expressed as:

[0122]

[0123] Where m is the vehicle mass; F y is the tire lateral force, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; δ f is the front wheel angle input; v y and v x is the lateral and longitudinal speed of the vehicle, respectively; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; φ r is the disturbance vector given by the road inclination angle; r is the yaw rate; φ is the roll angle; is the roll angular velocity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ for roll damping;

[0124] 12) During the vehicle's travel, the time-varying longitudinal velocity v x Uncertain parameters such as the nonlinear tire cornering stiffness will significantly affect the vehicle's dynamic characteristics, making it difficult for traditional linear time-invariant models to accurately represent the vehicle's motion state. To this end, the present invention uses a linear parameter variable method to construct a vehicle model. First, the tire cornering stiffness correction coefficient k is introduced. f and k r , to describe the tire dynamics under large lateral acceleration excitation. Cornering stiffness correction factor k f and k r It can be characterized as Figure 3 and Figure 4 The bounded mapping relationship between tire slip angle and road adhesion coefficient is shown. Therefore, the approximate linear tire model is expressed as:

[0125] F yf =k f C f α f, (2)

[0126] F yr =k r C r α r . (3)

[0127] Where, F yf and F yr are the lateral forces of the front and rear wheels respectively; k f and k r are the front and rear wheel cornering stiffness correction coefficients respectively; and C r are the linear cornering stiffness of the front and rear wheels respectively; α f and α r are the front and rear wheel slip angles, respectively;

[0128] 13) Longitudinal vehicle speed time-varying parameter v x , 1 / v x , 1 / v x 2 It will also affect the lateral dynamic characteristics of the vehicle during steering. In order to further reduce the number of time-varying parameters, a longitudinal speed auxiliary parameter ρ∈[-1,1] is designed to satisfy:

[0129]

[0130] Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds;

[0131] 14) Apply Taylor approximation method to convert the other two longitudinal speed related parameters v x and 1 / v x 2 Expressed as:

[0132]

[0133] Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds;

[0134] 15) The established linear parameter variable vehicle model is converted into a polyhedral form composed of a finite number of vertices. By utilizing the characteristics of convex sets, the controller at the vertex can be designed only. In addition, only one coefficient matrix discretization operation is required in the entire control process, thereby simplifying the controller design process. Since the linear parameter variable vehicle model has three bounded time-varying parameters ρ, k f 、k r , so there are 2 3 The convex combination coefficient λ of the corresponding vertex l (l=1,2,…,L) is:

[0135]

[0136] Where λl 为 The convex combination coefficient of the polyhedral vertex, subscript l = 1, 2, ..., L, the number of convex combinations L = 8; ρ is the longitudinal speed auxiliary parameter; k f and k r are the correction coefficients of the front and rear wheel cornering stiffness respectively; l is the vertex of the polyhedron; is the polyhedral vertex with the opposite extreme value of the corresponding coefficient, which is specifically expressed as:

[0137] o1=[ρ min ,k fmin ,k rmin ],o2=[ρ min ,k fmin ,k rmax ],

[0138] o3=[ρ min ,k fmax ,k rmin ],o4=[ρ min ,k fmax ,k rmax ],

[0139] o5=[ρ max ,k fmin ,k rmin ],o6=[ρ max ,k fmin ,k rmax ],

[0140] o7=[ρ max ,k fmax ,k rmin ],o8=[ρ max ,k fmax ,k rmax ]. (8)

[0141]

[0142] 16) Set the vehicle's center of mass sideslip angle, yaw rate, roll angle, and roll rate as system state variables The additional yaw moment and anti-roll moment are the control input variables u=[M z M φ ] T , the front wheel steering angle and road tilt disturbance vector are disturbance variables ω=[δ f φ r ] T , the polyhedral form of the state space equation of the vehicle dynamics system is expressed as:

[0143]

[0144] Where x is the system state variable; is the derivative of the system state variable; u is the control input variable; ω is the disturbance variable; λ l is the convex combination coefficient of the corresponding vertex; o l are the vertices of the polyhedron; the number of convex combinations L = 8; A, V, and D are the state matrix, input matrix, and external perturbation matrix, respectively, expressed as follows:

[0145]

[0146] Where, I eq =I x +mh 2 ; v x is the minimum longitudinal speed, is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; k f and k r are the correction coefficients of the front and rear wheel cornering stiffness respectively; C f and C r are the linear cornering stiffness of the front and rear wheels respectively; m is the vehicle mass; v x is the longitudinal speed; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ For roll damping.

