Vehicle lateral stability control method based on online state compensation MPC

Abstract

This invention relates to a vehicle lateral stability control method based on online state compensation (MPC), belonging to the field of vehicle safety control technology. The objective of this invention is to design an online adaptive neural network based on a linear two-degree-of-freedom vehicle dynamics model to compensate for uncertainties caused by low-adhesion road conditions, thus establishing a vehicle lateral stability control method based on online state compensation (MPC). This invention designs an online adaptive neural network based on a linear two-degree-of-freedom vehicle dynamics model to compensate for uncertainties caused by low-adhesion road conditions. Based on this compensation model, a vehicle lateral stability controller is designed within a model predictive control framework. The control objectives include tracking yaw rate and suppressing lateral velocity, and constraints are imposed on lateral velocity and control variables. This invention can effectively compensate for the system's state variables without extensive offline training, exhibiting better versatility.

Description

Technical Field

[0001] This invention belongs to the field of vehicle safety control technology. Background Technology

[0002] Under low-friction conditions, vehicles are prone to instability and traffic accidents. Equipping vehicles with lateral stability controllers (MPCs) can significantly reduce the occurrence of such accidents, thereby ensuring the safety of drivers and their property. When vehicles operate under low-friction conditions, their dynamics exhibit severely nonlinear characteristics. Model predictive control (MPC) can be used to solve nonlinear problems with multiple constraints and optimize performance indicators; therefore, MPCs are widely used in vehicle stability control under low-friction conditions.

[0003] Current research on vehicle stability control on low-adhesion road surfaces faces the following problems:

[0004] 1. Currently, most studies on vehicle lateral stability control use MPC based on a simple linear two-degree-of-freedom vehicle dynamics model. However, under low-adhesion conditions, the tire force of a car is often in the nonlinear region, and the prediction effect of the prediction model deviates significantly from the actual driving results. The MPC controller based on an inaccurate dynamics model will limit its control potential, resulting in a less than ideal control effect, which will greatly weaken the control effect and cause consequences such as drifting and rollover.

[0005] 2. In order to describe the tire model more accurately, most studies often use complex nonlinear tire models to describe the car model under low-adhesion driving. However, this method increases the difficulty of solving the model predictive controller, increases the computational burden in the solution process, reduces the computational efficiency of the controller solution, and makes it difficult to guarantee the real-time performance of the control system.

[0006] 3. In stability control under low-adhesion conditions, if data is needed to improve the controller, most studies often use offline neural networks to achieve this goal. However, obtaining accurate network prediction results requires a large amount of data. If the amount of data is insufficient, the transferability of the network model will be unsatisfactory when the training results of the offline neural network are applied to real-world complex road conditions, and the desired control effect cannot be achieved. Summary of the Invention

[0007] The purpose of this invention is to design an online adaptive neural network based on a linear two-degree-of-freedom vehicle dynamics model to compensate for uncertainties caused by low-adhesion road conditions, thus creating a vehicle lateral stability control method based on online state compensation (MPC).

[0008] The steps of this invention are:

[0009] S1. The compensation values ​​of the lateral velocity and yaw rate of the model are predicted by an online adaptive neural network, and the offset of the predicted model is compensated in real time in the controller based on these compensation values.

[0010] S01, Online Adaptive Neural Network Compensation: Based on the external input vector z = [V y com γcom Adaptive approximation of Δε, as shown below

[0011]

[0012] In the formula For state compensation, Let a be the weight from the m-th hidden node to the output node; m It is a randomly selected weight vector that connects the input layer to the m-th hidden node, b m G(·) is the random selection bias of the m-th hidden node; G(·) is the activation function of the neural network.

[0013] S02. Select the Sigmoid function as the activation function:

[0014]

[0015] Equation (1) can be rewritten as:

[0016]

[0017] where H = diag (α1, α2), α i =[G(a1,b1,z)G(a2,b2,z)...G(a N b N ,z)],

[0018]

[0019] S03, Ideal Output Weight Vector This allows an unknown nonlinearity to be approximated by a very small bounded error. Approaching, that is

[0020] To achieve stability of the closed-loop system, the target tracking error should be:

[0021]

[0022] Where κ is a constant between 0 and 1;

[0023] S04, the tracking error e(k) is defined as the estimated state vector. and the actual state vector x(k) = [V y The state offset value z = [V] between γ]y com γ com ], that is, the compensation value used:

[0024]

[0025] S05, Error of output weights Defined as:

[0026]

[0027] S06. The adaptive weight update algorithm is given as follows:

[0028]

[0029] When the custom learning rate is 0 < η < 1, the stability of the adaptive system within the proposed RPNN can be guaranteed under the proof of the Lyapunov stability theorem. The RPNN does not require any initial training data for offline training.

