A Learning Predictive Control Method for Electric Vehicle Yaw Stability Considering External Disturbances

Abstract

The present invention is applicable to the field of electric vehicle control technology, and provides a learning predictive control method for electric vehicle yaw stability considering external disturbances, which includes the following steps: building a data-mechanism hybrid model, aiming at the problem of large error in the traditional two-degree-of-freedom vehicle model, using a machine learning model to compensate for the error of the mechanism model to obtain a high-precision data-mechanism hybrid model; designing a yaw stability controller according to the control objectives of the vehicle yaw stability controller, considering the constraints of the vehicle actuators and the safety constraints of vehicle driving; aiming at the uncertainty in the environment, considering the propagation problem within the uncertainty prediction horizon, using the method of converting probabilistic constraints into deterministic constraints to transform the original stochastic optimization problem into a deterministic nonlinear programming problem. The yaw stability controller design is completed by solving the nonlinear programming problem. The present invention ensures the safety of electric vehicles during driving and further improves the performance of the electronic body stability system.

Description

Technical Field

[0001] The present invention belongs to the technical field of electric vehicle control, and particularly relates to a learning predictive control method for electric vehicle yaw stability considering external disturbances. Background Art

[0002] The safety issue of automobiles has always been a hot topic of concern. Improper operations by drivers can lead to vehicle instability phenomena such as skidding and rollover, and may even pose a life threat. Therefore, it is crucial to design control strategies to ensure the safety of vehicle driving. Four-wheel drive electric vehicles allow for multiple power sources and can independently deliver power to the wheels. Therefore, the torque of each wheel can be controlled through an electronic control unit, and its performance mainly depends on software, with advantages such as flexible control and fast acceleration speed. Regarding the safety issue of automobiles, the electronic stability program (ESP) is currently the mainstream active safety control system in automobiles. Especially under extreme conditions, by reasonably controlling the actuators of the vehicle, it is ensured that the tires of the vehicle maintain in the linear region to avoid dangerous situations such as skidding and wheel locking, thereby ensuring the stability of the vehicle.

[0003] Currently, the mainstream control methods for electric vehicle stability control are active front-wheel steering and direct torque control. The control strategies adopted mainly are model predictive control based on models. However, there are still many problems to be solved in the current electronic stability program, mainly including:

[0004] 1. The structure of the vehicle system is complex. The vehicle kinematics and tire system have characteristics such as non-linearity and strong coupling. When the electronic stability program controls the vehicle through model-based predictive control, a predictive model for controller design needs to be built. Due to the complexity of the vehicle system, the built model cannot accurately describe the kinematic characteristics of the vehicle, with a certain modeling error, which further affects the control performance of the control system and may even cause the vehicle to become unstable, leading to traffic accidents.

[0005] 2. During the driving process of the vehicle, due to the strong uncertainty of the environment, especially under extreme conditions, uncertain factors such as crosswinds and potholed roads may change the motion state of the vehicle, ultimately leading to vehicle instability. However, the current electronic stability program only considers some deterministic information and does not consider the impact of uncertain factors on the control system, and cannot meet the driving requirements in some extreme environments. Summary of the Invention

[0006] The purpose of the present invention is to provide a learning predictive control method for electric vehicle yaw stability considering external disturbances, aiming to solve the problems raised in the above background art.

[0007] To achieve the above purpose, the present invention provides the following technical solutions:

[0008] A learning predictive control method for the yaw stability of electric vehicles considering external disturbances, comprising the following steps:

[0009] Construction of a data-mechanism hybrid model: The data-mechanism hybrid model serves as the prediction model for the yaw stability controller of a four-wheel drive electric vehicle. By using a Gaussian process regression model to compensate for the errors of a two-degree-of-freedom vehicle model, a high-precision prediction model is obtained;

[0010] Design of a yaw stability prediction controller: Considering the constraints of vehicle actuators and the yaw stability of the vehicle, a cost function of the model predictive controller is constructed according to the control objectives of the yaw stability controller, and the final optimization problem is obtained;

[0011] Reconstruction of the predictive controller for environmental uncertainty: Propagate the uncertainty disturbances within the prediction horizon, and then convert the probabilistic constraints into deterministic constraints to obtain the final nonlinear programming optimization problem;

[0012] The control signal of the controller is obtained through optimization, and the obtained front wheel angle and the driving torques of the four wheels are applied to the vehicle to be controlled.

[0013] Further, in the step of constructing the data-mechanism hybrid model, the sideslip angle at the vehicle's center of mass and the yaw angular velocity are selected as the state variables of the controller, i.e., x = [β, γ], and the control variables of the controller are the front wheel angle of the vehicle and the driving torques of the four wheels, i.e., u = [δ f , T fl , T rl , T fr , T rr , and a two-degree-of-freedom vehicle model is constructed for the prediction of state variables. The dynamic equation of the data-mechanism hybrid model is expressed as:

[0014]

[0015] Where f 2dof (x, u) is a two-degree-of-freedom mechanism model, g c (x, u) is the model error of the two-degree-of-freedom vehicle model, ω is the random disturbance in the prediction model, which follows a Gaussian distribution with a mean of 0 and a standard deviation of σ, and B d is the weight coefficient of the model error and the uncertainty disturbance.

