Vehicle stability control method based on piecewise affine identification tire sliding mode control

Abstract

The present invention discloses a vehicle stability control method based on piecewise affine identification tire sliding mode control, comprising the steps of conducting tire longitudinal slip and lateral deviation characteristic experiments, obtaining experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters, constructing a piecewise affine identification model of tire longitudinal slip and lateral deviation, constructing a piecewise affine mathematical model of the vehicle lateral dynamics system, obtaining the final additional yaw moment, designing an optimal four-wheel torque distribution algorithm, obtaining the real-time optimal torque of the four wheels, and installing and applying the method. Beneficial effect: The present invention adopts a piecewise affine identification method to model the mechanical characteristics of tire longitudinal slip and lateral deviation, and adopts a global fast terminal sliding mode control strategy to comprehensively consider various instability factors to calculate the optimal additional yaw moment required by the current vehicle, and uses the affine of the objective function with equality constraints to obtain the real-time optimal torque required by the four wheels, thereby improving the lateral stability and safety of electric vehicles under special driving conditions.

Description

Technical Field

[0001] The present invention relates to a method for controlling automobile lateral stability, and in particular to a method for controlling vehicle stability based on segmented affine identification tire sliding mode control, belonging to the technical field of vehicle control. Background Art

[0002] With the rapid development of society, electric vehicles are playing an increasingly important role in the automotive and transportation industries. Lateral stability control is a key technology for the safe operation of distributed drive electric vehicles. Lateral stability control typically involves stabilizing a vehicle under unusual driving conditions, such as when driving on icy or snowy roads or making unexpected sharp turns.

[0003] Currently, users are increasingly demanding vehicle stability and safety, requiring vehicles to maintain excellent stability and reliability even in challenging driving conditions. However, because vehicle instability is related to multiple parameters and the complex coupling between longitudinal and lateral forces on tires during high-speed driving on slippery roads, previous research has often considered incomplete factors. As a result, vehicles are prone to instability under many unusual driving conditions, and further improvement is needed in vehicle lateral stability.

[0004] With the continuous development of automotive motion control systems, especially electric vehicles, which place higher demands on motion control performance under all-road driving conditions, the current modeling methods are not very accurate, resulting in limited improvements in system control performance, which has become an unavoidable problem. At the same time, from the perspective of vehicle dynamics control synthesis, the model must not only accurately describe the physical nature of the objective system but also be suitable for the application of dynamic control theory. Even if complex mechanism models can effectively reflect the nonlinear relationships between the variables in the controlled process, they may cause inconvenience in the design of the control system. Therefore, although complex mechanism models of tire longitudinal slip and sideways mechanical characteristics have been studied, most of them are complex and difficult to fit parameters. Simply focusing on tire mechanical characteristics without considering the subsequent motion control system synthesis based on this basis can result in the designed controller failing to perform to its full potential. Summary of the Invention

[0005] Purpose of the Invention: To address the problems in the prior art where the current modeling methods are not accurate enough, resulting in limited improvements in system control performance, and where the complex tire longitudinal slip and cornering mechanical characteristic models prevent the designed controller from fully utilizing its performance, the present invention provides a vehicle stability control method based on piecewise affine identification tire sliding mode control. The present invention uses a piecewise affine identification method to model the tire longitudinal slip and cornering mechanical characteristics, and employs a global fast terminal sliding mode control strategy to comprehensively consider various instability factors to calculate the optimal additional yaw moment required for the current vehicle. The affine equations of the objective function are substituted using equality constraints to obtain the optimal torque required in real time for the four wheels, thereby improving the lateral stability and safety of electric vehicles under special driving conditions.

[0006] Technical solution: A vehicle stability control method based on piecewise affine identification tire sliding mode control, comprising the following steps:

[0007] Step 1: A tire longitudinal slip and cornering characteristic test is performed to obtain experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters;

[0008] Step 2: constructing a tire longitudinal slip and cornering piecewise affine identification model, which is a tire longitudinal slip and cornering characteristic model established through piecewise affine identification based on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters;

[0009] Step 3: Construct a piecewise affine mathematical model of the vehicle's lateral dynamics system. This model is based on the tire's longitudinal slip piecewise affine identification model and combines the vehicle body's yaw rate and center of mass sideslip angle to construct a piecewise affine mathematical model of the vehicle's lateral dynamics system.

[0010] Step 4: Obtain the final additional yaw moment. Two optimal additional yaw moments are solved using the global fast terminal sliding mode control law based on the errors between the actual and reference values ​​of the yaw rate and the center of mass slip angle. The final additional yaw moment is obtained by assigning different weights to the two based on the instability determination results of the center of mass slip angle and center of mass slip rate phase diagram.

[0011] Step 5: Design an optimal four-wheel torque distribution algorithm, taking the minimum sum of the load rates of the four wheels as the objective function, and combining the front and rear wheel distribution weight coefficients to obtain the real-time optimal torque of the four wheels;

[0012] Step 6: Install the control system according to the method in steps 1-5 and flash it to the on-board control unit of the distributed drive electric vehicle. The controller obtains the parameters required by the existing sensors on the vehicle to determine the stability state of the vehicle. The control system calculates the real-time required yaw torque and then calculates the four wheel torques and distributes them to each wheel.

[0013] The present invention adopts a piecewise affine identification method to model the mechanical characteristics of tire longitudinal slip and cornering, and adopts a global fast terminal sliding mode control strategy to comprehensively consider various instability factors to calculate the optimal additional yaw moment required by the current vehicle. The affine of the objective function with equality constraints is used to obtain the optimal torque required by the four wheels in real time, thereby improving the lateral stability and safety of electric vehicles under special driving conditions.

[0014] Preferably, the step of constructing the tire longitudinal slip and cornering characteristic model in step 2 includes data clustering, affine sub-model parameter estimation, and calculation of the hyperplane coefficient matrix, and the specific implementation method is as follows:

[0015] (1) Define the piecewise affine model form of the tire longitudinal slip and cornering mechanical characteristics

[0016] The mathematical expression of the model is as follows:

[0017]

[0018] where y j ∈R p is the output of the system, θ i (i=1,...,s) is the parameter of each sub-model, x j ∈R n is the regression vector of the system, which always contains the past input and output of the system, x j It can be expressed as:

[0019]

[0020] where n y and n u represents the order of the piecewise affine model, u j is the system input, n=pn y +mn u .χ i (i=1,…,s) is a complete partition of the regression set χ, each region is a subset of a convex polyhedron, which can be written as:

[0021] χ i ={F i x j +g i ≤0}

[0022] Among them F i and g i Let H be the hyperplane coefficient matrix i =[F i g i ], (i=1,...,s), then the convex polyhedron region can be rewritten as:

[0023] χi ={H i [x j 1] T ≤0}

[0024] 1) Data clustering

[0025] The original data set is divided into s unrelated clusters, and a statistical data clustering method based on a Gaussian mixture model is used. Assume that N data samples are represented as:

[0026]

[0027] Based on the Gaussian mixture model, the data sample z j The probability density of can be expressed as:

[0028]

[0029] For Φ=(α,μ,∑) where the scalar parameter α:=(α1,α2,…,α s )satisfy (n+p)-dimensional vector and (n+p)×(n+p)-dimensional covariance matrix Σ:=(Σ1,Σ2,…,Σ s ), function p i (z; μ i ,∑ i ) is used to define and express multivariate Gaussian density, as follows:

[0030]

[0031] When the optimal parameter Φ is obtained, the data sample j is divided into clusters Γ i The probability can be expressed as:

[0032]

[0033] The above probability is used as the criterion for data clustering. The remaining part is to find the optimal parameter Φ based on the maximum likelihood estimation method. According to N data samples, the optimal parameter Φ that can maximize the log-likelihood function is found:

[0034]

[0035] The expectation maximization (EM) algorithm is used to obtain the maximum value by iteratively updating the parameter Φ. The EM algorithm consists of two steps, namely the expectation step (E step) and the maximization step (M step). In the M step, it involves maximizing the log-likelihood function, which is redefined in the E step of each iteration.

[0036] The execution process of the EM algorithm is as follows: (0)Starting with several initial parameters, the EM algorithm can improve the maximum value,

[0037] EM algorithm:

[0038] 1) Initialize Φ (0) =(α (0) ,μ (0) ,Σ (0) ) and set the iteration counter l=0 and ε>0;

[0039] 2)Φ (l) =(α (l) ,μ (l) ,Σ (l) ) Perform the following steps

[0040] Step E: Calculation

[0041]

[0042] M step: Update Φ (l) =(α (l) ,μ (l) ,Σ (l) )calculate

[0043]

[0044] 3) If the specified convergence conditions are met

[0045]

[0046] Then suppose l * =l+1, the optimal estimate of Ф is Otherwise, input l=l+1 and return to step 2);

[0047] The data clustering process is based on the known number of affine sub-models. Since the number of sub-models cannot be known in advance in practice, the number of sub-models is estimated based on the maximum likelihood estimation related information criterion:

[0048] First, given two positive integers s min and s max , so that the number of sub-models is in the interval [s min ,s max ], then, for all s=s min ,…,s max , calculate the parameter estimate Ф s , Ф s represents the estimate of Φ under fixed s, and the estimate of s is obtained as follows:

[0049]

[0050] Where J(Ф s ,s) represents the criteria shown below. Based on the existing model selection information criteria, the consistent Akaike Information Criterion (CAIC) and MDL criteria are adopted. The above criteria have the following forms:

[0051] J(Φ s ,s)=-2L(Φ s )+A(N)D(s)

[0052] Where L(Ф s ) is the Φ defined in the above formula s The log-likelihood function of the criterion represents the penalty for the data and the number of clusters, where D(s) represents Ф s The number of independent parameters in is expressed as:

[0053]

[0054] And A(N) is a function of the number of data samples N, which are

[0055]

[0056] (2) Sub-model parameter estimation

[0057] After completing the data clustering task, according to the set Г i The data points collected in the affine sub-model are used to estimate the parameters of the affine sub-model. This task is completed by the least squares algorithm. The N data samples are divided into s disjoint clusters. Assume that there are N in the i-th cluster. i samples, denoted as j i1 ,j i2 ,…,j iNi ; The first subscript represents the number of clusters, and the second subscript represents the number of samples in the i-th cluster. Based on the above description, the following equations and variables can be obtained:

[0058]

[0059]

[0060] Using the least squares algorithm, the parameters of each affine sub-model can be estimated as follows:

[0061]

[0062] (3) Calculation of hyperplane coefficient matrix

[0063] The data clustering and parameter estimation of each affine sub-model are realized. The last step is to calculate the Γ used to classify two adjacent clusters. i and G jThe hyperplane coefficient matrix of the data sample is divided into s non-overlapping clusters, and Г i The data points in j The hyperplane coefficient matrix separating the data points in , for any pair i, j and i≠j, reconstruct the entire set to achieve recognition of s(s-1) / 2 patterns;

[0064] According to the principle of statistical learning method, the improved proximal support vector machine method is selected to calculate the hyperplane coefficient matrix:

[0065] First, find two adjacent clusters Г i and G j , the basic equations for the calculation are defined as follows:

[0066]

[0067] Secondly, combined with the improved approximate support vector machine (PSVM) algorithm, the interface coefficient matrix is ​​obtained by solving the following optimization problem:

[0068]

[0069] wxya i (F i x i -eg i )=λ i -ξ i

[0070] Where V i and W i is a diagonal matrix, ξ i is the error vector, e is the unit vector, when W i =1, V i =v (v is the penalty factor), λ i =1, and W i =-1, V i =v(n + / n - ), λ i =a i (a i is a positive number), n + is the number of positive samples, n - is the number of negative samples, when 0 i <1, the classification hyperplane moves toward the negative sample direction. i When >1, the classification hyperplane moves toward the positive sample direction, and by adjusting a i The value of is used to adjust the deviation of the classification hyperplane; according to the KKT (Karush-Kuhn-Tucher) condition, the following Lagrange equation can be constructed:

[0071] ​

[0072] where η i is the Lagrange coefficient. Using the extreme value of the Lagrange condition, we can further obtain the following equation:

[0073]

[0074] According to the above equation, we can further obtain:

[0075]

[0076] On this basis, we can further obtain:

[0077]

[0078] Subtracting the above two formulas, we can get:

[0079]

[0080] Multiply both sides of the above formula by W i , we can get:

[0081]

[0082] Combining the above formula, we can get:

[0083]

[0084] so

[0085]

[0086] Calculate the hyperplane coefficient matrix F i and g j .