[0030] S2 and MPC controller design:

[0031] S0l, the simplified linear two-degree-of-freedom vehicle model is described by the following equations:

[0032]

[0033] in, and Let F represent the derivatives of the vehicle's lateral velocity and yaw rate, respectively. yf and F yr ΔM represents the lateral force of the front and rear tires, respectively. z To add yaw moment, the tire lateral force F yf =-2C f α f F yr =-2C r α r ;

[0034] The slip angles of the front and rear wheels are as follows:

[0035]

[0036] S02, Prediction Model

[0037] Considering the lateral and yaw motions of the vehicle, a two-degree-of-freedom vehicle dynamics model is obtained:

[0038]

[0039] Among them, V y F is the lateral velocity of the vehicle. yThe lateral force of the tire is represented by the subscripts fl, fr, rl, and rr, which represent the left front, right front, left rear, and right rear wheels, respectively. The subscript com represents the compensation amount for state compensation. The lateral force of the tire is F. yf =-2C f α f F yr =-2C r α r ;

[0040] α in tire lateral force f α r The formula is as follows

[0041]

[0042] According to formulas (11)-(12), the car model is described as follows:

[0043]

[0044] Its state variables x = [x1 x2] T =[V y γ] T The control quantity u = [u1u2] consists of the vehicle's lateral velocity and yaw rate. T =[ΔM z Δδ f ] T Add yaw moment to the tires and add front wheel steering angle;

[0045] In equation (13), A and B u B d They are represented as follows:

[0046]

[0047]

[0048] For the prediction model (13), discretization is performed according to the Euler equation, and T is set as follows: s Given the sampling time, the discrete prediction model is as follows:

[0049] x(k+1)=A d x(k)+B ud u(k)+B dd δ f +X c (15)

[0050] Where A d =AT s +I, B ud =B u T s B dd =Bd T s X c =x com ·T s , where I is the identity matrix;

[0051] The state variables in the prediction time domain are derived as follows:

[0052]

[0053] Where N p For the time domain prediction, k+1|k in parentheses represents the prediction of the system state at time k+1 from the current time k; the future N p The predicted system state X within the prediction time domain. k And the control quantity U in the prediction time domain k for:

[0054]

[0055] Combining (16) and (17), we can organize them into a matrix form:

[0056]

[0057] in,

[0058]

[0059]

[0060] S03, Objective Function and Constraints

[0061] ① Define the objective function as follows:

[0062]

[0063] ② Cost function:

[0064]

[0065] ③ Define a total objective function based on equations (20) and (21):

[0066]

[0067] st|u1(k i -1)|≤u 1max i = 0, 1, 2, ..., p-1

[0068] |u2(k i -1)|≤u 2max i = 0, 1, 2, ..., p-1

[0069] |γ(ki )|≤γ max , i = 1, 2, ..., p (22)

[0070] in and Γ γ These are the weighting coefficient matrices for lateral velocity and yaw rate, respectively. and These are the weighting coefficient matrices for the additional yaw moment and the additional front wheel steering angle of the control input, respectively, where [u 1max u 2max ] T =[ΔM zmax Δδ fmax ] T This is the maximum limit for the control quantity;

[0071] Solving equation (22) yields the following optimal control sequence U. * :

[0072] U * (k)=[u * (k), u * (k+1), ..., u * (k+N-1)] T (twenty three)

[0073] Among them, based on the principle of model predictive control, the final control sequence U obtained (23) is * The first value u * (k)=[ΔM2 Δδ f ] T Consider them as the optimal additional yaw moment and the optimal additional front wheel steering angle;

[0074] The additional driving torque and additional steering wheel angle of the following four motors are obtained:

[0075]

[0076] For the optimal additional steering wheel angle:

[0077] ΔSWA=180·Δδ f / π (25)

[0078] The additional driving torque and additional steering wheel angle work together with the driving torque and steering wheel angle applied by the driver to achieve the control effect.

[0079] The positive effects of this invention are:

[0080] 1. The state-compensation-based MPC controller designed in this invention can cover a wider range of operating conditions compared to MPC based on a simple linear two-degree-of-freedom vehicle dynamics model, especially low-adhesion road surface conditions with more prominent nonlinearity, thereby achieving better control of vehicle stability.

[0081] 2. Compared with most nonlinear model predictive controllers (NMPCs) based on nonlinear tire models, this invention achieves real-time compensation for vehicle state offset values, ensuring model accuracy without increasing the solution complexity of the controller, thus ensuring the real-time solution of the system.

[0082] 3. Compared with most offline network training methods, this invention designs an online adaptive neural network. This method can effectively compensate for the state variables of the system without extensive offline training, and has better versatility. Attached Figure Description

[0083] Figure 1 This is a flowchart of the present invention;

[0084] Figure 2 This is a schematic diagram of the vehicle dynamics model described in this invention;

[0085] Figure 3 This is a schematic diagram of training an online neural network, where t represents the current state value, t-2ms represents the previous state value, and the output is the lateral velocity V. y And the compensation value for the yaw rate γ;

[0086] Figure 4 This is a verification diagram of the double lane change condition under the condition of low friction coefficient (μ=0.35) at a speed of 70km / h as described in this invention. The solid line represents the lateral force calculated using the linear tire model, and the dashed line represents the longitudinal force of the tire output by the CarSim port. The vertical axis is in N and the horizontal axis is time in s.

