A stability control method and device suitable for steer-by-wire front wheel steering

Abstract

The application discloses a stability control method and device suitable for a by-wire front wheel steering, and is based on invariable yaw rate gain and lateral acceleration gain, and proposes a variable angle transmission ratio design scheme; local weighted regression and spline interpolation method are used to smooth the angle transmission ratio curve obtained through design, so that the continuity and stability of the transmission ratio curve are ensured; the collected vehicle yaw rate, lateral acceleration and ideal yaw rate and lateral acceleration are subtracted to obtain yaw rate and lateral acceleration errors; a linear quadratic regulator (LQR) controller is used to calculate an additional front wheel steering angle as an initial value; then, rolling optimization is carried out under a model predictive control (MPC) framework, the LQR output is taken as an initial reference, and a final control input is obtained through optimization. Through the method, the yaw rate error and lateral acceleration error of the vehicle can be effectively controlled, so that the stability and handling performance of the vehicle are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of vehicle control, in particular to a stability control method and device for a steer-by-wire active front wheel steering system. BACKGROUND

[0002] With the rapid development of the automotive industry, active safety and handling performance of vehicles have become the focus of consumers and manufacturers. As an advanced steering technology, steer-by-wire active front wheel steering system replaces traditional mechanical connection with electronic signals, achieving more flexible and intelligent steering control. However, how to achieve the best vehicle handling performance and stability under different driving conditions is still a problem to be solved.

[0003] Traditional mechanical steering systems transmit the rotation of the steering wheel to the front wheels through mechanical connection, achieving vehicle steering. Although this system has simple structure and high reliability, it also has many limitations. For example, the steering ratio is fixed and cannot be adjusted according to the speed and road conditions, resulting in different handling performance at low and high speeds. At low speed, steering is too heavy and flexible, and at high speed, steering is too sensitive and easy to cause vehicle instability. In addition, the traditional mechanical steering system has single steering force feedback for the driver, and cannot realize personalized steering characteristic adjustment, making it difficult to meet modern driving needs. Steer-by-wire steering system can adjust the transmission ratio in real time according to the driving state of the vehicle (such as speed, steering angle, yaw rate, etc.), providing the best steering response and handling performance; through the electric power steering system, the steer-by-wire steering system can simulate different steering force feedback, allowing the driver to obtain a more realistic road feel and handling experience; the steer-by-wire steering system can be linked with other active safety systems (such as ESP, ADAS, etc.), improving the overall safety and stability of the vehicle.

[0004] Existing steer-by-wire steering control methods mostly use fixed steering wheel and wheel angle transmission ratio or simple transmission ratio adjustment algorithms, which are difficult to adapt to different speed and working condition requirements. For example, some methods only set different transmission ratios in low and high speed zones, ignoring the characteristics of the medium speed zone, resulting in poor handling performance at medium speed. In addition, the change of transmission ratio is usually abrupt, which can easily cause discomfort for the driver and instability of the vehicle. In terms of control strategy, although the traditional PID controller is widely used, it is difficult to meet the requirements of control accuracy and response speed when facing complex vehicle dynamics and nonlinear characteristics. In recent years, advanced control methods such as model-based predictive control (MPC) and linear quadratic regulator (LQR) have been gradually applied to vehicle steering control, but how to effectively combine these control strategies to take advantage of each other and achieve the best steering control effect is still a difficulty. SUMMARY

[0005] Invention purpose: In view of the deficiencies in the prior art, the present application provides a stability control method suitable for drive-by-wire active front wheel steering, which realizes the best steering performance and stability in different speed intervals through reasonable design and smoothing processing of the transmission ratio, combined with LQR and MPC control strategies. Specifically, the present application solves the deficiencies in the prior art through the following innovations: (1) According to the vehicle speed, the transmission ratio is divided into low speed, medium speed and high speed for design, ensuring the best steering performance at different speeds. (2) The transmission ratio curve is smoothed by local weighted regression and spline interpolation method to ensure the continuity and smoothness of the transmission ratio change, avoiding the instability caused by sudden change. (3) LQR and MPC control strategies are combined to make full use of the fast response of LQR controller and the high precision optimization of MPC controller, effectively integrating the advantages of the two, significantly improving the precision and stability of steering control. Specifically, the LQR controller quickly calculates the front wheel additional angle according to the yaw rate error and lateral acceleration error, providing the initial control input. The MPC controller further optimizes the control input by predicting the vehicle state at multiple future times. This integrated control strategy can provide more accurate and stable steering control under various driving conditions.