[0087] Preferably, the method for constructing the segmented affine mathematical model of the vehicle lateral dynamics system in step 3 is as follows:

[0088] The equations for the two-degree-of-freedom vehicle model describing the lateral and yaw motions of the vehicle are as follows:

[0089]

[0090] Among them, F xij and F yij Represents the longitudinal force and lateral force of the tire respectively. The first subscript i=f or r represents the front axle or rear axle, and the second subscript j=l or r represents the left and right wheels; x Represent vehicle mass, longitudinal speed, l f and l rRepresent the length of the front and rear axles of the vehicle, B represents the wheelbase, r is the yaw rate of the vehicle, I z is the inertia moment of the vehicle Z axis; ΔM is the additional yaw moment, is the time derivative of the vehicle's yaw rate, Derivative of the center of mass sideslip angle with respect to time;

[0091] Based on the piecewise affine tire model, the four tire longitudinal and lateral forces under a specific vertical load can be described as:

[0092]

[0093] Wherein the above formula M i , N i and b i is the parameter of the vehicle longitudinal force on different affine sub-models, M j , N j and b j are the parameters of the vehicle lateral force on different affine sub-models, α1 and α3 are the sideslip angles of the front and rear wheels, λ1, λ2, λ3, and λ4 are the slip rates of each vehicle;

[0094] The tire's slip angle can be expressed as:

[0095]

[0096] Where β is the sideslip angle of the center of mass, r is the yaw rate, l f is the front axle length, v x is the longitudinal speed, δ is the front wheel turning angle;

[0097] According to the above formula, the vehicle lateral dynamics model can be rewritten as an equation about the sideslip angle β and the yaw rate r:

[0098]

[0099] L1~L 16 is the correlation coefficient of the lateral dynamics mathematical model, as follows:

[0100]

[0101] Combined with experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters, in the process of constructing a piecewise affine mathematical model of the vehicle lateral dynamics system, the working areas of the longitudinal force mathematical model and the lateral force mathematical model are divided into longitudinal affine sub-model and lateral affine sub-model respectively according to the differences in tire sideslip angle and slip rate.

[0102] Preferably, the method for obtaining the final additional yaw moment in step 4 is as follows:

[0103] The equations of the lateral two-degree-of-freedom model describing the vehicle's lateral and yaw motions are as follows:

[0104]

[0105] Where m is the mass of the vehicle, l f 、l r are the distances from the center of mass to the front and rear axles, δ is the front wheel slip angle, β is the center of mass slip angle, k f and k r is the cornering stiffness of the front and rear wheels, I z is the moment of inertia, v x is the longitudinal velocity of the vehicle in the vehicle coordinate system, r is the yaw rate of the vehicle, and ΔM is the additional yaw moment;

[0106] By solving the above formula, the reference values ​​of yaw rate and sideslip angle are obtained as follows:

[0107]

[0108] Where L is the wheelbase, μ is the road adhesion coefficient, and K is the stability factor. The expression is:

[0109]

[0110] (1) First, define the difference between the actual yaw rate and the reference yaw rate and the global fast terminal sliding mode surface as:

[0111]

[0112] where ρ r , γ r >0,p r and q r (p r >q r ) are all positive odd numbers;

[0113] The yaw moment of the vehicle can be expressed as:

[0114]

[0115] Where F represents the effect of tire force and ΔM is the additional yaw moment, which can be expressed as:

[0116]

[0117] Through the above formula, we get the sliding surface s r Derivative with respect to time:

[0118]

[0119] Select the exponential reaching law and replace the sign function in the exponential reaching law with a saturation function to reduce the system chattering:

[0120]

[0121] The optimal additional yaw moment expression based on the yaw rate tracking error is:

[0122]

[0123] (2) Then, the difference between the actual center of mass sideslip angle and the reference center of mass sideslip angle is defined. The global fast terminal sliding surface and the time derivative of the sliding surface are:

[0124]

[0125]

[0126] where ρ β , γ β >0,p β and q β (p β >q β ) are all positive odd numbers;

[0127] Choose an exponential reaching law with a saturation function to reduce the chattering of the system:

[0128]

[0129] Among them, K β and k β is the coefficient of the sliding surface reaching law, K β >0,k β >0;

[0130] The optimal additional yaw moment expression based on the center of mass sideslip angle tracking error is:

[0131]

[0132] (3) The range of the center of mass sideslip angle threshold is represented by two parallel lines in the stability region, which is expressed as follows:

[0133]

[0134] Among them, B1 and B2 are stability coefficients; when The vehicle can be considered to be in a stable state when The vehicle is considered to be in an unstable state;

[0135] When the vehicle's center of mass slip angle phase trajectory is within the stable region, the yaw rate and center of mass slip angle are jointly controlled. When the vehicle's center of mass slip angle phase trajectory exceeds the stable region, the center of mass slip angle is controlled.

[0136] ΔM r and ΔM β The weights of the two are set to 1-P and P respectively. P is calculated from the stable region expression in the phase plane. The final additional yaw moment ΔM is:

[0137] ΔM=(1-P)ΔM r +PΔM β

[0138] Where P is

[0139]

[0140] Among them, B1 and B2 are the correlation coefficients of the stable region.

[0141] Preferably, in step 5, an optimal four-wheel torque distribution algorithm is designed, with the minimum sum of the load rates of the four wheels as the objective function, combined with the front and rear wheel distribution weight coefficients, to obtain the real-time optimal torque of the four wheels; the specific distribution algorithm is as follows:

[0142] (1) Based on the difference between the actual speed and the target speed, the total torque is calculated using a proportional-integral (PI) controller. The control process can be expressed as follows:

[0143]

[0144] Among them, v xd and v x is the target speed and actual speed, k pu and k iu is the parameter of PI controller, T o is the total driving torque of the four wheels;

[0145] (2) In wheel torque control, the sum of the load rates of each tire is used as the objective function. The tire load rate represents the stability margin of the vehicle. When J is larger, the stability margin is smaller, and the possibility of vehicle instability is greater. On the contrary, the vehicle has more stability margin to overcome possible instability. The load rate of each tire is defined as:

[0146]

[0147] The motor can only control the longitudinal force and xij =T ij / R is substituted into it, where R is the tire radius, the tire load rate becomes:

[0148]

[0149] The objective function is the sum of the load rates of each tire and the weights assigned to them:

[0150] min J=minξ fl J fl +ξ fr J fr +ξ rl J rl +ξ rr J rr

[0151] Among them, min J is the sum of the tire utilization weights of each wheel, minξ fl J fl is the tire weight utilization rate of the left front wheel, minξ fr J fr is the tire weight utilization rate of the right front wheel, minξ rl J rl is the tire weight utilization rate of the left rear wheel, minξ rr J rr is the tire weight utilization of the right rear wheel;

[0152] The weight coefficients of each wheel are defined as follows:

[0153]

[0154] Among them, B1 and B2 are the correlation coefficients of the phase plane stability region of the sideslip angle at the center of mass, and Δr is the difference between the actual value and the reference value of the yaw rate;

[0155] The relationship between the total driving torque, yaw torque and each wheel torque is as follows:

[0156]

[0157] The two front wheel torques can be solved as:

[0158]

[0159] Substituting the above formula into the objective function, we get:

[0160]

[0161] Transform the objective function J to T rl and T rr Taking partial derivatives we get:

[0162]

[0163] make The optimal torque of the four wheels is obtained as:

[0164]

[0165] Beneficial effects: The technical solution of the present invention completes the piecewise affine identification of the tire longitudinal slip and sideslip mechanical characteristics, and then completes the construction of the piecewise affine mathematical model of the vehicle's lateral dynamics system on this basis. The two yaw moments are obtained by solving the errors between the actual value and the reference value of the yaw angular velocity and the center of mass sideslip angle through a global fast terminal sliding mode. The vehicle's lateral stability is then analyzed through the center of mass sideslip angle phase diagram, and different weights are given to the two to obtain the final yaw moment. The lower-level torque controller uses equality constraints to introduce the objective function to obtain real-time four-wheel torque, thereby improving the lateral stability control performance of the smart car under special driving conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0166] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only embodiments of the present invention. Those skilled in the art can also derive other drawings based on the provided drawings without inventive effort.