[0087] Figure 5a The results are the verification results of the lateral speed under the condition of state compensation MPC control verification of the present invention in the double lane change condition with a friction coefficient of 0.35 and a speed of 60km / h.

[0088] Figure 5b The results are the verification results of the yaw rate under the state compensation MPC control verification under the condition of double lane change operation with a friction coefficient of 0.35 and a speed of 60km / h.

[0089] Figure 5cThe curves are lateral velocity compensation curves trained by the adaptive neural network of the online compensation part under the verification of the state compensation MPC control of this invention in the double lane change condition with a friction coefficient of 0.35 and a speed of 60km / h.

[0090] Figure 5d The curves showing the yaw rate compensation under the dual lane change conditions with a friction coefficient of 0.35 and a speed of 60 km / h, as trained by the adaptive neural network of the online compensation part under the verification of the state compensation MPC control of this invention; Figure 5c and Figure 5d The midpoint line represents the actual measured value of the controlled object, the dashed line represents the state calculation value based on a simple linear two-degree-of-freedom model, and the solid line represents the state calculation value of the compensated model.

[0091] Figure 5e The diagram shows the additional yaw moment calculated by the controller under the state compensation MPC control verification condition of this invention, with a friction coefficient of 0.35 and a speed of 60 km / h in a double lane change operation.

[0092] Figure 5f The additional front wheel steering angle diagram is calculated by the controller under the state compensation MPC control verification condition of the present invention, with a friction coefficient of 0.35 and a speed of 60km / h in a double lane change operation. Figure 5e and Figure 5f The dashed line represents the control input of the controller before compensation, and the solid line represents the control input of the controller after compensation.

[0093] Figure 6a The figure shows the verification results of the lateral velocity under the state compensation MPC control verification under the condition of double lane change operation with a friction coefficient of 0.35 and a speed of 70km / h.

[0094] Figure 6b The figure shows the verification results of the yaw rate under the state compensation MPC control verification under the condition of double lane change operation with a friction coefficient of 0.35 and a speed of 70km / h.

[0095] Figure 6c This is a diagram showing the compensation of lateral velocity trained by the adaptive neural network in the online compensation section under the verification of the state compensation MPC control of this invention, in the double lane change condition with a friction coefficient of 0.35 and a speed of 70 km / h.

[0096] Figure 6d This is the compensation situation of the yaw rate trained by the adaptive neural network in the online compensation part under the verification of the state compensation MPC control of this invention in the double lane change condition with a friction coefficient of 0.35 and a speed of 70km / h.

[0097] Figure 6eThe control quantity plus yaw moment is calculated by the controller under the condition of state compensation MPC control verification of the present invention in the double lane change operation with a friction coefficient of 0.35 and a speed of 70km / h.

[0098] Figure 6f The additional front wheel steering angle is calculated by the controller under the condition of state compensation MPC control verification of the present invention, with a friction coefficient of 0.35 and a speed of 70km / h in the double lane change operation.

[0099] Figure 7a The figure shows the verification results of the lateral velocity under the state compensation MPC control verification under the condition of double lane change operation with a friction coefficient of 0.3 and a speed of 70km / h.

[0100] Figure 7b The figure shows the verification results of the yaw rate under the state compensation MPC control verification under the condition of double lane change operation with a friction coefficient of 0.3 and a speed of 70km / h.

[0101] Figure 7c This is a diagram showing the lateral velocity compensation situation trained by the adaptive neural network of the online compensation part under the verification of the state compensation MPC control of this invention in the double lane change condition with a friction coefficient of 0.3 and a speed of 70km / h.

[0102] Figure 7d This is a diagram showing the yaw rate compensation under the dual lane-switching condition with a friction coefficient of 0.3 and a speed of 70 km / h, trained by the adaptive neural network of the online compensation part under the verification of the state compensation MPC control of this invention.

[0103] Figure 7e The control quantity plus yaw moment is calculated by the controller under the condition of state compensation MPC control verification of the present invention in the double lane change operation with a friction coefficient of 0.3 and a speed of 70km / h.

[0104] Figure 7f The additional front wheel steering angle is calculated by the controller under the state compensation MPC control verification condition of this invention, with a friction coefficient of 0.3 and a speed of 70 km / h in a double lane change operation. Detailed Implementation

[0105] This invention relates to a vehicle stability control method based on a state-compensated model predictive control strategy. More specifically, this invention addresses the vehicle lateral stability control problem by designing a method to compensate and correct uncertain state variables in the vehicle dynamics model within the framework of model predictive control (MPC) and based on an adaptive neural network system.