[0147] Step 2: Design an electric vehicle chassis cooperative controller using a robust model predictive control method with online optimization solution, as follows:

[0148] 21) Chassis cooperative control strategy needs to determine the appropriate tracking target. Set the ideal lateral speed v yd =0, and the ideal yaw rate r d It is expressed as follows:

[0149]

[0150] Among them, r d is the ideal yaw rate; L d is the distance from the front axle to the rear axle; K u is the stability coefficient determined by the vehicle mass; v x is the longitudinal speed; δ f is the front wheel turning angle;

[0151] 22) Apply the forward Euler method to discretize the continuous state space equations at the vertices of the polyhedron, which can be expressed as:

[0152] x(k+1)=A d x(k)+B d u(k)+D d ω(k), (12)

[0153] Where A d 、B d 、D d are discrete state matrix, discrete input matrix, and discrete external disturbance matrix respectively; A d =A·T+I,B d =B·T,D d =D·T, where T is the sampling time interval, I is the unit matrix of the corresponding order; x(k+1) is the system state variable at time k+1; x(k) is the system state variable at time k; u(k) is the control input variable at time k; ω(k) is the disturbance variable at time k;

[0154] 23) For the chassis cooperative control method considering lateral and roll stability, the feedback control law of the system can be obtained by solving the optimal problem of a robust model predictive control cost function subject to constraints. Set the reference value of the state variable x r (k)=[0 r d (k )0 0] T Next, define the feedback gain matrix F and design the feedback control law as follows:

[0155] u(k+i|k)=F(k)(x(k+i)-x r (k+i)). (13)

[0156] Where u(k+i|k) is the control input variable at the i-th prediction moment; F(k) is the feedback gain matrix at time k; x(k+i) is the system state variable at the i-th prediction moment; x r (k+i) is the reference system state variable at the i-th prediction moment;

[0157] 24) Apply the min-max method to minimize the upper bound of the cost function in the worst case caused by the changing system model and external random input disturbances; define a multi-objective cost function in the infinite time domain and describe the optimization problem as:

[0158]

[0159] Where, J ∞ (k) is the cost function in the infinite time domain; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices, and the coefficient matrix is ​​a convex set

[0160] 25) Define the symmetric positive definite Lyapunov matrix P, and the quadratic Lyapunov function of the system is:

[0161]

[0162] Where V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; P(k) is the Lyapunov matrix at time k;

[0163] According to the stability theorem, it is assumed that the quadratic function is monotonically decreasing and satisfies the following robust inequality constraints:

[0164]

[0165] Where V(k+i+1|k) is the Lyapunov function at the i+1th prediction moment; V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices;

[0166] For a stable system, x(∞|k)=xr (∞|k) and V(∞|k)=0, and accumulating inequality (16) from i=0 to i→∞, we get:

[0167]

[0168] Where, J ∞ (k) is the cost function in infinite time domain; A d 、D d are the discrete state matrix and the discrete external disturbance matrix respectively; Ω is the convex set of the coefficient matrix; V(k|k) is the Lyapunov function at time k;

[0169] Assume that there exists a scalar γ>0, and the upper bound of the Lyapunov function V(k|k) satisfies:

[0170] V(k|k)≤γ, (18)

[0171] 26) In order to satisfy the condition that the function V(k|k) has an upper bound, it is necessary to restrict the initial state x(k)-x r (k) In the corresponding elliptical domain, that is, Define Q(k) = γP(k) -1 , based on Schur's complement lemma, the initial state condition is converted into the following matrix positive definiteness condition:

[0172]

[0173] Where x(k) is the system state variable at time k; x r (k) is the reference system state variable at time k; Q(k) is the transformation matrix calculated from the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P;

[0174] In order to ensure the robust stability condition (16) of the closed-loop system, the corresponding constraints need to be set as follows:

[0175]

[0176] 27) Only defining the quadratic Lyapunov function is conservative to a certain extent. In order to facilitate the design of constraints and ensure the stability of the controller under less conservative conditions, an asymmetric positive definite relaxation matrix G(k) is introduced, which needs to meet the following conditions:

[0177] G(k) T Q(k) -1 G(k)≥G(k) T +G(k)-Q(k), (21)

[0178] The matrix is ​​expressed as a convex combination, that is, According to the previous definition, we can get F j =Y j Q -1 , the robust stability condition is simplified to the following form:

[0179]

[0180] Where G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Q and R are given positive definite weighting matrices; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; I is the unit matrix of the corresponding order; γ is the upper bound of the Lyapunov function;

[0181] 28) For vehicle systems with external interference, additional constraints need to be added to ensure the feasibility of the recursion. Considering that the initial state constraint (19) is related to the time k, it is necessary to satisfy ‖x(k)- Referring to the quadratic boundedness theorem and applying Schur's complement lemma, this condition is equivalent to:

[0182]

[0183] Where τ is a predefined scalar and τ∈(0,1); G is an asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j ; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; P ω is an external perturbation bounded matrix and satisfies

[0184] In practice, the control input variable u is subject to the saturation constraint of the vehicle actuator motor. Therefore, we set the amplitude constraint to |u n (k+i|k)|≤U nmax ,n=1,2. Among them, U nmax is the limit value of the corresponding component of the given control input. Since this form is difficult to further encode and calculate, it is necessary to further process the physical constraints. According to the Cauchy inequality, it can be obtained:

[0185]

[0186] Where U nmax is the limit value of the corresponding component of the given control input; I is the unit matrix of the corresponding order; G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j The transformation matrix calculated by and matrix Q;

[0187] 29) The constraints of the optimization problem include robust stability conditions (22), initial state conditions (19), recursive feasibility conditions (23), and physical constraints (24). By satisfying the positive definiteness constraints of the above matrices, the robust stability and recursive feasibility of the closed-loop system can be guaranteed. Finally, the online optimization problem of robust model predictive control can be summarized as:

[0188]

[0189] Where γ(k) is the upper bound of the Lyapunov function at time k;

[0190] Since the system has recursive feasibility, the optimization problem can be solved online. Set the system prediction time domain to N, and the specific steps of the solution algorithm are as follows:

[0191] (1) Initialization time k;

[0192] (2) Predict x(i)-x in N steps r (i), i=1,2,…N, satisfying x(i+1)-x r (i+1)=e -0.3i+0.3 (x(i)-x r (i));

[0193] (3) Solve the optimization problem separately and add the constraints G(i)≥G(i-1),Q(i)≥Q(i-1),γ(i)≤γ(i-1);

[0194] (4) Update matrices G(k) and Q(k);

[0195] (5) Calculate the system control input u(k) = F(k)(x(k)-x r (k));

[0196] (6) Update the time to k+1 and go to step (1).

[0197] Step 3: Optimize the distribution of the additional yaw moment by solving the problem of minimizing the adhesion utilization of the four-wheel tires. Adjust the anti-roll moment distribution of the front and rear active suspensions based on the difference between the actual yaw rate and the reference value, as follows:

[0198] The present invention outputs an additional yaw moment M to the controller. z and anti-roll moment M φ Optimize the allocation. z The allocation of M can be achieved by solving the quadratic programming (QP) problem. φ The distribution of the active suspension forces at the four wheels is calculated based on the corresponding distribution weights.

[0199] 31) The optimal objective function is defined as the minimization problem of the four-wheel tire adhesion utilization rate, which is specifically expressed as:

[0200]

[0201] Where J is the optimal objective function; F xij is the longitudinal force of the four wheels in the vehicle body coordinate system; ε ij is the weighting coefficient corresponding to the four wheels; F zij is the vertical load of the four tires, the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; μ is the road adhesion coefficient;

[0202] 32) In order to achieve the desired additional yaw moment M z The optimal allocation of , defines the quadratic programming equality constraints as follows:

[0203]

[0204] Where M z is the desired additional yaw moment; F xij is the longitudinal force of the four wheels, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; l f is the distance from the vehicle's center of mass to the front axle; δ f is the front wheel turning angle; B t is the wheelbase;

[0205] 33) Considering that the active suspension will change the vertical force of the wheel, thus affecting the lateral stability of the vehicle, it is necessary to calculate the difference between the actual yaw rate and the reference value rr d Adjust the torque distribution of the front and rear active suspensions. Assuming that the actuating forces generated by the active suspension actuators on the left and right sides are equal in magnitude and opposite in direction, the actuating forces F output by the active suspension actuators at the four wheels are aij Expressed as:

[0206]

[0207] Where, the force F of the active suspension at the four wheels is aij, the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; r is the actual yaw angular velocity; r d is the ideal yaw rate; M φ is the desired anti-roll moment; d f and d r They are the distances between the left and right mounting points of the front and rear axle suspensions respectively.