[0167] Figure 1 This is a flow chart of the segmented affine identification of the tire longitudinal slip and cornering mechanical characteristics of the present invention;

[0168] Figure 2 This is a flow chart of lateral dynamic control based on piecewise affine system;

[0169] Figure 3 This is the vehicle dynamics control flow chart of the present invention. DETAILED DESCRIPTION

[0170] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0171] In the description of the present invention, it should be understood that the terms "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating directions or positional relationships, are based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore should not be understood as limiting the present invention.

[0172] In the present invention, unless otherwise expressly specified or limited, a first feature being "above" or "below" a second feature may include the first and second features being in direct contact, or may include the first and second features being in contact not directly but through another feature between them. Furthermore, a first feature being "above," "above," and "above" a second feature may include the first feature being directly above or obliquely above the second feature, or may simply mean that the first feature is higher in level than the second feature. A first feature being "below," "below," and "below" a second feature may include the first feature being directly below or obliquely below the second feature, or may simply mean that the first feature is lower in level than the second feature.

[0173] As shown in the figure, a vehicle stability control method based on piecewise affine identification tire sliding mode control includes the following steps:

[0174] Step 1: The mechanical properties of the tire under combined operating conditions were measured on a high-performance flatbed test bench to obtain experimental data reflecting the nonlinear relationship between the tire's longitudinal and lateral forces and tire operating parameters. Analysis revealed that under a specific vertical load, the tire's longitudinal and lateral forces are primarily influenced by three factors: tire slip rate, slip angle, and road adhesion coefficient. Furthermore, experimental results indicate that the ratio of the tire's longitudinal force to its lateral force is approximately equal to the ratio of the road adhesion coefficients. Therefore, modeling the tire's longitudinal slip and cornering characteristics is defined as a three-dimensional piecewise affine identification problem.

[0175] Step 2: Construct a segmented affine identification model for the tire's longitudinal slip and sideslip, and perform segmented affine identification on the tire's nonlinear mechanical characteristics based on the test data. The steps mainly include: data clustering, affine sub-model parameter estimation, and calculation of the hyperplane coefficient matrix.

[0176] The specific implementation methods for completing tire longitudinal slip and cornering mechanical characteristics test data clustering, affine sub-model parameter estimation, and interface coefficient matrix solution are as follows:

[0177] (1) Define the piecewise affine model form of the tire longitudinal slip and cornering mechanical characteristics

[0178] The mathematical expression of the model is as follows:

[0179]

[0180] where y j ∈R p is the output of the system, θ i (i=1,...,s) is the parameter of each sub-model, x j ∈R n is the regression vector of the system, which always contains the past input and output of the system, x j It can be expressed as:

[0181]

[0182] where n y and n u represents the order of the piecewise affine model, u j is the system input, n=pn y +mn u .χ i (i=1,…,s) is a complete partition of the regression set χ, each region is a subset of a convex polyhedron, which can be written as:

[0183] χ i ={F i x j +g i ≤0}

[0184] Among them F i and g i is the hyperplane coefficient matrix. Let H i =[F i g i ], (i=1,...,s) then the convex polyhedron region can be rewritten as:

[0185] χ i ={H i [x j 1] T ≤0}

[0186] 1) Data clustering

[0187] In this embodiment, the goal of data clustering is to divide the original data set into s independent clusters. To this end, a statistical data clustering method based on a Gaussian mixture model is used. Assume that N data samples are represented as:

[0188]

[0189] Based on the Gaussian mixture model, the data sample z j The probability density of can be expressed as:

[0190]

[0191] For Φ=(α,μ,∑) where the scalar parameter α:=(α1,α2,…,α s )satisfy (n+p)-dimensional vector and (n+p)×(n+p)-dimensional covariance matrix Σ:=(Σ1,Σ2,…,Σ s ), function p i (z; μ i ,∑ i ) is used to define and express multivariate Gaussian density, as follows:

[0192]

[0193] When the optimal parameter Φ is obtained, the data sample j is divided into clusters Γ i The probability can be expressed as:

[0194]

[0195] This probability can be used as a criterion for data clustering. Therefore, the remaining part shows how to find the optimal parameter Φ based on the maximum likelihood estimation method. Based on N data samples, find the optimal parameter Φ that can maximize the log-likelihood function:

[0196]

[0197] For a single Gaussian model, the optimal parameter Φ that maximizes the value of the above function can be derived. However, for the Gaussian mixture model adopted, this approach is not feasible. Therefore, the well-known expectation maximization (EM) algorithm is used to obtain the (possibly local) maximum value by iteratively updating the parameter Φ. The EM algorithm consists of two steps, the expectation step (E step) and the maximization step (M step). In the M step, it involves the maximization of the log-likelihood function, which is redefined in the E step of each iteration. The execution process of the EM algorithm is shown below. From Φ (0) Starting with several initial parameters, the EM algorithm can improve the maximum value.

[0198] EM algorithm:

[0199] 4) Initialize Φ (0) =(α (0) ,μ (0) ,Σ (0) ) and set the iteration counter l = 0 and ε > 0.

[0200] 5)Φ (l) =(α (l) ,μ (l) ,Σ (l) ) Perform the following steps

[0201] Step E: Calculation

[0202]

[0203] M step: Update Φ (l) =(α (l) ,μ (l) ,Σ (l) )calculate

[0204]

[0205] 6) If the specified convergence conditions are met

[0206]

[0207] Then suppose l * =l+1, the optimal estimate of Ф is Otherwise, input l=l+1 and return to step 2).

[0208] From the above description, we can see that the data clustering process is based on the known number of affine sub-models. However, since the number of sub-models cannot be known in advance in practice, we further introduce the estimation of the number of sub-models based on the maximum likelihood estimation related information criterion.