[0106] To improve the driving stability and safety of high-speed turning vehicles under low-adhesion road conditions, this invention proposes a stability control strategy based on real-time state compensation using an online adaptive neural network within the framework of model predictive control (MPC). Based on a linear two-degree-of-freedom vehicle dynamics model, an online adaptive neural network is designed to compensate for the uncertainties caused by low-adhesion road conditions. This method enables the predictive model to more accurately predict the future state of the controlled object, allowing the linear two-degree-of-freedom vehicle dynamics predictive model to achieve the predictive performance of a complex nonlinear model under extreme conditions. Based on this compensation model, a vehicle lateral stability controller is designed within the MPC framework. The control objectives include tracking the yaw rate and suppressing lateral velocity, with constraints imposed on the lateral velocity and control variables. Simulation results show that for vehicles turning at high speed under low-adhesion road conditions, the proposed controller outperforms the uncompensated MPC controller in both tracking the desired yaw rate and suppressing lateral velocity, indicating that this controller can further improve vehicle handling stability and ensure driving stability.

[0107] The vehicle stability control method based on state compensation MPC includes the following steps:

[0108] Step 1: Use the simulation software CarSim to obtain a motor-driven car model, thereby providing real-time status information of the car.

[0109] Step 2: Design a two-degree-of-freedom reference model and use it to obtain the expected values ​​of the vehicle's yaw rate and lateral velocity, taking into account the road adhesion coefficient, so as to determine the ideal motion state of the vehicle.

[0110] Step 3: Compensate for the predicted vehicle state based on the neural network model. This step is based on a linear two-degree-of-freedom vehicle dynamics model. The online adaptive neural network is used to predict the compensation values ​​of the model's lateral velocity and yaw rate. Based on these compensation values, the controller performs real-time compensation for the predicted model's offset, so that the predicted model achieves higher accuracy and can more accurately reflect the nonlinear motion trend of the vehicle under low-adhesion road conditions.

[0111] Step 4: Design of MPC controller based on state compensation. Based on the compensated vehicle dynamics model, the MPC controller can more accurately predict the vehicle state, thereby obtaining more precise control variables, so as to achieve the desired value of suppressing lateral speed and better tracking yaw angle.

[0112] Functionally, the present invention may include the following parts: a four-wheel motor driven electric vehicle model, a reference model, an online adaptive network compensation part, and an MPC stability controller based on state compensation.

[0113] The function of each part is explained in detail below:

[0114] The four-wheel motor driven electric vehicle model is used to simulate a real controlled object. Its main function is to provide real-time road condition information and various state information of the vehicle, and to change the motion state of the vehicle by using additional motor torque and steering wheel angle as inputs.

[0115] The main function of the reference model is to obtain the desired yaw rate and vehicle lateral velocity, considering the road adhesion coefficient limit, through a two-degree-of-freedom vehicle model, and to determine the ideal motion state of the vehicle.

[0116] The main function of the online adaptive network compensation section is to compensate for the state variables caused during vehicle operation, so as to enable the controller's predictive model to better predict the state of the controlled object, thereby achieving better suppression of lateral velocity and tracking of yaw rate reference values ​​under low adhesion conditions.

[0117] The main function of the state-compensated MPC controller is to ensure vehicle stability as the primary control objective. Its prediction model takes into account the real-time compensation of vehicle state, as well as lateral safety constraints and actuator saturation constraints. By solving the constructed optimization problem, additional yaw moment and additional front wheel angle are obtained. Then, through lower-level static allocation and angle transformation, additional motor torque and additional steering wheel angle are obtained as inputs to the electric vehicle.

[0118] The present invention will now be described in further detail:

[0119] The flow chart of the state compensation MPC control method of this invention is as follows: Figure 1 As shown in the diagram, the inputs to the MPC controller are the desired yaw rate, the desired lateral velocity of the vehicle, and the measured output values ​​of the controlled object. The outputs are the additional yaw moment and the additional front wheel steering angle. The two-degree-of-freedom dynamics model takes the longitudinal velocity of the actual vehicle and other measured output values ​​of the controlled object as inputs, and outputs the measured values ​​obtained from the model solution. The adaptive network compensation part takes the lateral velocity and yaw rate of the controlled object as inputs, as well as the lateral velocity and yaw rate obtained from the model solution. The output is the difference between the lateral velocity and yaw rate of the controlled object and the lateral velocity and yaw rate obtained from the model solution, i.e., the state compensation value. The state compensation MPC controller, reference model, and torque distribution are all built in MATLAB / Simulink; the controlled object is a four-wheel hub-driven electric vehicle model constructed using CarSim.

[0120] The control objective of this invention is that, based on real-time feedback signals, the control system considers the deviation between the lateral velocity and yaw rate obtained from the MPC controller and the actual values. It solves for the lateral velocity and yaw rate using a linear two-degree-of-freedom vehicle dynamics model, and uses online adaptive neural network compensation to adjust the lateral velocity and yaw rate. The compensation is incorporated into the prediction model, making the prediction model more accurate. At the same time, it also enables the actual yaw rate and vehicle lateral velocity to better track their expected values, and imposes constraints on the vehicle yaw rate to ensure vehicle driving safety.