[0006] To achieve the above purpose, a drive-by-wire steering angle following control method based on linear quadratic regulation is designed, and the specific process is as follows:

[0007] Step 1, design the ideal transmission ratio curve, set the transmission ratio according to different intervals of different vehicle speeds, and the vehicle speed interval is divided into low speed [0, 20], medium speed [20, 70] and high speed [70, ∞];

[0008] Step 2, set a fixed transmission ratio in the low speed zone, set the transmission ratio to 9.6;

[0009] Step 3, in the medium speed zone, according to the fixed lateral acceleration gain, realize variable transmission ratio by collecting different vehicle speeds v;

[0010]

[0011]

[0012] Step 4, in the high speed zone, in order to improve the stability of the vehicle, the vehicle speed is constantly increasing, and the transmission ratio is continuously increasing, which causes the steering response to be sluggish, therefore, a method of combining fixed yaw rate gain and lateral acceleration gain is used to design the transmission ratio;

[0013]

[0014]

[0015]

[0016] wherein,

[0017]

[0018] Step 5 The collected vehicle speed and corresponding transmission ratio are taken as data points, and the data points are subjected to local weighted regression processing to obtain a preliminarily smoothed steering transmission ratio curve; on the basis of the preliminary smoothing, the steering transmission ratio curve is further subjected to refinement and smoothing processing by using a spline interpolation method to obtain an ideal steering transmission ratio curve meeting the variable transmission ratio requirement;

[0019] Step 6 A dynamics model of the steer-by-wire execution mechanism is established;

[0020] Step 7 The equation of the dynamics model in Step 6 is transformed into a form of a spatial state equation;

[0021] Step 8 When designing the LQR controller, state information of the steering system is obtained, including a difference between a yaw rate and an ideal yaw rate, denoted as e1, and a difference between a lateral acceleration and an ideal lateral acceleration, denoted as e2;

[0022] Step 9 The control amount of the LQR controller is △θ LQR =-Ke;

[0023] Step 10 The MPC controller is designed, wherein a prediction model is obtained by discretizing the 2DOF model of the four-wheel steering by using a first-order difference quotient method to obtain a discrete model;

[0024] x k+1 =Ax k +Bu k

[0025] wherein, x k is a state vector at a time step k, including state variables such as a yaw rate and a lateral acceleration, u k is a control input at the time step k, i.e., a front wheel additional steering angle, A is a system matrix describing relationships between the state variables, and B is an input matrix describing an influence of the control input on the state;

[0026] A prediction horizon length N is selected, and the prediction horizon length determines a number of steps in the future predicted by the controller at each time. A typical prediction horizon length depends on dynamic characteristics of the system and computing resources;

[0027] A performance index (objective function) is defined to optimize the MPC controller, and the performance index generally includes a weighted sum of state deviations and control inputs, and the objective function is in the form of:

[0028]

[0029] wherein Q is a state weight matrix reflecting the influence of state variable deviation on performance, and R is a control weight matrix reflecting the cost of control input.

[0030] The beneficial effects of the present application are:

[0031] 1. According to the driving speed of the vehicle, the transmission ratio is divided into low-speed, medium-speed and high-speed zones for design, ensuring the adaptability of the transmission ratio at different speeds. In the low-speed zone, a fixed transmission ratio is set to ensure the flexibility and high sensitivity of the vehicle when driving at low speed, so that the driver can easily control the vehicle when driving at low speed and parking. In the medium-speed zone, the transmission ratio is designed according to the fixed lateral acceleration gain method, ensuring good steering response and control stability of the vehicle when driving at medium speed. In the high-speed zone, the transmission ratio is designed by combining the fixed yaw rate gain and lateral acceleration gain, improving the stability and safety of the vehicle when driving at high speed. This phased design of transmission ratio enables the vehicle to achieve optimal control performance at different speeds, meeting the needs of various driving conditions.