[0208] Example 2

[0209] This embodiment uses a joint simulation platform based on MATLAB / Simulink and vehicle dynamics software CarSim to test the electric vehicle chassis cooperative control method designed in this patent. The serpentine working condition is selected to evaluate the handling stability of the vehicle under large lateral acceleration when it is close to skidding or rolling over. The road adhesion coefficient is set to 0.2, the target speed is 75km / h, and the reference trajectory is as follows: Figure 5 shown.

[0210] The simulation results under serpentine working conditions are as follows Figure 6a-6d As shown. Figure 6a-6d The trend of the vehicle's side slip angle, yaw rate, roll angle, and roll rate can be seen in the figure. Compared with the instability without a controller, the presence of a controller can ensure stability during driving, thus proving the effectiveness of the applied control strategy. Specifically, the presence of a controller can significantly reduce the side slip angle, roll angle, and roll rate to improve stability and roll comfort. The tire torque and active suspension force calculated by the controller are shown in Figure 2. Figure 7a-7d shown.

[0211] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for cooperative control of an electric vehicle chassis considering lateral and roll stability, characterized in that: The following steps are involved: Step 1: Construct a polyhedral linear parameter variable model based on the longitudinal vehicle speed auxiliary parameter and the tire cornering stiffness correction coefficient; Step 2: Based on the polyhedral linear parameter variable vehicle model, a robust model predictive control method with online optimization is used to design an electric vehicle chassis cooperative controller; Step 3: Based on the additional yaw moment and anti-roll moment output by the chassis cooperative controller, the additional yaw moment is optimally distributed by solving the problem of minimizing the adhesion utilization of the four-wheel tires, and the anti-roll moment distribution of the front and rear active suspensions is adjusted according to the difference between the actual yaw angular velocity and the reference value.

2. The electric vehicle chassis coordinated control method considering lateral and roll stability according to claim 1, characterized in that: The specific method of step one is as follows: 11) Lateral, yaw, and roll motions are expressed as: Where m is the vehicle mass; F y is the tire lateral force, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; δ f is the front wheel angle input; v y and v x are the lateral and longitudinal vehicle speeds, respectively; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; φ r is the disturbance vector given by the road inclination angle; r is the yaw rate; φ is the roll angle; is the roll angular velocity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ for roll damping; 12) The approximate linear tire model is expressed as: F yf =k f C f a f , (2) F yr =k r C r a r . (3) Where, F yf and F yr are the lateral forces of the front and rear wheels respectively; k f and k r are the front and rear wheel cornering stiffness correction coefficients respectively; and C r are the linear cornering stiffness of the front and rear wheels respectively; α f and α r are the front and rear wheel slip angles, respectively; 13) Design a longitudinal speed auxiliary parameter ρ∈[-1,1] that satisfies: Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds; 14) Apply Taylor approximation method to convert the other two longitudinal speed related parameters v x and 1 / v x 2 Expressed as: Where, v x is the longitudinal speed; v x is the minimum longitudinal speed; is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; v0 and v1 are the auxiliary speeds calculated based on the extreme longitudinal speeds; 15) The established linear parameter variable vehicle model is converted into a polyhedral form composed of a finite number of vertices convex combination. The characteristics of the convex set are used to design only the controller at the vertex, and only one coefficient matrix discretization operation is required in the entire control process. Since the linear parameter variable vehicle model has three bounded time-varying parameters ρ, k f 、k r , so there are 2 3 polytope vertices; the convex combination coefficient λ of the corresponding vertices l (l=1,2,…,L) is: Where λ l is the convex combination coefficient of the polyhedral vertex, subscript l=1,2,…,L, the number of convex combinations L=8; ​​ρ is the longitudinal speed auxiliary parameter; k f and k r are the front wheel and rear wheel cornering stiffness correction coefficients respectively; l is the vertex of the polyhedron; is the polyhedral vertex with the opposite extreme value of the corresponding coefficient, which is specifically expressed as: o1=[ρ min ,k fmin ,k rmin ],o2=[ρ min ,k fmin ,k rmax ], o3=[ρ min ,k fmax ,k rmin ],o4=[ρ min ,k fmax ,k rmax ], o5=[ρ max ,k fmin ,k rmin ],o6=[ρ max ,k fmin ,k rmax ], o7=[ρ max ,k fmax ,k rmin ],o8=[ρ max ,k fmax ,k rmax ]. (8) 16) Set the vehicle's center of mass sideslip angle, yaw rate, roll angle, and roll rate as system state variables The additional yaw moment and anti-roll moment are the control input variables u=M z M φ ] T , the front wheel steering angle and road tilt disturbance vector are disturbance variables ω=[δ f φ r ] T , the polyhedral form of the state space equation of the vehicle dynamics system is expressed as: Where x is the system state variable; is the derivative of the system state variable; u is the control input variable; ω is the disturbance variable; λ l is the convex combination coefficient of the corresponding vertex; l are the vertices of the polyhedron; the number of convex combinations L = 8; A, B, and D are the state matrix, input matrix, and external perturbation matrix, respectively, expressed as follows: Where, v x is the minimum longitudinal speed, is the maximum longitudinal speed; ρ is the longitudinal speed auxiliary parameter; k f and k r are the correction coefficients of the front and rear wheel cornering stiffness respectively; C f and C r are the linear cornering stiffness of the front and rear wheels respectively; m is the vehicle mass; v x is the longitudinal speed; h is the distance from the center of gravity of the sprung mass to the roll center; g is the acceleration due to gravity; l f and l r are the distances from the vehicle's center of mass to the front and rear axles, respectively; I z is the moment of inertia around the z axis; I x is the moment of inertia around the x-axis; k φ is the roll angle stiffness; C φ For roll damping.