[0121] This invention provides a co-simulation model based on the above operating principles and processes, and its construction and operation process are as follows:

[0122] 1. Software Selection

[0123] The simulation models of the controller and the controlled object of this control system were built using MATLAB / Simulink and CarSim software, respectively, with MATLAB R2022a and CarSim 2019.1, and a simulation step size of 0.02s. CarSim is a commercial simulation software specifically designed for vehicle dynamics. Its main role in this invention is to provide a high-fidelity vehicle dynamics model, replacing a real four-wheel drive electric vehicle as the object of control in the simulation experiment, and providing a simulation environment for low-adhesion conditions. MATLAB / Simulink is used to build the simulation model of the controller, that is, to perform the controller's calculations in the control system through Simulink programming.

[0124] 2. Co-simulation settings

[0125] To achieve co-simulation between MATLAB / Simulink and CarSim, first, set the CarSim working path to the specified Simulink Model. Then, add the configured vehicle model and road information from CarSim to Simulink, and run Simulink to achieve co-simulation and communication. If the model structure or parameter settings in CarSim are modified, it needs to be resent.

[0126] 3. Construction of a four-wheel hub-driven electric vehicle model in co-simulation software

[0127] The CarSim electric vehicle model mainly consists of the body, drivetrain, steering system, braking system, tires, suspension, aerodynamics, and operating configuration systems. A four-wheel drive vehicle is selected, with its power unit consisting of four in-wheel motors. The auxiliary motor torque inputs are IMP_MYUSM_L1, IMP_MYUSM_L2, IMP_MYUSM_R1, and IMP_MYUSM_R2, and the auxiliary steering wheel angle is IMP_STEER_SW. The electric vehicle parameters are shown in Table 1.

[0128] Table 1 Electric Vehicle Parameter Table

[0129] symbol Physical description Value / Unit m Overall vehicle quality 1430 / kg <![CDATA[E e ]]> Wheel radius 0.325 / m <![CDATA[L f ]]> Distance from the vehicle's center of gravity to the front axle 1.05 / m <![CDATA[L r ]]> Distance from the vehicle's center of gravity to the rear axle 1.61 / m d Left and right wheel track 1.55 / m <![CDATA[C f ]]> Front tire lateral stiffness <![CDATA[90700 / N·m -1 ]]> <![CDATA[C r ]]> Rear tire lateral stiffness <![CDATA[109000 / N·m -1 ]]> <![CDATA[I z ]]> Moment of inertia of the vehicle about the z-axis <![CDATA[2059.2 / kg·m -2 ]]>

[0130] 4. Principle of vehicle stability control under low adhesion conditions

[0131] The controlled object of this invention is a four-wheel hub-driven electric vehicle, and the control objective is to improve the vehicle's operational stability. The main design process of the control method is described as follows: First, a four-wheel hub-driven electric vehicle model is obtained using the simulation software CarSim; second, a two-degree-of-freedom reference model is designed, and the expected values ​​of the vehicle's lateral velocity and yaw rate are derived from the two-degree-of-freedom reference model; then, a two-degree-of-freedom vehicle dynamics model is selected, and the model output state variables are obtained through partial measurements of the controlled object; and state compensation values ​​are obtained using online adaptive neural network compensation. Finally, a state compensation MPC controller is designed and adopted, with the control objective of ensuring the vehicle's lateral stability. The lateral safety constraints are considered for optimization, and the obtained state compensation values ​​are taken into account. The controller solves for the additional yaw moment and the additional front wheel angle, and then, through lower-level static allocation and the conversion of the front wheel angle to the steering wheel angle, the final required control quantities, additional motor torque and additional steering wheel angle, are obtained.

[0132] The following describes the specific steps of the control method of the present invention:

[0133] A method for vehicle stability control under low-adhesion conditions includes the following steps:

[0134] Step 1: Use the simulation software CarSim to obtain a four-wheel hub motor driven electric vehicle model: The four-wheel hub motor driven electric vehicle model simulates the real controlled object. Its main function is to provide real-time information on the vehicle's various states and to change the vehicle's motion state by using the additional torque of the motor as an input.

[0135] Step 2: Design of a two-degree-of-freedom reference model:

[0136] To obtain the ideal yaw and lateral motion states of the vehicle, a two-degree-of-freedom reference model was established. This model is a linear vehicle model that neglects the nonlinear characteristics of tire forces. Using the transient response of the vehicle obtained from the two-degree-of-freedom vehicle model as the expectation, and based on the steering angle given by the driver, the ideal yaw rate and lateral velocity are obtained, and their equations are as follows:

[0137]

[0138] Among them, V y γ is the lateral velocity, β is the yaw rate, and β is the sideslip angle of the vehicle's center of gravity.

[0139] The steady-state gain of yaw rate and the steady-state gain of center of mass sideslip angle are defined as follows:

[0140]

[0141] Furthermore, the distance L from the front axle to the rear axle and the vehicle's stability factor K are:

[0142]

[0143] The differential coefficients are defined as follows:

[0144]

[0145] The system's oscillation frequency and damping coefficient:

[0146]

[0147] Step 3: Online Adaptive Neural Network Compensation Design: To compensate for the unknown nonlinear relationship between the actual driving state variables of the vehicle and the calculated state variables of the model during predicted motion, a method is proposed as follows: Figure 3 The improved RPNN shown in the figure uses the actual state value of the controlled object and its previous state value, along with the calculated model state value and its previous state value from step three, as inputs for online compensation. The measured value of the controlled object and the calculated model state value are selected as the network outputs.