[0032] 2. The present application combines LQR control and MPC control strategies, making full use of their advantages. The LQR controller quickly calculates the front wheel additional angle according to the vehicle's yaw rate error and lateral acceleration error, providing initial control input and having the advantage of fast response. The MPC controller performs rolling optimization on this basis, predicting the vehicle state at multiple future times and further optimizing the control input, with the advantages of high precision and foresight. By using the LQR output as the initial reference for MPC optimization, the present application can quickly respond to the driver's steering demand and further improve the control accuracy through rolling optimization, ultimately obtaining more accurate and stable front wheel angle instructions. This integrated control strategy effectively improves the vehicle's handling performance, especially in complex road conditions and high dynamic driving environments, providing more stable and safe steering control.

[0033] 3. The method of the present application is not only suitable for traditional active front wheel steering systems, but also for steering control systems of electric vehicles and autonomous vehicles. Electric vehicles and autonomous vehicles have higher requirements for response speed and control accuracy of the steering system, and the present application can meet these requirements through advanced control strategies and reasonable transmission ratio design, having wide application prospects. At the same time, the method of the present application has low cost for the modification of existing steering systems, having high market value and promotion potential. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is the SBW active front wheel steering comprehensive control block diagram of the present application;

[0035] Figure 2 Flow chart for designing ideal transmission ratio curve of the present application;

[0036] Figure 3 MPC block diagram based on model of the present application;

[0037] Figure 4 Ideal transmission ratio curve chart. DETAILED DESCRIPTION

[0038] The present application is further described below in conjunction with the accompanying drawings.

[0039] As shown in the figure, it is the overall schematic block diagram of the embodiment of the present application. First, design the ideal transmission ratio curve, set transmission ratio in different intervals according to different vehicle speeds, divided into low speed zone [0, 20], medium speed zone [20, 70], high speed zone [70, ∞]; Figure 1 Then, set fixed transmission ratio in low speed zone stage, set transmission ratio as 9.6;

[0040] In medium speed zone stage, according to fixed lateral acceleration gain, realize variable transmission ratio by collecting different vehicle speeds v:

[0041]

[0042]

[0043] In high speed zone stage, in order to vehicle stability, vehicle speed is constantly increasing, avoid transmission ratio continuously increasing, cause steering reaction sluggish, therefore, adopt the method of combining fixed yaw rate gain and lateral acceleration gain to design transmission ratio:

[0044]

[0045]

[0046]

[0047]

[0048] Wherein, θ fw is front wheel turning angle, θ sw is steering wheel turning angle, k1 is front wheel tire cornering stiffness, k2 is rear wheel tire cornering stiffness, v is vehicle speed, m is vehicle mass, a is distance from mass center to front axle, b is distance from mass center to rear axle, L is vehicle wheelbase, K w and K ay are weight coefficients, K w + K ay = 1, i is transmission ratio, i ay is transmission ratio obtained by fixed lateral acceleration, i​w is the transmission ratio for fixing yaw rate gain, w r is the yaw rate, a y is the lateral acceleration, G ay is the lateral acceleration gain, G wr is the steady-state yaw rate gain, which is 0.16-0.33 s -1 ;

[0049] By designing the transmission ratio in different stages, a variable transmission ratio segmented function is obtained

[0050]

[0051] Finally, the collected vehicle speed and the corresponding transmission ratio are taken as data points, and the data points are processed by local weighted regression to obtain a preliminary smoothed steering transmission ratio curve. On the basis of preliminary smoothing, the steering transmission ratio curve is further refined and smoothed by using spline interpolation method to obtain an ideal steering transmission ratio curve that meets the variable transmission ratio requirement, as shown in Figure 2 , 4 .

[0052] The local weighted regression is a non-parametric regression method, which assigns different weights to the data points near the given point to achieve local fitting. The weight decreases with the increase of distance, so the data points closer to the target point have larger weights.

[0053] Then the local weighted regression needs to select a bandwidth parameter in the smoothing process, which determines the range of the local area. The larger the bandwidth, the more adjacent points are considered; and the weight needs to be calculated, for each fitting point, the weight is calculated according to the distance from other data points; finally, at each fitting point, a model is fitted by using the weighted least squares method (Weighted Least Squares) for local linear regression or polynomial regression, and the value of the fitting point is predicted using the locally fitted model.