[0016] Further, the two-degree-of-freedom vehicle model simplifies the left and right wheels of the front and rear axles into one wheel. The dynamic equations of the sideslip angle at the center of mass and the yaw angular velocity are:

[0017]

[0018]

[0019] where β and γ are the sideslip angle and yaw rate of the vehicle's center of mass, m is the body mass, V is the vehicle's longitudinal speed, F yf and F yr are the lateral forces of the front and rear wheels, L f and L r are the distances from the front and rear axles to the center of mass respectively, I z is the yaw moment of inertia of the body, M z is the yaw moment of the vehicle; ignoring the influence of the longitudinal force on the lateral force, a simplified magic formula tire model under the pure sideslip condition is adopted, and the lateral force is expressed as:

[0020]

[0021]

[0022] where C f and C r are the sideslip stiffnesses of the front and rear wheels respectively, K a and K b are the tire force fitting parameters of the front and rear wheels, α f and α r are the sideslip angles of the front and rear wheels, and the sideslip angle is expressed as:

[0023]

[0024]

[0025] where δ f is the front wheel steering angle. Ignoring the rolling resistance, air resistance, and acceleration resistance during the tire rolling process, the yaw moment of the vehicle is expressed as:

[0026]

[0027] where T fr 、T rr 、T fl 、T rl are the driving torques of the front right, rear right, front left, and rear left wheels respectively, and R e is the effective rolling radius during the tire rolling process;

[0028] The error of the two-degree-of-freedom vehicle model is compensated by the Gaussian process regression model. The output of the model is the yaw rate error of the model, and the yaw rate errors follow a Gaussian joint distribution, which is expressed as:

[0029]

[0030] where e γ is the collected yaw rate error, is the yaw rate error to be predicted, X is the training data vector, i.e., X = [x gp,1 , x gp,2 , L, x gp,900 , where x gp = (β, γ, V, δ f , T fl , T fr , T rl , T rr ), is the input data for training the Gaussian process regression model, X * is the data vector to be predicted, i.e., The mean of the yaw rate to be predicted is obtained through the Gaussian joint distribution inference formula and the variance The prediction formula is expressed as:

[0031]

[0032]

[0033] where is the data to be predicted;

[0034] In the Gaussian joint distribution inference formula, the size n of the training set used is 900, and the covariance matrix is expressed as:

[0035]

[0036] where k(x gp,u , x gp,v ) represents the kernel function of the model, which measures the distance between two points, u and v represent each sample in the training sample vector, with the range from 1 to n. The Automatic Relevance Determination Gaussian kernel function is used as the kernel function in the Gaussian process regression model, and its specific form is:

[0037]

[0038] There are parameters θ = (s f , l 1 , l 2 , l 3 , l 4 , l 5 , l 6 , l 7 , l 8 , σ n ), also known as hyperparameters, which are optimized through model training to solve the hyperparameters existing after the Gaussian process regression model is established.

[0039] Further, the training of the Gaussian process regression model adopts maximizing the marginal likelihood function, and the specific formula of the marginal likelihood function logP(e γ |X) is as follows:

[0040]

[0041] where P(e γ |X) is the conditional probability of e γ under the condition of the given training data X, represents the fitting degree of the data, is the complexity of the model, and n is the number of samples;

[0042] Perform a simple cross-validation on the model. Divide the data set into two parts, one part is the training set and the other part is the validation set. The training set comes from the historical data collected by the model, and the validation set uses the new data generated by the operation of the controller. Adjust the hyperparameters of the Gaussian process regression through prior knowledge, change the weight coefficients and variance coefficients of each feature, and obtain the expected generalization error.

[0043] Further, in the design steps of the yaw stability prediction controller, discretize the data mechanism hybrid model to obtain the following discrete state space equation:

[0044]

[0045]

[0046] where T s is the sampling time of the system, the state variables of the vehicle yaw stability controller are x = [β(k), γ(k)], and the control quantity is u = [δ f (k), T fl (k), T rl (k), T fr (k), T rr (k)], and the objective function is as follows:

[0047]

[0048] where x ref (k + i|k) is the reference sequence tracked by the system. The reference value of the yaw rate is calculated by the steady-state steering model through the input front wheel angle, and the reference value of the sideslip angle of the center of mass is set to 0. (k + i|k) represents the value predicted at the k-th moment for the (k + i)-th moment. Δu(k + i|k) = u(k + i|k) - u(k + i - 1|k), which represents the change rate of the control quantity. N is the prediction horizon of the controller, i is a specific moment within the prediction horizon, ranging from 0 to N - 1, and both P and Q are the weight matrices of the controller.

[0049] Furthermore, the vehicle yaw stability constraint is:

[0050] β min ≤β(k + i|k)≤β max

[0051] γ min ≤γ(k + i|k)≤γ max

[0052] where β min and β max and γ min and γ max are respectively the minimum and maximum values of the sideslip angle of the center of mass and the minimum and maximum values of the yaw rate for maintaining vehicle stability;

[0053] The vehicle actuator constraint is:

[0054]

[0055] T min <T j (k + i|k)<T max

[0056] where T min and T max are respectively the minimum and maximum values of the front wheel steering angle and the minimum and maximum values of the driving torque; j represents the four tires of the vehicle, and the range is from 1 to 4.