[0209] First, given two positive integers s min and s max , so that the number of sub-models is in the interval [s min ,s max ] inside. Then, for all s=s min ,…,s max , calculate the parameter estimate Ф s , Ф s represents the estimate of Φ for a fixed s. The estimate of s is obtained as follows:

[0210]

[0211] Where J(Ф s ,s) represents the criteria shown below. Based on the existing model selection information criteria, the consistent Akaike Information Criterion (CAIC) and the MDL criterion are adopted. The above criteria have the following form:

[0212] J(Φ s ,s)=-2L(Φ s )+A(N)D(s)

[0213] Where L(Ф s ) is the Φ defined in the above formula s The log-likelihood function of the criterion represents the penalty for the data and the number of clusters, where D(s) represents Ф s The number of independent parameters in is expressed as:

[0214]

[0215] And A(N) is a function of the number of data samples N, which are

[0216]

[0217] (2) Sub-model parameter estimation

[0218] After completing the data clustering task, you can i The parameters of the affine sub-model are estimated from the data points collected in . Obviously, this task can be completed by the least squares algorithm. Since N data samples are divided into s disjoint clusters, it is assumed that there are N i samples, denoted as j i1 ,j i2 ,…,j iNi The first subscript represents the number of clusters, and the second subscript represents the number of samples in the i-th cluster. Based on the above description, the following equations and variables can be obtained:

[0219]

[0220] On this basis, the least squares algorithm can be used to estimate the parameters of each affine sub-model as follows:

[0221]

[0222] (3) Calculation of hyperplane coefficient matrix

[0223] So far, data clustering and parameter estimation of each affine sub-model have been achieved. The last step is to calculate the Γ used to classify two adjacent clusters i and G j It is worth noting that once the data samples are divided into s disjoint clusters, by calculating Г i The data points in j The hyperplane coefficient matrix that separates the data points in the cluster can be used to reconstruct the entire cluster for any pair i, j where i≠j. This work actually solves the s(s-1) / 2 pattern recognition problem. Based on the principles of statistical learning methods, the improved proximal support vector machine method is selected to solve this problem. The process of calculating the hyperplane coefficient matrix using this method is then introduced in detail. First, find two adjacent clusters Г i and G j , the basic equations for the calculation are defined as follows:

[0224]

[0225] Next, the parameters of the switching hyperplane are calculated to minimize the following cost function established by the improved PSVM:

[0226]

[0227] wxya i (β i x i -eg i )=λ i -ξ i

[0228] Where V i and W i is a diagonal matrix, ξ i is the error vector, e is the unit vector, when W i =1, V i =v (v is the penalty factor), λ i =1, and W i =-1, V i =v(n + / n - ), λ i =a i (a i is a positive number). + is the number of positive samples, n - is the number of negative samples. i <1, the classification hyperplane moves toward the negative sample direction. i When a > 1, the classification hyperplane moves toward the positive sample. Therefore, by adjusting a i The value of is used to adjust the deviation of the classification hyperplane. For the above, according to the KKT condition, the following Lagrange equation can be constructed:

[0229]

[0230] where η i is the Lagrange coefficient. Using the Lagrange condition extreme value, we can further obtain the following equation:

[0231]

[0232] According to the above equation, we can further obtain:

[0233]

[0234] On this basis, we can further obtain:

[0235]

[0236] Subtracting the above two formulas, we can get:

[0237]

[0238] Multiply both sides of the above formula by W i , we can get:

[0239]

[0240] Combining the above formula, we can get:

[0241] ​

[0242] so

[0243]

[0244] Then we can calculate the hyperplane coefficient matrix F i and g j .

[0245] Step 3: Construct a piecewise affine mathematical model of the vehicle's lateral dynamics system. This model is based on the tire's longitudinal slip piecewise affine identification model and combines the vehicle body's yaw rate and center of mass sideslip angle to construct a piecewise affine mathematical model of the vehicle's lateral dynamics system.

[0246] Based on the tire longitudinal slip and sideslip segmented affine identification model, a segmented affine mathematical model of the intelligent vehicle lateral dynamics system is further constructed. The lateral dynamics system model is mainly used to reflect the changes in the vehicle body yaw angular velocity and center of mass sideslip angle.

[0247] The equations for the two-degree-of-freedom vehicle model describing the lateral and yaw motions of the vehicle are as follows:

[0248]

[0249] Among them, F xij and F yij Represents the longitudinal force and lateral force of the tire respectively. The first subscript i=f or r represents the front axle or rear axle, and the second subscript j=l or r represents the left and right wheels; x Represent vehicle mass, longitudinal speed, l f and l r Represent the length of the front and rear axles of the vehicle, B represents the wheelbase, r is the yaw rate of the vehicle, I z is the inertia moment of the vehicle Z axis; ΔM is the additional yaw moment, is the time derivative of the vehicle's yaw rate, Derivative of the center of mass sideslip angle with respect to time;

[0250] Based on the piecewise affine tire model, the four tire longitudinal and lateral forces under a specific vertical load can be described as:

[0251]

[0252] Wherein the above formula M i , N i and b i is the parameter of the vehicle longitudinal force on different affine sub-models, M j , N j and b jare the parameters of the vehicle lateral force on different affine sub-models, α1 and α3 are the sideslip angles of the front and rear wheels, λ1, λ2, λ3, and λ4 are the slip rates of each vehicle;

[0253] The tire's slip angle can be expressed as:

[0254]

[0255] Where β is the sideslip angle of the center of mass, r is the yaw rate, l f is the front axle distance, v x is the longitudinal velocity and δ is the front wheel turning angle.

[0256] According to the above formula, the vehicle lateral dynamics model can be further rewritten as an equation about the sideslip angle β and the yaw rate r:

[0257]

[0258] L1~L 16 is the correlation coefficient of the lateral dynamics mathematical model, as follows:

[0259]

[0260] Combined with experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters, in the process of constructing a piecewise affine mathematical model of the vehicle lateral dynamics system, the working area of ​​the mathematical model of longitudinal force is divided into 14 parts, and the working area of ​​the mathematical model of lateral force is divided into 10 parts according to the differences in tire sideslip angle and slip rate.

[0261] Step 4: Obtain the final additional yaw moment. Two optimal additional yaw moments are solved using the global fast terminal sliding mode control law based on the errors between the actual and reference values ​​of the yaw rate and the center of mass slip angle. The final additional yaw moment is obtained by assigning different weights to the two based on the instability determination results of the center of mass slip angle and center of mass slip rate phase diagram.

[0262] Both the yaw rate and the sideslip angle have a significant impact on the lateral stability of the vehicle during steering. The vehicle's stability state is analyzed based on the strategy of the sideslip angle and the sideslip rate being in the same plane.

[0263] The lateral two-degree-of-freedom state equation that can accurately reflect the vehicle's lateral motion and yaw motion is as follows:

[0264]

[0265] Where m is the mass of the vehicle, l f 、l r are the distances from the center of mass to the front and rear axles, δ is the front wheel slip angle, β is the center of mass slip angle, kf and k r is the cornering stiffness of the front and rear wheels, I z is the moment of inertia, v x is the longitudinal velocity of the car in the vehicle coordinate system, r is the yaw rate of the vehicle, and ΔM is the additional yaw moment.