[0054] However, the spline interpolation method is an interpolation method for fitting data points by using piecewise polynomials. Among them, the cubic spline uses a cubic polynomial in each interval and ensures continuous first and second derivatives at the interval connection.

[0055] The smoothing process of the spline interpolation method includes selecting the type of spline used (cubic spline), then selecting the type of spline used (cubic spline), and constructing a cubic polynomial for each segment of data:

[0056] S i (x)=a i +b i (x-x i )+c i(x-x i ) 2 +d i (x-x i ) 3

[0057] To ensure the smoothness of the spline, continuity conditions are imposed at the endpoints of adjacent intervals:

[0058] S i (x i+1 ) = S i+1 (x i+1 ) (continuity of function values)

[0059] S i ′(x i+1 ) = S i ′ +1 (x i+1 ) (continuity of first derivatives)

[0060] S i ″(x i+1 ) = S i ″ +1 (x i+1 ) (continuity of second derivatives)

[0061] where S i (x) is the spline function of the ith segment, x is the independent variable, representing the input value of the function, which can take any value within the domain of definition, used to calculate the value of the spline function S i (x), x i is the independent variable value of the ith known data point, representing the node of the spline function segment, a i is the constant term, representing the function value of the spline function at the start of the interval x i , b i is the first-order term coefficient, representing the slope of the spline function at the start of the interval x i , c i is the second-order term coefficient, affecting the curvature of the spline function within the interval, d i is the third-order term coefficient, further adjusting the curvature change of the spline function, making it smoother within the interval.

[0062] Then, combined with the boundary conditions at the endpoints (such as the natural boundary condition, i.e. the second derivative at the endpoints is zero), a system of linear equations is formed, and all polynomial coefficients are solved. Finally, the spline function obtained is used for interpolation or prediction.

[0063] At the same time, the yaw rate is collected, and the collected lateral acceleration and yaw rate are subtracted from the ideal lateral acceleration and yaw rate to obtain an input signal of a linear quadratic regulator (LQR) controller. The LQR output is used as an initial reference, and the final control input is obtained by optimization to track the ideal yaw rate w r The output of the MPC controller is calculated as an additional front wheel angle Δθ fw The sum of the additional front wheel angle Δθ fw and the initial front wheel angle θ fw is used as a new vehicle front wheel angle θ fw which is output to the controlled vehicle, so that the yaw rate w r of the vehicle better tracks the ideal yaw rate of the vehicle.

[0064] A dynamic model of the steer-by-wire execution motor is established

[0065]

[0066] In the formula, T M is the output torque of the steering motor; J M is the rotational inertia of the steering motor; θ M is the steering motor angle; B M is the damping coefficient of the steering motor; K2 is the torsional stiffness of the steering motor; G M is the reduction ratio of the steering motor reducer; X r is the rack and pinion displacement; and r p is the radius of the pinion gear.

[0067] The steering execution motor model is simplified according to Kirchhoff's law:

[0068]

[0069] According to the electromagnetism principle of the DC motor, the relationship between the current and the electromagnetic torque of the motor is:

[0070] T M = K t2 i M

[0071] In the formula, U M is the voltage across the steering motor; R M is the armature resistance of the steering motor; L M is the inductance of the steering motor; i M is the current of the steering motor; K M is the electromagnetic torque coefficient of the steering motor; and K t2 is the back electromotive force coefficient of the steering motor.

[0072] The mathematical model expression of the rack and pinion module is established as:

[0073]

[0074] In the formula, M r is the mass of the rack and pinion; B r is the damping coefficient of the rack and pinion; K kpi is the steering wheel kingpin torsional stiffness; N Li is the rack to front wheel transmission ratio; θ fwi is the steering wheel rotation angle i = 1, 2, respectively representing the front wheel and the rear wheel.

[0075] The steering wheel system dynamics differential equation is established as:

[0076]

[0077]

[0078] In the formula, J fwi is the front wheel kingpin moment of inertia; B kpi is the steering wheel damping coefficient; T Zi is the steering wheel rotation return torque, i = 1, 2, respectively representing the front wheel and the rear wheel.