[0148] This process is based on the external input vector z = [V y com γ com Adaptive approximation of Δε, as shown below:

[0149]

[0150] In the formula For state compensation, Let a be the weight from the m-th hidden node to the output node; m It is a randomly selected weight vector that connects the input layer to the m-th hidden node, bm G(·) is the random selection bias of the m-th hidden node; G(·) is the activation function of the neural network.

[0151] In this process, the present invention selects the Sigmoid function as the activation function:

[0152]

[0153] Equation (1) can be rewritten as:

[0154]

[0155] where H = diag (α1, α2), α i =[G(a1,b1,z)G(a2,b2,z)...G(a N b N ,z)], The total number of hidden nodes is N = 24.

[0156] There exists an ideal output weight vector. This allows an unknown nonlinearity to be approximated by a very small bounded error. Approaching, that is

[0157]

[0158] Typically, the ideal output weight vector It is unknown and needs to be estimated in a closed-loop system.

[0159] To achieve stability of the closed-loop system, the target tracking error should be:

[0160]

[0161] Where κ is a constant between 0 and 1; the tracking error e(k) is defined as the estimated state vector. and the actual state vector x(k) = [V y The state offset value z = [V] between γ] y com γ com ], that is, the compensation value used in this invention:

[0162]

[0163] Error of output weights Defined as:

[0164]

[0165] If the adaptive weight update algorithm is given as:

[0166]

[0167] When the custom learning rate is 0 < η < 1, the stability of the adaptive system within the proposed RPNN can be guaranteed by the proof of the Lyapunov stability theorem. The RPNN does not require any initial training data for offline training.

[0168] The compensation results for the state variables are shown in Figures 5(c), 5(d), 6(c), 6(d), 7(c), and 7(d). These figures represent values ​​at a friction coefficient μ = 0.35 and a vehicle speed V. x =60km / h, friction coefficient μ=0.35, vehicle speed V x =70km / h, friction coefficient μ=0.3, vehicle speed V x The model state values ​​and compensation under the double lane change condition at 70 km / h are shown in the figure. It can be seen from the figure that without compensation, the calculated state value of the model is far from the actual state. However, after using the RPNN network to compensate for the state of the controlled object, the similarity between the model output state and the actual state is significantly improved. Therefore, this method can effectively calculate the offset between the reference compensation model and the controlled object. Then, by feeding the offset value back to the prediction model, the control accuracy can be effectively improved, thereby achieving better control performance under low-adhesion road surfaces.

[0169] Step 4: MPC Controller Design

[0170] ①Based on a linear two-degree-of-freedom vehicle dynamics model, we can use the measured values ​​of the controlled variables to obtain the model calculation values ​​we need, thus preparing for subsequent state compensation.

[0171] The simplified linear two-degree-of-freedom vehicle model can be described by the following equations:

[0172]

[0173] in, and Let F represent the derivatives of the vehicle's lateral velocity and yaw rate, respectively. yf and F yr ΔM represents the lateral force of the front and rear tires, respectively. z To add yaw moment, the tire lateral force F yf =-2C f α f F yr =-2C r α r .

[0174] The slip angles of the front and rear wheels are calculated as follows:

[0175]

[0176] Figure 5 compares the lateral force calculated by the tire model with the lateral force output by CarSim under the same low-adhesion double lane change condition. Figure 5 shows that the tire model cannot accurately calculate the tire's lateral force under nonlinear conditions, leaving room for future design of the state-compensated MPC. Therefore, the predictive model of the MPC controller needs improvement, adding compensation to the MPC's state to more accurately predict future states, enabling the vehicle's yaw rate and lateral velocity to better track their expected values ​​and improve control performance.

[0177] ②Prediction Model

[0178] The schematic diagram of the vehicle dynamics model described in this invention is as follows: Figure 2 As shown, considering the lateral and yaw motions of the vehicle, a two-degree-of-freedom vehicle dynamics model is obtained:

[0179]

[0180] Among them, V y For the vehicle's velocity, F y The lateral force of the tire is represented by the subscripts fl, fr, rl, and rr, which represent the left front, right front, left rear, and right rear wheels, respectively. The subscript com represents the compensation amount for state compensation. The lateral force of the tire is F. yf =-2C f α f F yr =-2Crα r , where α f α r The calculation is shown in the following formula.

[0181]

[0182] According to formulas (11)-(12), the car model can be described as follows:

[0183]

[0184] Its state variables x = [x1 x2] T =[V y γ] T The control quantity u = [u1u2] consists of the vehicle's lateral velocity and yaw rate. T =[ΔM z Δδ f ] T Add yaw moment to the tire and add front wheel steering angle, where A and B u B d They are represented as follows:

[0185]

[0186]

[0187] For the above prediction model (13), discretized according to the Euler equation, let T s Given the sampling time, the discrete prediction model is as follows:

[0188] x(k+1)=A d x(k)+B ud u(k)+B dd δ f +X c (15)

[0189] Where A d =AT s +I, B ud =B u T s B dd =B d T s X c =x com ·T s , where I is the identity matrix.