[0057] Furthermore, in the design steps of the yaw stability predictive controller, the final optimization problem description is expressed as:

[0058]

[0059] Furthermore, in the reconstruction steps of the vehicle yaw stability predictive controller for environmental random disturbances, uncertainty propagation is performed on the state - space equation of the yaw rate. When at the first prediction time domain, the first two terms in the prediction model are both deterministic values, and the last term is the output of a Gaussian process regression model with a deterministic input, which is a random variable. The yaw rate obtained at the second prediction time domain is a random variable with mean and variance information. When iteratively predicting to the second prediction time domain, the input of the Gaussian process regression is a random variable, which is expressed as:

[0060]

[0061] Using the iterative expectation and conditional variance formulas, the distribution of the input as a random variable is obtained. Since the output of the model when the input is a random variable does not necessarily follow a Gaussian distribution, it needs to be approximated by Taylor expansion, which is expressed as:

[0062] m(x) = E x (μ(x)) ≈ μ(μ(x))

[0063]

[0064] The finally obtained function distribution is expressed as:

[0065] f 2dof (x(k+i|k), u(k+i|k)) ~ N(m 2dof , v 2dof )

[0066]

[0067] where μ(x) and σ 2 (x) are functions of x, and x follows a Gaussian distribution;

[0068] The joint Gaussian distribution is expressed as:

[0069]

[0070] The overall state - space equation of the yaw rate is expressed as:

[0071]

[0072] Furthermore, the constraints of the yaw rate are as follows:

[0073] γ min ≤ γ(k+i|k) ≤ γ max

[0074] where:

[0075]

[0076] The yaw - rate constraint is a probabilistic constraint, expressed as:

[0077]

[0078] where 1 - ε is the confidence level. Taking 95% as an example, the yaw rate satisfies this constraint with a probability of 95%. By querying the standard normal distribution table, the probabilistic constraint is transformed into:

[0079]

[0080] The objective function is expressed in the form of an expectation and transformed through the expectation - square formula into:

[0081]

[0082] where Tr represents the trace of the matrix, and Σ x is the covariance matrix of the state variables.

[0083] Furthermore, in the reconstruction step of the predictive controller for environmental uncertainty, the final non-linear programming optimization problem is obtained, which is expressed as:

[0084]

[0085] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0086] 1. The present invention uses a data-mechanism hybrid model to compensate for model errors, improve the accuracy of the prediction model, and thus improve the control performance of the electronic vehicle stability system;

[0087] 2. In view of the uncertainty in the environment, the present invention quantifies the uncertainty using expectation and variance, takes into account the uncertainty propagation within the prediction horizon, transforms the probabilistic constraints into deterministic constraints, tightens the constraints to suppress the interference of environmental uncertainty, and further enhances the stability of the controlled vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] Figure 1 is a block diagram of the yaw stability learning predictive control system for an electric vehicle in the present invention.

[0089] Figure 2 is a schematic diagram of a two-degree-of-freedom mechanism vehicle model in the present invention.

[0090] Figure 3 is a comparison diagram of the model errors between the two-degree-of-freedom vehicle mechanism model and the data-mechanism hybrid model in the present invention.

[0091] Figure 4 is a schematic diagram of a prediction model without uncertainty propagation in the present invention.

[0092] Figure 5 is a schematic diagram of a prediction model with uncertainty propagation in the present invention.

[0093] Figure 6 is the yaw rate tracking curve when the road adhesion coefficient is 0.8 and the initial speed is 60 km / h in the present invention.

[0094] Figure 7 is the centroid side slip angle curve when the road adhesion coefficient is 0.8 and the initial speed is 60 km / h in the present invention.

[0095] Figure 8 is the yaw rate tracking curve of the controller designed when the two-degree-of-freedom vehicle mechanism model and the data-mechanism hybrid model are used as prediction models in the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0096] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0097] The following describes in detail the specific implementation of the present invention in combination with specific embodiments.

[0098] As Figure 1-8 shown, a learning predictive control method for electric vehicle yaw stability considering external interference provided by an embodiment of the present invention includes the following steps:

[0099] Construction of a data-mechanism hybrid model: The data-mechanism hybrid model serves as the prediction model of the four-wheel drive electric vehicle yaw stability controller. By using the Gaussian process regression model to compensate for the errors of the two-degree-of-freedom vehicle model, a high-precision prediction model is obtained;

[0100] Design of the yaw stability predictive controller: Considering the constraints of the vehicle actuators and the vehicle yaw stability constraints, the cost function of the model predictive controller is constructed according to the control objectives of the yaw stability controller, and the final optimization problem is obtained;

[0101] Reconstruction of the predictive controller for environmental uncertainty: Propagate the uncertainty disturbances within the prediction horizon, and then convert the probabilistic constraints into deterministic constraints to obtain the final non-linear programming optimization problem;

[0102] The control signal of the controller is obtained through optimization, and the obtained front wheel angles and the driving torques of the four wheels are applied to the controlled vehicle.

[0103] In the embodiment of the present invention, the data-mechanism hybrid model serves as the prediction model of the model predictive controller, and the motion state of the controlled vehicle is predicted in open loop, providing the motion state trajectory for the controller for a period of time in the future, enabling the controller to respond to environmental changes in advance and thus making corresponding control actions. The yaw stability predictive controller is based on the control objectives of tracking the desired yaw angular velocity and suppressing the sideslip angle of the center of mass. Under the conditions of the physical constraints of the actuators and the vehicle stability constraints, the front wheel angles and the driving torques of the four wheels of the electric vehicle are obtained through optimization, and the control signal is applied to the controlled vehicle. The reconstruction of the predictive controller for environmental uncertainty is aimed at the uncertainty existing in the environment, considering the propagation problem of the uncertainty within the prediction horizon, and converting the existing probabilistic constraints into deterministic constraints, thereby transforming the intractable stochastic optimization problem into a deterministic non-linear optimization problem, reducing the solution difficulty and computational burden of the controller.