[0079] Then the equation of the dynamics model is transformed into the form of the spatial state equation, and the design of the linear quadratic regulator (LQR) controller is performed; specifically:

[0080] In the LQR controller, the dynamics model of the vehicle is linearized to obtain the state space equation:

[0081]

[0082]

[0083] Wherein, x is the state error vector, including the state variables such as yaw rate and lateral acceleration error, u is the control input, that is, the additional front wheel rotation angle Δθ fw , A is the system matrix, which describes the relationship between the state variables, and B is the input matrix, which describes the influence of the control input on the state.

[0084]

[0085] The design goal of the LQR controller is to minimize a quadratic performance index, which is composed of state variables and control inputs. The performance index J is defined as

[0086]

[0087] To design the LQR controller, the state weight matrix Q and the control weight matrix R need to be chosen. These matrices are used to define the performance index, which reflects the preference of the control objective to different state variables and control inputs; Q is a positive definite matrix, the greater the weight, the greater the impact of the corresponding state variable error on the performance index, and R is a positive definite matrix, the greater the weight, the higher the cost of the control input.

[0088]

[0089] Q is the weight matrix of state error, reflecting the importance of state error, and R is the weight matrix of control input, reflecting the cost of control input size.

[0090] The feedback law of the LQR controller is:

[0091] u=-Cx

[0092] A symmetric positive definite matrix P is constructed, and the Riccati equation is established as:

[0093] A T P+PA-PBR -1 B T P+Q=0

[0094] The optimal feedback matrix C is calculated by solving P:

[0095] C=R -1 B T P

[0096] The additional front wheel steering angle is obtained:

[0097] △θ fw =-Ce

[0098] Where e is the current state error vector, e=[e1 e2] T , which contains the current yaw rate and lateral acceleration error, and C is the feedback gain matrix.

[0099] When designing the LQR controller, the state information of the steering system is obtained, including the difference between the yaw rate and the ideal yaw rate, denoted as e1, and the difference between the lateral acceleration and the ideal lateral acceleration, denoted as e2; the output control quantity of the LQR controller is △θ fw =-Ce;

[0100] Then, the MPC controller is designed, as shown in Figure 3 , to predict the vehicle driving state in the future period of time, a linear 2DOF vehicle model is selected as the controlled object, and its motion differential equation is as follows.

[0101]

[0102] where C f and C r are the cornering stiffness of the front and rear wheels, l f and l r are the distances from the front and rear wheels to the center of mass of the vehicle, I z is the moment of inertia of the vehicle about the center of mass, v is the longitudinal velocity of the vehicle, a y is the lateral acceleration, v y is the lateral velocity.

[0103] The above motion differential equations are converted into state space equations as follows:

[0104] The state vector x and the input vector u are respectively:

[0105]

[0106] The model assumes that the center of mass of the vehicle is located between the front and rear wheels, and ignores the roll and pitch motions of the vehicle, and is simplified to a 2DOF model of planar motion model as shown in the following formula:

[0107]

[0108]

[0109] Then, in order to reduce the amount of calculation, simplify the control system, the linear continuous system is discretized by using the forward Euler method:

[0110] X(k+1) = A k X(k) + B k U(k)

[0111] where X(k) is the state vector, representing the state of the system at time step k, U(k) is the control vector, representing the control input of the system at time step k, Y(k) is the predicted value of the output quantity in the prediction horizon, this vector contains the output prediction value at each future time step in the prediction horizon starting from time step k, A k = AT + I, B k = TB, T is the discrete sampling period, and I is the unit matrix;

[0112] The control increment is defined as follows:

[0113] △U(k) = U(k) - U(k-1)

[0114] The prediction model is derived as follows:

[0115]

[0116] where, n is the number of state variables, m is the number of control variables, ξ(k) is the state vector, representing the state of the system at time step k, η(k) is the output vector, representing the output of the system at time step k; 0 m×n , 0 m represents a 0 matrix with different dimensions, I m represents the unit matrix.

[0117] Then in the prediction horizon, the predicted value of the output quantity can be calculated by the following formula:

[0118] Y(k) = ψ k ξ(k) + O k ΔU(k)

[0119] In the formula,

[0120] where N p is the prediction horizon, N c is the control horizon;

[0121] A performance index (objective function) is defined to optimize, which includes the weighted sum of state deviation and control input, and the objective function is in the form of:

[0122]

[0123] where x k represents the state variable at time k, x ref represents the ideal reference value of the state at time k, u k represents the control variable at time k, u LQR is the ideal additional front wheel angle calculated by the LQR controller, Q is the state weight matrix, reflecting the influence of state variable deviation on performance, R is the control weight matrix, reflecting the cost of control input, and N is the prediction horizon length.