[0266] By solving the above formula, the reference values ​​of yaw rate and sideslip angle are obtained as follows:

[0267]

[0268] Where L is the wheelbase, μ is the road adhesion coefficient, and K is the stability factor. The expression is:

[0269]

[0270] (1) First, define the difference between the actual yaw rate and the reference yaw rate and the global fast terminal sliding mode surface as:

[0271]

[0272] where ρ r , γ r >0,p r and q r (p r >q r ) are all positive odd numbers;

[0273] The yaw moment of the vehicle can be expressed as:

[0274]

[0275] Where F represents the effect of tire force and ΔM is the additional yaw moment, which can be expressed as:

[0276]

[0277] Through the above formula, we can further obtain the sliding surface s r Derivative with respect to time

[0278]

[0279] To address the large step response control issues common in special driving conditions, an exponential reaching law was selected. This allows the system to approach the sliding surface more quickly. Furthermore, the sign function in the exponential reaching law was replaced with a saturation function to reduce system chattering:

[0280]

[0281] Therefore, the optimal additional yaw moment expression based on the yaw rate tracking error is:

[0282]

[0283] (2) Then, the difference between the actual center of mass sideslip angle and the reference center of mass sideslip angle is defined. The global fast terminal sliding surface and the time derivative of the sliding surface are:

[0284]

[0285] where ρ β , γ β >0,p β and q β (p β >q β ) are all positive odd numbers;

[0286] Similarly, an exponential reaching law with a saturation function is selected to reduce the system chattering.

[0287]

[0288] Among them, K β and k β is the coefficient of the sliding surface reaching law, K β >0,k β >0.

[0289] Therefore, the optimal additional yaw moment expression based on the center of mass sideslip angle tracking error is:

[0290]

[0291] (3) The main function of the lateral stability control system is to ensure that the phase trajectory of the vehicle's lateral motion is in a stable region. In the stability analysis of slippery roads, the phase plane of the center of mass slip angle and the center of mass slip angular velocity has a better accuracy for stability analysis. Taking a given road adhesion coefficient as an example, the phase trajectory of the center of mass slip angle is obtained by giving different initial values ​​(β(0), r(0)). In the phase diagram, there is a stability region that can be represented by two parallel lines, and its expression is as follows:

[0292]

[0293] Among them, B1 and B2 are stability coefficients; when The vehicle can be considered to be in a stable state when When , the vehicle is considered to be in an unstable state. Combined with the specific vehicle parameters studied, the stability region under different road adhesion coefficients is obtained.

[0294] The joint control strategy specified here is to select the joint control of yaw rate and center of mass sideslip angle when the vehicle's center of mass sideslip angle phase trajectory is within the stable region, and to select the control of the center of mass sideslip angle when the vehicle's center of mass sideslip angle phase trajectory exceeds the stable region.

[0295] Therefore, ΔM r and ΔM β The weights of the two are set to 1-P and P respectively. P is calculated by the stable region expression in the phase plane. The final additional yaw moment ΔM is:

[0296] ΔM=(1-P)ΔM r +PΔM β

[0297] Where P is

[0298]

[0299] Among them, B1 and B2 are the correlation coefficients of the stable region.

[0300] Step 5: Design an optimal four-wheel torque distribution algorithm, taking the minimum sum of the load rates of the four wheels as the objective function, and combining the front and rear wheel distribution weight coefficients to obtain the real-time optimal torque of the four wheels;

[0301] Taking the minimum sum of the load rates of the four wheels as the objective function, different weight coefficients are assigned to each wheel considering the actual situation. The weight coefficients are related to the instability judgment expression of the phase plane between the center of mass sideslip velocity and the center of mass sideslip angle, and the real-time torque of each wheel is obtained.

[0302] (1) The vehicle's longitudinal speed should track the target speed along the path in real time. Therefore, a speed tracking controller is designed to determine the total torque acting on the four wheels. Based on the difference between the actual speed and the target speed, a proportional-integral (PI) controller is used to calculate the total torque. The control process can be expressed as follows:

[0303]

[0304] Among them, v xd and v x is the target speed and actual speed, k pu and k iu is the parameter of PI controller. o is the total four-wheel drive torque.

[0305] (2) In the wheel torque control module, the sum of the load rates of each tire is used as the objective function. The tire load rate can be used to characterize the stability margin of the vehicle. The larger J is, the smaller the stability margin is, and the greater the possibility of vehicle instability. On the contrary, the vehicle has more stability margin to overcome possible instability. The load rate of each tire can be defined as:

[0306]

[0307] Because the motor can only control the longitudinal force, while F xij =T ij / R is substituted into it, where R is the tire radius, the tire load rate becomes:

[0308]

[0309] The objective function is the sum of the load rates of each tire and the weights assigned to them:

[0310] min J=minξ fl J fl +ξ fr J fr +ξ rl J rl +ξ rr J rr

[0311] Among them, min J is the sum of the tire utilization weights of each wheel, minξ fl J fl is the tire weight utilization rate of the left front wheel, minξ fr J fr is the tire weight utilization rate of the right front wheel, minξ rl J rl is the tire weight utilization rate of the left rear wheel, minξ rr J rr is the tire weight utilization of the right rear wheel;

[0312] In order to improve the stability of the vehicle, the vehicle should have a certain degree of understeer. Therefore, the weight value of the rear axle should be greater than that of the front axle, and the difference in weight coefficient between the front and rear axles should not be too large.

[0313] Therefore, the weight coefficients of each wheel are defined as follows:

[0314]

[0315] Among them, B1 and B2 are the correlation coefficients of the phase plane stability region of the center of mass sideslip angle, and Δr is the difference between the actual value and the reference value of the yaw rate.

[0316] From the above, we can see that the relationship between the total driving torque, yaw torque and each wheel torque is as follows:

[0317]

[0318] The two front wheel torques can be solved as:

[0319]

[0320] Substituting the above formula into the objective function, we get:

[0321]

[0322] Transform the objective function J to T rl and T rr Taking the partial derivative we get:

[0323]

[0324] make The optimal torque of the four wheels is obtained as:

[0325]

[0326] Step 6: Vehicle Application: The designed system control law is flashed to the onboard control unit of the distributed drive electric vehicle. The controller's parameters are obtained using existing sensors on the production vehicle. The speed sensor measures longitudinal velocity, the wheel speed sensors measure individual wheel speeds, the vehicle's ESP outputs yaw rate, the body's center of mass slip angle sensor outputs center of mass slip angle, and the tire slip angle outputs. These signal parameters are used to determine the vehicle's stability. The upper-level yaw moment decision module calculates the real-time required yaw torque, which is then transmitted to the lower-level torque distribution module. The calculated torque is then distributed to each wheel.