3. The electric vehicle chassis coordinated control method considering lateral and roll stability according to claim 1, characterized in that: The specific method of step 2 is as follows: 21) Set the ideal lateral speed v yd =0, and the ideal yaw rate r d It is expressed as follows: Among them, r d is the ideal yaw rate; L d is the distance from the front axle to the rear axle; K u is the stability coefficient determined by the vehicle mass; v x is the longitudinal speed; δ f is the front wheel turning angle; 22) Apply the forward Euler method to discretize the continuous state space equations at the vertices of the polyhedron, which can be expressed as: x(k+1)=A d x(k)+B d u(k)+D d ω(k), (12) Where A d 、B d 、D d are discrete state matrix, discrete input matrix, and discrete external disturbance matrix respectively; A d =A·T+I,B d =B·T,D d =D·T, where T is the sampling time interval, I is the unit matrix of the corresponding order; x(k+1) is the system state variable at time k+1; x(k) is the system state variable at time k; u(k) is the control input variable at time k; ω(k) is the disturbance variable at time k; 23) Set the reference value x of the state variable r (k)=[0 r d (k) 0 0] T ; Define the feedback gain matrix F and design the feedback control law as follows: u(k+i|k)=F(k)(x(k+i)-x r (k+i)). (13) Where u(k+i|k) is the control input variable at the i-th prediction moment; F(k) is the feedback gain matrix at time k; x(k+i) is the system state variable at the i-th prediction moment; x r (k+i) is the reference system state variable at the i-th prediction moment; 24) Apply the min-max method to minimize the upper bound of the cost function in the worst case caused by the changing system model and external random input disturbances; define a multi-objective cost function in the infinite time domain and describe the optimization problem as: Where, J ∞ (k) is the cost function in the infinite time domain; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices, and the coefficient matrix is ​​a convex set 25) Define the symmetric positive definite Lyapunov matrix P, and the quadratic Lyapunov function of the system is: Where V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; P(k) is the Lyapunov matrix at time k; According to the stability theorem, it is assumed that the quadratic function is monotonically decreasing and satisfies the following robust inequality constraints: Where V(k+i+1|k) is the Lyapunov function at the i+1th prediction moment; V(k+i|k) is the Lyapunov function at the i-th prediction moment; x(k+i|k) is the system state variable at the i-th prediction moment; x r (k+i|k) is the reference system state variable at the i-th prediction moment; u(k+i|k) is the control input variable at the i-th prediction moment; Q and R are given positive definite weight matrices; For a stable system, x(∞|k)=x r (∞|k) and V(∞|k)=0, and accumulating inequality (16) from i=0 to i→∞, we get: Where, J ∞ (k) is the cost function in infinite time domain; A d 、D d are the discrete state matrix and the discrete external disturbance matrix respectively; Ω is the convex set of the coefficient matrix; V(k|k) is the Lyapunov function at time k; Assume that there exists a scalar γ>0, and the upper bound of the Lyapunov function V(k|k) satisfies: V(k|k)≤γ, (18) 26) In order to satisfy the condition that the function V(k|k) has an upper bound, it is necessary to restrict the initial state x(k)-x r (k) In the corresponding elliptical domain, that is, Define Q(k) = γP(k) -1 , based on Schur's complement lemma, the initial state condition is converted into the following matrix positive definiteness condition: Where x(k) is the system state variable at time k; x r (k) is the reference system state variable at time k; Q(k) is the transformation matrix calculated from the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; In order to ensure the robust stability condition (16) of the closed-loop system, the corresponding constraints need to be set as follows: 27) Introducing an asymmetric positive definite relaxation matrix G(k), the following conditions must be met: G(k) T Q(k) -1 G(k)≥G(k) T +G(k)-Q(k), (21) The matrix is ​​expressed as a convex combination, that is, According to the previous definition, we can get F j =Y j Q -1 , the robust stability condition is simplified to the following form: Where G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Q and R are given positive definite weighting matrices; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; I is the unit matrix of the corresponding order; γ is the upper bound of the Lyapunov function; 28) Referring to the quadratic boundedness theorem and applying Schur's complement lemma, this is equivalent to: Where τ is a predefined scalar and τ∈(0,1); G is an asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j ; A dl 、D dl are the convex combination forms corresponding to the discrete state matrix and the discrete external disturbance matrix respectively; B d is the discrete input matrix; P ω is an external perturbation bounded matrix and satisfies Set the magnitude constraint to |u n (k+i|k)|≤U nmax ,n=1,2; where U nmax is the limit value of the corresponding component of the given control input; according to the Cauchy inequality: Where U nmax is the limit value of the corresponding component of the given control input; I is the unit matrix of the corresponding order; G is the asymmetric positive definite relaxation matrix; Q is the transformation matrix calculated by the upper bound γ of the Lyapunov function V(k|k) and the Lyapunov matrix P; Y j is the convex combination form of the feedback gain matrix F j The transformation matrix calculated by and matrix Q; 29) The constraints of the optimization problem include robust stability conditions (22), initial state conditions (19), recursive feasibility conditions (23), and physical constraints (24). By satisfying the positive definiteness constraints of the above matrices, the robust stability and recursive feasibility of the closed-loop system can be guaranteed. Finally, the online optimization problem of robust model predictive control can be summarized as: Where γ(k) is the upper bound of the Lyapunov function at time k; Since the system has recursive feasibility, the optimization problem can be solved online. Set the system prediction time domain to N, and the specific steps of the solution algorithm are as follows: (1) Initialization time k; (2) Predict x(i)-x in N steps r (i), i=1,2,…N, satisfying x(i+1)-x r (i+1)=e -0.3i+0.3 (x(i)-x r (i)); (3) Solve the optimization problem formula (25) respectively and add the constraints G(i) ≥ G(i-1), Q(i) ≥ Q(i-1), γ(i) ≤ γ(i-1); (4) Update matrices G(k) and Q(k); (5) Calculate the system control input u(k) = F(k)(x(k)-x r (k)); (6) Update the time to k+1 and go to step (1).