[0104] As a preferred embodiment of the present invention, in the step of constructing the data-mechanism hybrid model,

[0105] The purpose of the yaw stability control of an electric vehicle is to prevent the vehicle from skidding or even rolling over during driving due to the tires entering the non-linear region. The sideslip angle of the vehicle mainly depends on the yaw angular velocity and the sideslip angle of the center of mass of the vehicle. Therefore, the sideslip angle of the center of mass and the yaw angular velocity of the vehicle are selected as the state variables of the controller, that is, x = [β, γ]. The control variables of the controller are the front wheel steering angle and the driving torques of the four wheels, that is, u = [δ f ,T fl ,T rl ,T fr ,T rr , and a two-degree-of-freedom vehicle model is built for the prediction of state variables. The dynamic equation of the data mechanism hybrid model is expressed as:

[0106]

[0107] where f 2dof (x, u) is a two-degree-of-freedom mechanism model, g c (x, u) is the model error of the two-degree-of-freedom vehicle model, ω is the random perturbation in the prediction model, which follows a Gaussian distribution with a mean of 0 and a standard deviation of σ, and B d is the weight coefficient of the model error and the uncertainty perturbation.

[0108] As a preferred embodiment of the present invention, the two-degree-of-freedom vehicle mechanism model assumes that the steering angles of the two front wheels of the vehicle are equal, and the influence between the left and right wheelbases is ignored. The left and right wheels of the front and rear axles are simplified into one wheel. The dynamic equations of the sideslip angle of the center of mass and the yaw angular velocity are:

[0109]

[0110] where β and γ are the sideslip angle of the center of mass and the yaw angular velocity of the vehicle, m is the vehicle body mass, V is the longitudinal velocity of the vehicle, F yf and F yr are the lateral forces of the front and rear wheels, L f and L r are the distances from the front and rear axles to the center of mass respectively, I z is the yaw moment of inertia of the vehicle body, M z is the yaw moment of the vehicle; ignoring the influence of the longitudinal force on the lateral force and adopting the simplified magic formula tire model under the pure sideslip condition, the lateral force is expressed as:

[0111]

[0112] where C f and C r are the sideslip stiffnesses of the front and rear wheels respectively, K a and K bis the fitting parameter of the tire forces for the front and rear wheels, α f and α r are the sideslip angles of the front and rear wheels, and the sideslip angle is expressed as:

[0113]

[0114] where δ f is the front wheel steering angle. Ignoring the rolling resistance, air resistance, and acceleration resistance during the tire rolling process, the yaw moment of the vehicle is expressed as:

[0115]

[0116] where T fr , T rr , T fl , T rl are the driving torques of the front right, rear right, front left, and rear left wheels, and R e is the effective rolling radius during the tire rolling process;

[0117] The two-degree-of-freedom vehicle model has a large model error, which has a great impact on the design of the vehicle yaw stability controller. The present invention uses a Gaussian process regression model to compensate for the error of the two-degree-of-freedom vehicle model, that is, the g c (x,u)+ω term in Equation 1;

[0118] First is data acquisition. The two-degree-of-freedom vehicle model needs to be used for controller design. The designed controller is applied to the controlled vehicle to obtain the real-time data of the controlled vehicle during driving, and compared with the data of the two-degree-of-freedom vehicle model to obtain the error data of the two-degree-of-freedom vehicle model for training the error model.

[0119] Since the Gaussian process regression model is a non-parametric machine learning model that measures the correlation between data by measuring the distance between points, each training sample needs to be stored during the prediction process, and the prediction process depends on each training sample. Therefore, the training set capacity of the Gaussian process regression cannot be too large, otherwise it will bring a serious computational burden. For the vehicle stability control system of the present invention, the selected data set capacity is 900 samples. The input data of the model is the yaw rate, sideslip angle of the center of mass, longitudinal speed, front wheel steering angle, and the driving torques of the four wheels, and the output is the yaw rate deviation of the two-degree-of-freedom vehicle model.

[0120] The Gaussian process regression assumes that the hypothesis function follows a prior distribution, and then continuously corrects the hypothesis made through the evidence factor to finally obtain the posterior distribution of the function to be fitted. Each target value is considered to follow a joint Gaussian distribution. In the present invention, error compensation is selected for the yaw rate in the prediction model. Therefore, the output of the model is the yaw rate error of the model, and the yaw rate errors follow a Gaussian joint distribution, which is expressed as:

[0121]

[0122] where e γ is the yaw rate error collected, is the yaw rate error to be predicted, X is the training data vector, that is, X = [x gp,1 , x gp,2 , L, x gp,900 , where x gp = (β, γ, V, δ f , T fl , T fr , T rl , T rr ), which is the input data for training the Gaussian process regression model. X * is the data vector to be predicted, that is The mean and variance of the yaw rate to be predicted are obtained through the Gaussian joint distribution inference formula. The prediction formula is expressed as:

[0123]

[0124] where is the data to be predicted;