[0190] The state variables in the prediction time domain can be deduced as follows:

[0191]

[0192] Where N p For the time domain prediction, k+1|k in parentheses means predicting the system state at time k+1 from the current time k, and so on.

[0193] Furthermore, in the future N p The predicted system state X within the prediction time domain. k And the control quantity U in the prediction time domain k for:

[0194] Combining (16) and (17), they can be rearranged into matrix form:

[0195]

[0196] in

[0197]

[0198]

[0199] ③ Objective function and constraints

[0200] To ensure the vehicle's handling stability under low-adhesion conditions, the main control objectives of the state-compensated MPC controller are to track the yaw rate against its reference value and to suppress lateral velocity.

[0201] As mentioned above, the objective function is defined as follows:

[0202]

[0203] Simultaneously, comfort needs to be improved, and excessive control actions should be avoided. Furthermore, the control strategy of this invention also considers the energy consumption of the motor. Therefore, the following cost function is obtained:

[0204]

[0205] Based on the above objective functions (20) and (21), and considering the relevant constraints of control quantity and yaw rate, the proposed control strategy can adopt a weighted driving definition to define a total objective function. The optimization problem can be described as follows:

[0206]

[0207] st|u1(k i -1)|≤u 1max i = 0, 1, 2, ..., p-1

[0208] |u2(k i -1)|≤u 2max i = 0, 1, 2, ..., p-1

[0209] |γ(k i )|≤γ max , i = 1, 2, ..., p (22)

[0210] in and Γ γ These are the weighting coefficient matrices for lateral velocity and yaw rate, respectively. and These are the weighting matrices for the additional yaw moment and the additional front wheel steering angle of the control input, respectively, where [u 1max u 2max ] T =[ΔM zmax Δδ fmax ] T This is the maximum limit for the control quantity.

[0211] Solving the above problem (22) yields the following optimal control sequence U. * :

[0212] U * (k)=[u * (k), u* (k+1), ..., u * (k+N-1)] T (twenty three)

[0213] Among them, based on the principle of model predictive control, the final control sequence U obtained (23) is * The first value u * (k)=[ΔM z Δδ f ] T Consider the optimal additional yaw moment and the optimal additional front wheel steering angle, such as Figure 5e , Figure 5f , Figure 6e , Figure 6f , Figure 7e , Figure 7f The values ​​are respectively: friction coefficient μ = 0.35, vehicle speed V x =60km / h, friction coefficient μ=0.35, vehicle speed V x =70km / h, friction coefficient μ=0.3, vehicle speed V x The control quantities obtained under the double lane change condition at 70km / h are the additional yaw moment and the additional front wheel steering angle.

[0214] This results in the additional driving torque and additional steering wheel angle of the four motors:

[0215]

[0216] As for the optimal additional steering wheel angle:

[0217] ΔSWA=180·Δδ f / π (25)

[0218] The additional driving torque and additional steering wheel angle work together with the driving torque and steering wheel angle applied by the driver to achieve the control effect.

[0219] The parameters and weighting coefficients used in the simulation experiment are shown in Table 2.

[0220] Table 2 Simulation Experiment Parameters

[0221]

[0222] Figures 5, 6, and 7 show the simulation curves of the lateral velocity and yaw rate of the vehicle under different speeds in the double lane change condition. It can be seen that compared with the linear MPC control system without state compensation, the yaw rate of the vehicle can more accurately track its expected value under the action of the state-compensated MPC controller, and the lateral velocity can also be more effectively suppressed, thus ensuring the lateral stability of the vehicle under nonlinear conditions.

[0223] Among them, the verification results of lateral velocity and yaw rate under the condition of low speed (60km / h) and friction coefficient of 0.35, as shown in Figure 5, show that the condition is mainly in the linear region. It can be seen from the figure that the lateral velocity is suppressed at 7.8 seconds and the yaw rate is closer to the reference value, indicating that under linear conditions, the state compensation can still play a good control role.

[0224] The verification results of lateral velocity and yaw rate under the double lane change condition with a high speed (70 km / h) and low friction coefficient (μ = 0.35) are shown in Figure 6. As can be seen from Figure 6(a), after applying state compensation, the lateral velocity suppression is more ideal, effectively suppressed within ±0.15 m / s. Figure 6(b) shows that after state compensation, the yaw rate tracking effect is also more ideal, exhibiting better tracking performance at 3 seconds, 4.7 seconds, 6.3 seconds, and 8 seconds, proving the effectiveness of the invention.

[0225] The verification results of lateral velocity and yaw rate under the double lane change condition with higher speed (70km / h) and lower friction coefficient (μ=0.3) shown in Figure 7 are as follows. It can also be seen from Figure 7(a) that the lateral velocity was significantly suppressed after applying state compensation control. Figure 7(b) shows that the tracking performance of tracking yaw rate was also significantly improved under this condition.