4. The electric vehicle chassis coordinated control method considering lateral and roll stability according to claim 1, characterized in that: The specific method of step three is as follows: 31) The optimal objective function is defined as the minimization problem of the four-wheel tire adhesion utilization rate, which is specifically expressed as: Where J is the optimal objective function; F xij is the longitudinal force of the four wheels in the vehicle body coordinate system; ε ij is the weighting coefficient corresponding to the four wheels; F zij is the vertical load of the four tires, the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; μ is the road adhesion coefficient; 32) Define the quadratic programming equality constraints as follows: Where M z is the desired additional yaw moment; F xij is the longitudinal force of the four wheels, and the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; l f is the distance from the vehicle's center of mass to the front axle; δ f is the front wheel turning angle; B t is the wheelbase; 33) According to the difference between the actual yaw rate and the reference value rr d Adjust the torque distribution of the front and rear active suspensions; assume that the actuating forces generated by the active suspension actuators on the left and right sides are equal in magnitude and opposite in direction, and then adjust the actuating forces F output by the active suspension actuators at the four wheels. aij Expressed as: Where, the force F of the active suspension at the four wheels is aij , the subscripts ij∈{fl,fr,rl,rr} represent the left front wheel, left rear wheel, right front wheel, and right rear wheel respectively; r is the actual yaw angular velocity; r d is the ideal yaw rate; M φ is the desired anti-roll moment; d f and d r They are the distances between the left and right mounting points of the front and rear axle suspensions respectively.

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