[0125] It can be seen that the most computationally intensive part of the prediction process of Gaussian process regression is the inversion of the covariance matrix, and the computational complexity is O(n 3 ). In order to reduce the computational complexity in the model inference process, Cholesky decomposition is used to simplify the matrix inversion operation. In Equation 6, K(X, X) is the covariance matrix of Gaussian process regression, which is a positive semi-definite matrix used to measure the distance between input data points, and the mean and variance of this point are predicted according to the distance. In the present invention, the training set size n used is 900. Therefore, the covariance matrix in Equation 6 is expressed as:

[0126]

[0127] where k(x gp,u , x gp,v) represents the kernel function of the model, which measures the distance between two points. u and v represent each sample in the training sample vector, ranging from 1 to n. The Automatic Relevance Determination Gaussian kernel function is used as the kernel function in the Gaussian process regression model, and its specific form is:

[0128]

[0129] There are parameters θ=(s f ,l 1 ,l 2 ,l 3 ,l 4 ,l 5 ,l 6 ,l 7 ,l 8 ,σ n ) to be optimized in the Gaussian process regression model, which are also called hyperparameters. After the Gaussian process regression model is established, these hyperparameters exist in the model, and model training is required to optimize and solve these hyperparameters. Since Gaussian process regression belongs to Bayesian machine learning, the common method for training Bayesian machine learning models is to maximize the marginal likelihood function.

[0130] As a preferred embodiment of the present invention, the training of the Gaussian process regression model uses the maximization of the marginal likelihood function, and the specific formula of the marginal likelihood function logP(e γ |X) is:

[0131]

[0132] where P(e γ |X) is the conditional probability of e γ given the training data X, represents the fitting degree of the data, is the complexity of the model, and n is the number of samples;

[0133] The training of the Gaussian process regression model requires maximizing the marginal likelihood function, that is, Equation 10. The present invention uses a gradient-based Newton optimization algorithm. It should be noted that Equation 10 is a non-convex function, and the hyperparameters obtained by optimization may be local minima. Therefore, cross-validation of the model is required. The present invention performs simple cross-validation on the model, divides the data set into two parts, one part is the training set, and the other part is the validation set. The training set comes from the historical data collected by the model, and the validation set uses the new data generated by the controller operation. The hyperparameters of the Gaussian process regression are adjusted through prior knowledge, and the weight coefficients and variance coefficients of each feature are changed to obtain the desired generalization error.

[0134] By modeling the two-degree-of-freedom mechanism model and the Gaussian process regression error model, a mechanism data hybrid model is obtained. To verify the mechanism data hybrid model, the obtained prediction model is used for controller design. The comparison result of the obtained model error and the model error of the two-degree-of-freedom vehicle model is shown in Figure 3 , it can be seen that the model error of the data mechanism hybrid model is much smaller than that of the two-degree-of-freedom vehicle model, which improves the model accuracy of the model predictive controller, and further enhances the control performance of the vehicle yaw stability controller.

[0135] As a preferred embodiment of the present invention, after obtaining a high-precision data mechanism hybrid prediction model, a vehicle yaw stability controller is designed according to the control objectives and constraint conditions of the yaw stability controller. To facilitate controller design, the data mechanism hybrid model is discretized to obtain the following discrete state-space equation:

[0136]

[0137] where T s is the sampling time of the system. The state variables of the vehicle yaw stability controller are x = [β(k), γ(k)], and the control quantity is u = [δ f (k), T fl (k), T rl (k), T fr (k), T rr (k)]. The control objective of the controller is to track the desired yaw angular velocity of the vehicle as much as possible and suppress the sideslip angle of the vehicle's center of mass. At the same time, the comfort of the vehicle during driving should be ensured, and the change amplitude of the control action of the controller should be as small as possible. Therefore, the objective function is as follows:

[0138]

[0139] where x ref (k + i|k) is the reference sequence tracked by the system. The reference value of the yaw angular velocity is obtained by calculating through the steady-state steering model with the input front wheel angle. The reference value of the sideslip angle of the center of mass is set to 0. (k + i|k) represents the value predicted at the k-th moment for the (k + i)-th moment. Δu(k + i|k) = u(k + i|k) - u(k + i - 1|k), which represents the change rate of the control quantity and affects the comfort during vehicle driving. N is the prediction horizon of the controller, i is a specific moment within the prediction horizon, ranging from 0 to N - 1, and both P and Q are the weight matrices of the controller.

[0140] As a preferred embodiment of the present invention, the controller design should satisfy the constraints of the vehicle actuator and the driving stability constraints of the vehicle. The vehicle yaw stability constraints are:

[0141]

[0142] where β min and β max and γ min and γ max are respectively the minimum and maximum values of the sideslip angle of the center of mass for maintaining vehicle stability and the minimum and maximum values of the yaw rate;

[0143] The constraints of the vehicle actuators are:

[0144]

[0145] where T min and T max are respectively the minimum and maximum values of the front wheel steering angle and the minimum and maximum values of the driving torque; j represents the four tires of the vehicle, and the range is from 1 to 4.

[0146] As a preferred embodiment of the present invention, in the design steps of the yaw stability prediction controller, the final optimization problem description is expressed as:

[0147]

[0148] As a preferred embodiment of the present invention, the above-designed yaw stability controller for electric vehicles does not consider the influence of environmental uncertainties on the controller. For environmental uncertainties, it is necessary to process the external disturbances in the prediction model, and at the same time, the constraint conditions and the objective function in the optimization problem also need to be reconstructed accordingly, and finally, the reconstructed optimization problem description is obtained.