[0327] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0328] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A vehicle stability control method based on piecewise affine identification tire sliding mode control, characterized in that: The following steps are involved: Step 1: A tire longitudinal slip and cornering characteristic test is performed to obtain experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters; Step 2: constructing a tire longitudinal slip and cornering piecewise affine identification model, which is a tire longitudinal slip and cornering characteristic model established through piecewise affine identification based on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters; Step 3: Construct a piecewise affine mathematical model of the vehicle's lateral dynamics system. This model is based on the tire's longitudinal slip piecewise affine identification model and combines the vehicle body's yaw rate and center of mass sideslip angle to construct a piecewise affine mathematical model of the vehicle's lateral dynamics system. Step 4: Obtain the final additional yaw moment. Two optimal additional yaw moments are solved using the global fast terminal sliding mode control law based on the errors between the actual and reference values ​​of the yaw rate and the center of mass slip angle. The final additional yaw moment is obtained by assigning different weights to the two based on the instability determination results of the center of mass slip angle and center of mass slip rate phase diagram. Step 5: Design an optimal four-wheel torque distribution algorithm, taking the minimum sum of the load rates of the four wheels as the objective function, and combining the front and rear wheel distribution weight coefficients to obtain the real-time optimal torque of the four wheels; Step 6: Install and apply the control system designed according to the methods in steps 1-5 and flash it to the on-board control unit of the distributed drive electric vehicle. The controller obtains the parameters required by the existing sensors on the vehicle to determine the stability of the vehicle. The control system calculates the real-time required yaw moment and then calculates the four wheel torques and distributes them to each wheel. The method for constructing the segmented affine mathematical model of the vehicle lateral dynamics system in step 3 is as follows: The equations for the two-degree-of-freedom vehicle model describing the lateral and yaw motions of the vehicle are as follows: ； Among them, F xij and F yij Represents the longitudinal force and lateral force of the tire respectively. The first subscript i=f or r represents the front axle or rear axle, and the second subscript j=l or r represents the left and right wheels; among them, m and v x Represent vehicle mass, longitudinal velocity, l f and l r Represent the length of the front and rear axles of the vehicle, B represents the wheelbase, r is the yaw rate of the vehicle, I z is the inertia moment of the vehicle about the Z axis; ∆M is the additional yaw moment, is the time derivative of the vehicle's yaw rate, Derivative of the center of mass sideslip angle with respect to time; Using the piecewise affine tire model, the four tire longitudinal and lateral forces under vertical load are described as: ； Wherein the above formula M i , N i and b i is the parameter of the vehicle longitudinal force on different affine sub-models, M j , N j and b j are the parameters of the vehicle lateral force on different affine sub-models, α1 and α3 are the sideslip angles of the front and rear wheels, λ1, λ2, λ3, and λ4 are the slip rates of each vehicle; The tire's slip angle is expressed as: ； Where β is the sideslip angle of the center of mass, r is the yaw rate, l f is the front axle length, v x is the longitudinal speed, δ is the front wheel turning angle; According to the above formula, the vehicle lateral dynamics model is rewritten as the equation about the sideslip angle β and the yaw rate r: ； L1 ~L 16 is the correlation coefficient of the lateral dynamics mathematical model, as follows: ； Combined with experimental data on the nonlinear relationship between tire longitudinal force and lateral force and tire operating parameters, in the process of constructing a piecewise affine mathematical model of the vehicle lateral dynamics system, the working areas of the longitudinal force mathematical model and the lateral force mathematical model are divided into longitudinal affine sub-model and lateral affine sub-model respectively according to the differences in tire sideslip angle and slip rate.

2. The vehicle stability control method based on piecewise affine identification tire sliding mode control according to claim 1, characterized in that: The steps of constructing the tire longitudinal slip and cornering characteristic model in step 2 include data clustering, affine sub-model parameter estimation, and calculation of the hyperplane coefficient matrix. The specific implementation method is as follows: (1) Define the piecewise affine model form of the tire longitudinal slip and cornering mechanical characteristics The mathematical expression of the model is as follows: ； where y j ∈R p is the output of the system, θ i (i=1,..., s) is the parameter of each sub-model, x j ∈R n is the regression vector of the system, which always contains the past input and output of the system, x j Expressed as: ； where n y and n u represents the order of the piecewise affine model, u j is the system input, n=pn y +mn u . χ i (i=1,…, s) is a complete partition of the regression set χ, each region is a subset of a convex polyhedron, written as: ； Among them F i and g i Let H be the hyperplane coefficient matrix i = [F i g i ], (i=1,..., s), then the convex polyhedron region can be rewritten as: ； 1) Data clustering The original data set is divided into s unrelated clusters, and a statistical data clustering method based on a Gaussian mixture model is used. Assume that N data samples are represented as: ； Based on the Gaussian mixture model, the data sample z j The probability density of is expressed as: ； For Φ=(α,μ,∑) where the scalar parameter satisfy , (n+p)-dimensional vector and (n+p)×(n+p)-dimensional covariance matrix ,function It is used to define and express multivariate Gaussian density, as follows: ； When the optimal parameter Φ is obtained, the data sample j is divided into clusters Γ i The probability is expressed as: ； The above probability is used as the criterion for data clustering. The remaining part is to find the optimal parameter Φ based on the maximum likelihood estimation method. According to N data samples, the optimal parameter Φ that can maximize the log-likelihood function is found: ； The expectation maximization (EM) algorithm is used to obtain the maximum value by iteratively updating the parameter Φ. The EM algorithm consists of two steps, namely the expectation step (E step) and the maximization step (M step). In the M step, it involves maximizing the log-likelihood function, which is redefined in the E step of each iteration. The execution process of the EM algorithm is as follows: (0) Starting with several initial parameters, the EM algorithm improves the maximum value, EM algorithm: 1) Initialization At the same time, set the iteration counter l=0 and set ε > 0; 2) Perform the following steps Step E: Calculation ; ； Step M: Update calculate ； ； ； 3) If the specified convergence conditions are met ； Then suppose l * =l+1, the optimal estimate of Ф is Otherwise, input l=l+1 and return to step 2); The data clustering process is based on the known number of affine sub-models. Since the number of sub-models cannot be known in advance in practice, the number of sub-models is estimated based on the maximum likelihood estimation related information criterion: First, given two positive integers s min and s max , so that the number of sub-models is in the interval [s min , s max ], then, for all s= s min ,…,s max , calculate the parameter estimate Ф s , Ф s represents the estimate of Φ under fixed s, and the estimate of s is obtained as follows: ； Where J(Ф s , s) represents the criteria shown below. Based on the existing model selection information criteria, the consistent Akaike Information Criterion (CAIC) and MDL criteria are adopted. The above criteria have the following form: ； Where L(Ф s ) is the Φ defined in the above formula s The log-likelihood function of the criterion represents the penalty for the data and the number of clusters, where D(s) represents Ф s The number of independent parameters in is expressed as: ； And A(N) is a function of the number of data samples N, which are ； (2) Sub-model parameter estimation After completing the data clustering task, according to the set Г i The data points collected in the affine sub-model are used to estimate the parameters of the affine sub-model. This task is completed by the least squares algorithm. The N data samples are divided into s disjoint clusters. Assume that there are N in the i-th cluster. i samples, denoted as j i1 , j i2 ,…,j iNi ; The first subscript represents the number of clusters, and the second subscript represents the number of samples in the i-th cluster. Based on the above description, the following equations and variables are obtained: ； Using the least squares algorithm, the parameters of each affine sub-model are estimated as follows: ； (3) Calculation of hyperplane coefficient matrix The data clustering and parameter estimation of each affine sub-model are realized. The last step is to calculate the Γ used to classify two adjacent clusters. i and G j The hyperplane coefficient matrix of the data sample is divided into s non-overlapping clusters, and Г i The data points in j The hyperplane coefficient matrix separating the data points in , for any pair i, j and i≠j, reconstruct the entire set to achieve recognition of s(s-1) / 2 patterns; According to the principle of statistical learning method, the improved proximal support vector machine method is selected to calculate the hyperplane coefficient matrix: First, find two adjacent clusters Г i and G j , the basic equations for the calculation are defined as follows: ； Secondly, combined with the improved approximate support vector machine (PSVM) algorithm, the interface coefficient matrix is ​​obtained by solving the following optimization problem: ； Where V i and W i is a diagonal matrix, ξ i is the error vector, e is the unit vector, when W i =1, V i =v (v is the penalty factor), λ i =1, and W i =-1, V i = v (n + / n - ), λ i =a i (a i is a positive number), n + is the number of positive samples, n - is the number of negative samples, when 0< a i <1, the classification hyperplane moves toward the negative sample direction. i When >1, the classification hyperplane moves toward the positive sample direction, and by adjusting a i The value of is used to adjust the deviation of the classification hyperplane; the following Lagrange equation is constructed according to the KKT (Karush-Kuhn-Tucher) condition: ； where η i is the Lagrange coefficient. Using the extreme value of the Lagrange condition, we can further obtain the following equation: ； According to the above equation, we can further obtain: ； On this basis, we can further obtain: ； Subtracting the above two formulas, we get: ； Multiply both sides of the above formula by W i ,get: ； Combining the above formula, we get: ； so ； Calculate the hyperplane coefficient matrix F i and g j .