Claims

1.A vehicle lateral stability control method based on online state compensation MPC, characterized in that: The steps are: S1, using online adaptive neural network to predict the lateral velocity and yaw rate compensation value of the model, and according to the compensation value, the prediction model offset is compensated in real time in the controller; S01, Online adaptive neural network compensation: adaptively approximate Δε from external input vector z = [V y com γ com ] as follows wherein is an approximation variable for state compensation, is the weight from the mth hidden node to the output node; a m is a randomly selected weight vector connecting the input layer to the mth hidden node, b m is a randomly selected bias for the mth hidden node; G(·) is an activation function for the neural network; S02, the activation function is selected as Sigmoid function: Rewrite formula (1) as: where H = diag (ai, a2), a i = [G (ai, bi, z) G (a2, b2, z)... G (an, bn, z)], and N = [G (ai, bi, z) G (a2, b2, z)... G (an, bn, z)], and N = [G (ai, bi, z) G (a2, b2, z)... G (an, bn, z)], and S03, ideal output weight vector unknown nonlinearities can be approximated with a very small bounded approximation error approximation, i.e. To realize the stability of the closed-loop system, the target tracking error should be Where κ is a constant between 0 and 1; S04The tracking error e(k) is defined as the state offset value z = [V x(k) = [V y γ] between the estimated state vector y com γ com ] between the estimated state vector y com γ com and the actual state vector x(k) = [V y com γ com , i.e. the used compensation value: S05, error of output weight is defined as: S06, the adaptive weight update algorithm is given as: When the custom learning rate 0 < η < 1, under the proof of Lyapunov stability theorem, the stability of the adaptive system in the proposed RPNN can be guaranteed, and the RPNN does not need any initial training data for offline training; S2, MPC controller design: S0l, the simplified linear vehicle two-degree-of-freedom model is described by the following equation: wherein, and respectively denote a derivative of the lateral velocity and a derivative of the yaw rate of the vehicle, F yf and F yr respectively denote tire lateral forces of the front and rear tires, ΔM z is an additional yaw moment, the tire lateral forces F yf = -2C f α f , F yr = -2C r α r ; The side slip angles of the front and rear wheels are as follows: S02, prediction model Considering the lateral and yaw motion of the vehicle, a two-degree-of-freedom vehicle dynamics model is obtained: where V y is the vehicle lateral velocity, F y represents the lateral force of the tire, the subscripts fl, fr, rl, and rr represent the front left, front right, rear left, and rear right wheels, respectively, and the subscript com represents the compensation amount of the state compensation, the tire lateral force F yf = -2C f α f , F yr = -2C r α r ; α in tire lateral force f α r The formula is as follows According to formulas (11)-(12), the vehicle model is described as: its state variable x = [x1 x2] T = [V y γ] T consists of the vehicle lateral velocity and the yaw rate, the control variable u = [ul u2] f = [AM z Aδ f ] T is the additional yaw moment and the additional front wheel steering angle. A, B u , B d respectively as: For the prediction model (13), according to the Euler equation discretization, let T s be the sampling time, the discretized prediction model is obtained as follows: x(k + 1) = A d x(k) + B ud u(k) + B dd δ f + X c (15) where A d = AT s + I, B ud = B u T s , B dd = B d T s , X c = x com · T s , where I is the identity matrix; The state quantity in the prediction time domain is derived as where N p is the prediction horizon, k + 1 | k in the brackets indicates predicting the system state at k + 1 time instant at current k time instant; the system state X p predicted in the future N k predicted time horizon, and the control amount U k is: Combine (16) (17) and arrange it into matrix form: Where, S03, objective function and constraint ① Define the objective function as follows: ② Cost function: ③ According to formula (20), (21), define a total objective function: s.t. |u1(k i -1)|≤u 1max , i = 0, 1, 2,..., p - 1 |u2(k i -1)|≤u 2max , i = 0, 1, 2,..., p - 1 | γ(k i )|≤ γ max , i = 1, 2,..., p (22) wherein and Γ γ are weight coefficient matrices of lateral velocity and yaw rate, respectively, and are weight coefficient matrices of the control amount additional yaw moment and additional front wheel steering angle, respectively, wherein [u 1max u 2maxa ] T = [ΔM zmax Δδ fmax ] T limit maximum value of the control quantity; Solving the above equation (22) gives the optimal control sequence U * : U * (k) = [u * (k), u * (k+1),..., u * (k+N-1)] T (23) wherein the control sequence U * The first value u * (k) = [AM z Δδ f ] T is considered as the optimal additional yaw moment and the optimal additional front wheel steering angle; Get the following four motor additional driving torque and additional steering wheel angle: For the optimal additional steering wheel angle: ASWA = 180 - ASW f / π (25) The additional driving torque and the additional steering wheel angle work together with the driving torque and the steering wheel angle punched by the driver to achieve the control effect.

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