[0149] First, it is necessary to consider the problem of the propagation of uncertainties in the prediction model over the prediction horizon. The prediction model of the discretized vehicle yaw stability controller is shown in Equation 11. In the reconstruction steps of the vehicle yaw stability prediction controller for environmental random disturbances, the present invention only propagates the uncertainties in the state space equation of the yaw rate. When at the first prediction horizon, the first two terms in the prediction model are both determined values, and the last term is the output of a Gaussian process regression model with a determined input, which is a random variable. The yaw rate obtained at the second prediction horizon is a random variable with mean and variance information. When iteratively predicting to the second prediction horizon, the input of the Gaussian process regression is a random variable, which is expressed as:

[0150]

[0151] When the input is a random variable, the iterative expectation and conditional variance formulas are used to obtain the distribution of the input as a random variable, as follows:

[0152]

[0153] where μ(x) and σ2 (x) is a function of x, and x follows a Gaussian distribution. Since the output of the model may not follow a Gaussian distribution when the input is a random variable, it is necessary to perform Taylor expansion approximation processing, and Equation 17 is transformed into:

[0154]

[0155] The finally obtained function distribution is expressed as:

[0156]

[0157] After obtaining the probability distributions of the two functions, the probability distributions of the three terms in the yaw rate prediction model in Equation 11 have been obtained, and all three terms follow a Gaussian distribution. Therefore, it is necessary to consider the influence of the covariance matrix between the three terms on the prediction model, and the joint Gaussian distribution is expressed as:

[0158]

[0159] The overall state space equation of the yaw rate is expressed as:

[0160]

[0161] Figure 4 is a schematic diagram of uncertainty prediction without uncertainty propagation, Figure 5 is a schematic diagram of uncertainty prediction with uncertainty propagation. It can be seen that after considering uncertainty propagation, the uncertainty within the prediction horizon gradually increases, and the controller can design different degrees of constraint tightening strategies according to the uncertainty information to improve the safety performance of the controller.

[0162] As a preferred embodiment of the present invention, after the uncertainty propagation design is completed, the probability constraint of the yaw rate needs to be processed, otherwise the controller optimization problem cannot be solved. By converting the probability constraint into a deterministic constraint for processing, the present invention uses the standard normal distribution to find the standard deviation corresponding to the probability interval, and finally converts it into a deterministic constraint. The constraint of the yaw rate is as follows:

[0163] γ min ≤γ(k+i|k)≤γ max (22)

[0164] Where:

[0165]

[0166] The yaw rate within the prediction horizon should all satisfy this constraint. Since the yaw rate within the prediction horizon follows a probability distribution, the yaw rate constraint is a probability constraint, expressed as:

[0167]

[0168] Among them, 1 - ε is the confidence level. Taking 95% as an example, the yaw rate satisfies this constraint with a probability of 95%. By querying the standard normal distribution table, the probability constraint is transformed into:

[0169]

[0170] After the probability constraint is converted into a deterministic constraint, finally, the objective function needs to be reconstructed. Since there are random variables in the objective function, the objective function is expressed in the form of expectation as:

[0171]

[0172] It is transformed into:

[0173]

[0174] Among them, Tr represents the trace of the matrix, and Σ x is the covariance matrix of the state variables.

[0175] As a preferred embodiment of the present invention, in the reconstruction step of the prediction controller for environmental uncertainty, the final nonlinear programming optimization problem is obtained, which is expressed as:

[0176]

[0177] This optimization problem takes into account the propagation of uncertainty within the prediction horizon, uses probability constraints to tighten the constraints on the uncertainty in the environment, and finally reconstructs the objective function, realizing the transformation from an intractable stochastic optimization problem to a deterministic nonlinear programming problem. By solving the nonlinear optimization problem, the front wheel steering angle signal and the driving torque signals of the four wheels of the controlled vehicle can be obtained and applied to the controlled vehicle. The above optimization problem further improves the safety performance of the vehicle yaw stability controller by considering the uncertainty disturbances existing in the environment.

[0178] Experimental verification

[0179] To verify the effectiveness of the controller of the present invention, the Simulink - CarSim simulation platform is used to verify the effectiveness of the controller. The sampling time of the simulation environment is set to 10 ms, the prediction horizon and control horizon of the controller are 10, and the condition of continuously increasing the steering wheel angle is used as the experimental condition of the yaw stability controller. The initial speed of the electric vehicle is 60 km / h, and the road adhesion coefficient is 0.8 to verify the effectiveness of the yaw stability controller. Figure 6 For the yaw rate tracking expected value curve, Figure 7It is the centroid sideslip angle suppression curve. It can be seen that the yaw rate curve can better track the expected value, and the peak value of the centroid sideslip angle is close to 0.05 rad, about 2.86°, which is much smaller than the boundary value of 5° for vehicle instability. Figure 8 It is the yaw rate tracking comparison curve between the controller designed by the present invention and the controller designed by the two-degree-of-freedom vehicle model. It can be seen that due to the large model error of the two-degree-of-freedom model, the tracking performance of the yaw rate is poor. While the data-mechanism hybrid model is used to compensate for the error of the two-degree-of-freedom vehicle model, reducing the model error and significantly improving the control performance. Through the above experiments, it is proved that the yaw stability controller of this electric vehicle has good control performance, can further improve the control performance of the electronic vehicle stability system, and at the same time improve the handling stability of vehicle driving.