3. The vehicle stability control method based on piecewise affine identification tire sliding mode control according to claim 2, characterized in that: The method for obtaining the final additional yaw moment in step 4 is as follows: The equations of the lateral two-degree-of-freedom model describing the vehicle's lateral and yaw motions are as follows: ； Where m is the mass of the vehicle, l f 、l r are the distances from the center of mass to the front and rear axles, δ is the front wheel slip angle, β is the center of mass slip angle, k f and k r is the cornering stiffness of the front and rear wheels, I z is the moment of inertia, v x is the longitudinal velocity of the vehicle in the vehicle coordinate system, r is the yaw rate of the vehicle, and ∆M is the additional yaw moment; By solving the above formula, the reference values ​​of yaw rate and sideslip angle are obtained as follows: ； Where L is the wheelbase, μ is the road adhesion coefficient, and K is the stability factor. The expression is: ； (1) First, define the difference between the actual yaw rate and the reference yaw rate and the global fast terminal sliding surface as: ； where ρ r , γ r >0,p r and q r (p r > q r ) are all positive odd numbers; The yaw moment of the vehicle is expressed as: ； Where F represents the effect of the tire force and ∆M is the additional yaw moment, and the two are expressed as: ； Through the above formula, we get the sliding surface s r Derivative with respect to time: ； Select the exponential reaching law and replace the sign function in the exponential reaching law with a saturation function to reduce the system chattering: ； The optimal additional yaw moment expression based on the yaw rate tracking error is: ； (2) Secondly, the difference between the actual center of mass sideslip angle and the reference center of mass sideslip angle is defined. The global fast terminal sliding surface and the time derivative of the sliding surface are: ； where ρ β , γ β >0,p β and q β (p β > q β ) are all positive odd numbers; Choose an exponential reaching law with a saturation function to reduce the chattering of the system: ； Among them, K β and k β is the coefficient of the sliding surface reaching law, K β >0,k β >0; The optimal additional yaw moment expression based on the center of mass sideslip angle tracking error is: ； (3) The range of the center of mass sideslip angle threshold is represented by two parallel lines in the stability region, which is expressed as follows: ； Among them, B1 and B2 are stability coefficients; when The vehicle is considered to be in a stable state when The vehicle is considered to be in an unstable state; When the vehicle's center of mass slip angle phase trajectory is within the stable region, the yaw rate and center of mass slip angle are jointly controlled. When the vehicle's center of mass slip angle phase trajectory exceeds the stable region, the center of mass slip angle is controlled. ∆M r and ∆M 𝛽 The weights of the two are set to 1-P and P respectively. P is calculated from the stable region expression in the phase plane. The final additional yaw moment ∆M is: ； Where P is ； Among them, B1 and B2 are the correlation coefficients of the stable region.

4. The vehicle stability control method based on piecewise affine identification tire sliding mode control according to claim 3, characterized in that: In step 5, an optimal four-wheel torque distribution algorithm is designed. The objective function is to minimize the sum of the load rates of the four wheels. Combined with the front and rear wheel distribution weight coefficients, the real-time optimal torque of the four wheels is obtained. The specific distribution algorithm is as follows: (1) Based on the difference between the actual speed and the target speed, the total torque is calculated using a proportional integral (PI) controller. The control process is expressed as follows: ； Among them, v xd and v x are the target speed and actual speed, k pu and k iu is the parameter of PI controller, T o is the total driving torque of the four wheels; (2) In wheel torque control, the sum of the load rates of each tire is used as the objective function. The tire load rate represents the stability margin of the vehicle. When J is larger, the stability margin is smaller, and the possibility of vehicle instability is greater. On the contrary, the vehicle has more stability margin to overcome the instability. The load rate of each tire is defined as: ； The motor can only control the longitudinal force and Substituting this into R, where R is the tire radius, the tire load factor becomes: ； The objective function is the sum of the load rates of each tire and the weights assigned to them: ； in, is the sum of the tire utilization weights of each wheel is the tire weight utilization rate of the left front wheel, is the tire weight utilization rate of the right front wheel, is the tire weight utilization rate of the left rear wheel, is the tire weight utilization of the right rear wheel; The weight coefficients of each wheel are defined as follows: ； Where B1 and B2 are the correlation coefficients of the center of mass sideslip angle phase plane stability region, ∆r is the difference between the actual value and the reference value of the yaw rate; The relationship between the total driving torque, yaw torque and each wheel torque is as follows: ； The two front wheel torques are solved as: ； Substituting the above formula into the objective function, we get: ； Transform the objective function J to T rl and T rr Taking the partial derivative we get: ； make , the optimal torque of the four wheels is: 。

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