[0180] The working principle of the present invention is:

[0181] First, a two-degree-of-freedom vehicle model is built as a prediction model to design the initial yaw stability controller of the electric vehicle. The controller is applied to the controlled vehicle. During the vehicle operation, real vehicle data or data from high-precision simulation software is collected. The collected data is compared with the prediction data of the two-degree-of-freedom vehicle model to obtain the error data of the two-degree-of-freedom vehicle model. The Gaussian process regression model is trained with this data, and the model is used to realize the error compensation of the two-degree-of-freedom vehicle model to obtain a data-mechanism hybrid prediction model. Subsequently, the design of the yaw stability controller of the electric vehicle is carried out. The model predictive control method is adopted, considering the constraints of the electric vehicle actuators and vehicle stability constraints, tracking the expected yaw rate and suppressing the centroid sideslip angle of the vehicle, and constructing the corresponding cost function. Finally, by quantifying the uncertainty in the environment and considering the uncertainty propagation problem within the prediction horizon, the probabilistic constraints are transformed into deterministic constraints, and finally the intractable stochastic optimization problem is transformed into a typical nonlinear programming problem. The final front wheel angle and the driving torques of the four wheels are obtained through optimization and applied to the system to ensure the yaw stability of the controlled vehicle.

[0182] The above is only the preferred embodiment of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several deformations and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicability of the patent.

Claims

1. A learning predictive control method for the yaw stability of electric vehicles considering external disturbances, Characterized in that, It includes the following steps: Construction of a data-mechanism hybrid model: The data-mechanism hybrid model serves as the predictive model of the yaw stability controller for four-wheel drive electric vehicles. By using the Gaussian process regression model to compensate for the errors of the two-degree-of-freedom vehicle model, a high-precision predictive model is obtained; Design of the yaw stability predictive controller: Considering the constraints of vehicle actuators and the yaw stability of the vehicle, according to the control objective of the yaw stability controller, the cost function of the model predictive controller is constructed to obtain the final optimization problem; Reconstruction of the predictive controller for environmental uncertainty: Propagate the uncertainty disturbances within the prediction horizon, and then convert the probabilistic constraints into deterministic constraints to obtain the final non-linear programming optimization problem; Obtain the control signal of the controller through optimization and solution, and apply the obtained front wheel steering angle and the driving torques of the four wheels to the controlled vehicle; In the step of reconstructing the predictive controller for environmental uncertainty, perform uncertainty propagation on the state space equation of the yaw rate. When at the first prediction horizon, the first two terms in the prediction model are both determined values, and the last term is the output of the Gaussian process regression model with a determined input, which is a random variable. The yaw rate obtained at the second prediction horizon is a random variable with mean and variance information. When iteratively predicting to the second prediction horizon, the input of the Gaussian process regression is a random variable, expressed as: Adopt the iterative expectation and conditional variance formulas to obtain the distribution of the input as a random variable. Since the output of the model when the input is a random variable does not necessarily follow a Gaussian distribution, it needs to be approximated by Taylor expansion, expressed as: m(x) = E x (μ(x)) ≈ μ(μ(x)) The finally obtained function distribution is expressed as: f 2dof (x(k+i|k), u(k+i|k)) ~ N(m 2dof , v 2dof ) where μ(x) and σ 2 (x) are functions of x, and x follows a Gaussian distribution; The joint Gaussian distribution is expressed as: The overall state space equation of the yaw rate is expressed as: The constraints of the yaw rate are as follows: γ min ≤γ(k + i|k) ≤ γ max Where: The yaw rate constraint is a probabilistic constraint, expressed as: Where 1 - ε is the confidence level. Taking 95% as an example, the yaw rate satisfies this constraint with a probability of 95%. By querying the standard normal distribution table, the probabilistic constraint is converted to: Express the objective function in the form of expectation and convert it through the expectation square formula to: where Tr represents the trace of the matrix, and Σ x is the covariance matrix of the state variables.

2. The learning predictive control method for the yaw stability of electric vehicles considering external disturbances according to claim 1, Characterized in that, In the steps of building the data-mechanism hybrid model, the sideslip angle and yaw rate of the vehicle are selected as the state variables of the controller, i.e., x = [β, γ], and the control variables of the controller are the front wheel steering angle and the driving torques of the four wheels, i.e., u = [δ f , T fl , T rl , T fr , T rr . A two-degree-of-freedom vehicle model is built for predicting the state variables, and the dynamic equation of the data-mechanism hybrid model is expressed as: where f 2dof (x, u) is a two-degree-of-freedom mechanism model, and g c (x, u) is the model error of the two-degree-of-freedom vehicle model, ω is the random perturbation in the prediction model, which follows a Gaussian distribution with a mean of 0 and a standard deviation of σ, and B d is the weight coefficient of the model error and the uncertainty perturbation.

3. The learning predictive control method for the yaw stability of electric vehicles considering external disturbances according to claim 2, Characterized in that, The two-degree-of-freedom vehicle model simplifies the left and right wheels of the front and rear axles into one wheel. The dynamic equations of the sideslip angle and the yaw rate are: where β and γ are the sideslip angle and yaw rate of the vehicle's center of mass, m is the vehicle body mass, V is the vehicle's longitudinal speed, F yf and F yr are the lateral forces of the front and rear wheels, L f and L r are the distances from the front and rear axles to the center of mass respectively, I z is the yaw moment of inertia of the vehicle body, M z is the yaw moment of the vehicle; neglecting the influence of longitudinal forces on lateral forces, a simplified magic formula tire model under pure sideslip conditions is adopted, and the lateral force is expressed as: Among them, C f and C r are the cornering stiffnesses of the front and rear wheels respectively, K a and K b are the tire force fitting parameters of the front and rear wheels, α f and α r are the cornering angles of the front and rear wheels, and the cornering angle is expressed as: where δ f is the front wheel steering angle. Ignoring the rolling resistance, air resistance and acceleration resistance during the tire rolling process, the yaw moment of the vehicle is expressed as: Among which T fr 、T rr 、T fl 、T rl are the driving torques of the front right, rear right, front left, and rear left wheels, and R e is the effective rolling radius during the tire rolling process; Compensate for the errors of the two-degree-of-freedom vehicle model through the Gaussian process regression model. The output of the model is the yaw rate error of the model. The yaw rate errors follow a Gaussian joint distribution, expressed as: where e γ is the collected yaw rate error, is the yaw rate error to be predicted, X is the training data vector, i.e., X = [x gp,1 , x gp,2 , L, x gp,900 , where x gp = (β, γ, V, δ f , T fl , T fr , T rl , T rr ), is the input data for training the Gaussian process regression model, X * is the data vector to be predicted, i.e., the mean of the yaw rate to be predicted is obtained through the Gaussian joint distribution inference formula and the variance The prediction formula is expressed as: Among them is the data to be predicted; In the Gaussian joint distribution inference formula, the training set capacity n used is 900, and the covariance matrix is expressed as: where \(k(x gp,u , x gp,v )\) represents the kernel function of the model, which measures the distance between two points. \(u\) and \(v\) represent each sample in the training sample vector, ranging from 1 to \(n\). The Automatic Relevance Determination Gaussian kernel function is used as the kernel function in the Gaussian process regression model, and its specific form is: There are parameters θ=(s f ,l 1 ,l 2 ,l 3 ,l 4 ,l 5 ,l 6 ,l 7 ,l 8 ,σ n ) to be optimized in the Gaussian process regression model, also known as hyperparameters, which are optimized through model training to solve the hyperparameters existing after the Gaussian process regression model is established.

4. The learning predictive control method for the yaw stability of electric vehicles considering external disturbances according to claim 3, Characterized in that, The training of the Gaussian process regression model adopts maximizing the marginal likelihood function, and the specific formula of the marginal likelihood function logP(e γ |X) is as follows: where P(e γ |X) is the conditional probability of e γ given the training data X, represents the goodness of fit of the data, is the complexity of the model, and n is the number of samples; Perform simple cross-validation on the model. Divide the dataset into two parts, one part is the training set and the other part is the validation set. The training set comes from the historical data collected by the model, and the validation set uses the new data generated by the operation of the controller. Adjust the hyperparameters of the Gaussian process regression through prior knowledge, change the weight coefficients and variance coefficients of each feature, and obtain the desired generalization error.

5. The electric vehicle yaw stability learning and predictive control method considering external disturbances according to claim 1, characterized in that, in the design steps of the yaw stability predictive controller, discretize the data mechanism hybrid model to obtain the following discrete state-space equation: where T s is the sampling time of the system, the state variables of the vehicle yaw stability controller are x = [β(k), γ(k)], and the control variables are u = [δ f (k), T fl (k), T rl (k), T fr (k), T rr (k)], and the objective function is as follows: where x ref (k+i|k) is the reference sequence tracked by the system. The reference value of the yaw rate is obtained by calculating through the steady-state steering model with the input front-wheel steering angle. The reference value of the sideslip angle of the center of mass is set to 0. (k+i|k) represents the value predicted at the (k+i)-th moment at the k-th moment. Δu(k+i|k) = u(k+i|k) - u(k+i-1|k), representing the change rate of the control quantity. N is the prediction horizon of the controller. i is a specific moment within the prediction horizon, with the range from 0 to N-1. Both P and Q are the weight matrices of the controller.

6. The electric vehicle yaw stability learning and predictive control method considering external disturbances according to claim 1, characterized in that, the vehicle yaw stability constraint is: β min ≤β(k + i|k)≤β max γ min ≤γ(k + i|k)≤γ max where β min and β max and γ min and γ max are respectively the minimum and maximum values of the sideslip angle of the center of mass and the minimum and maximum values of the yaw rate for maintaining vehicle stability; the vehicle actuator constraint is: Among them T min and T max are the minimum and maximum values of the front wheel steering angle and the minimum and maximum values of the driving torque, respectively; j represents the four tires of the vehicle, ranging from 1 to 4.

7. The electric vehicle yaw stability learning and predictive control method considering external disturbances according to claim 5, characterized in that, in the design steps of the yaw stability predictive controller, the description of the final optimization problem is expressed as:

8. The electric vehicle yaw stability learning and predictive control method considering external disturbances according to claim 1, characterized in that, in the reconstruction steps of the predictive controller for environmental uncertainty, obtain the final nonlinear programming optimization problem, which is expressed as:

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