[0124] In practical applications, the constraints of control input and state need to be considered. For example, the physical limits of front wheel angle, yaw rate and lateral acceleration;

[0125]

[0126] where δ i represents the front wheel angle, w i represents the yaw rate, δ min and δ max are the minimum and maximum values of the front wheel angle, w min and w max are the minimum and maximum values of the yaw rate, a ymaxMaximum value of lateral acceleration.

[0127] These constraints are considered as limiting conditions in the optimization process, ensuring that the steering system operates within its physical range, preventing the steering system from being damaged.

[0128] Based on the above control method, the application further provides a stability control device for the by-wire front wheel steering, comprising a processor and a memory, the memory stores the program code of the above control method, and the processor can execute the program code of the memory.

[0129] Through the above steps, the precise control of the front wheel steering angle of the vehicle is realized by the segmented design of the transmission ratio and the curve smoothing processing, combined with the advanced control strategy, the stability and the handling performance of the vehicle are improved, and the application value is high and the application prospect is wide.

[0130] The series of detailed descriptions listed above are only specific descriptions for the feasible implementation manners of the application, and are not used to limit the protection scope of the application, and any equivalent manners or changes without departing from the technology of the application should be included in the protection scope of the application.

Claims

1. A stability control method for a by-wire front wheel steering, characterized by, Comprise the following: Step 1, design ideal transmission ratio curve, set transmission ratio according to different intervals of different vehicle speeds, the different intervals of the vehicle speed include low speed area, medium speed area, high speed area; Step 2, set fixed transmission ratio in low speed area stage; Step 3, in medium speed area stage, realize variable transmission ratio according to different vehicle speeds according to fixed lateral acceleration gain; In the step 3, the variable transmission ratio of the medium speed area is set as follows: Step 4 in high speed area stage, adopt the method of comprehensive fixed yaw angular velocity gain and lateral acceleration gain to design transmission ratio; In the step 4, the transmission ratio of the high speed area is set as follows: wherein, θ fw is the front wheel steering angle, θ sw is the steering wheel angle, k1 is the tire cornering stiffness of the front wheel, k2 is the tire cornering stiffness of the rear wheel, v is the vehicle speed, m is the vehicle mass, a is the distance from the mass center to the front axle, b is the distance from the mass center to the rear axle, L is the wheelbase of the vehicle, K w and K ay are weight coefficients, K w + K ay = 1, i is the transmission ratio, i ay is the transmission ratio obtained by fixing the lateral acceleration, i w is the transmission ratio obtained by fixing the yaw rate gain, ω r is the yaw rate, a y is the lateral acceleration, G ay is the lateral acceleration gain, G wr is the steady-state yaw rate gain, and has a value of 0.16 to 0.33 s -1 ; Step 5, take the collected vehicle speed and corresponding transmission ratio as data points, carry out local weighted regression processing on the data points, obtain preliminary smoothed steering transmission ratio curve;On the basis of preliminary smoothing, further adopt spline interpolation method to refine and smooth the steering transmission ratio curve, obtain ideal steering transmission ratio curve meeting variable transmission ratio requirement; Step 6, establish dynamics model of the steer-by-wire execution mechanism, and transform into state space equation form; In the step 6, the dynamics model is modeled as follows: Establish the dynamics model of the steer-by-wire execution motor wherein T M J is the steering motor output torque; J M J is the steering motor moment of inertia; θ M J is the steering motor angle; B M J is the steering motor damping coefficient; K2 is the steering motor torsional stiffness; G M X is the steering motor reducer reduction ratio; X r r is the rack displacement; r p r is the steering gear pitch circle pinion radius; Simplify the motor model of the steering execution motor: The relationship between the current of the motor and the electromagnetic torque is: T M = K t2 i M wherein U M is the voltage across the steering motor; R M is the armature resistance of the steering motor; L M is the inductance of the steering motor; i M is the current of the steering motor; K M is the electromagnetic torque coefficient of the steering motor; K t2 is the counter electromotive force coefficient of the steering motor; The mathematical model expression of the rack and pinion module is established as: where M r is the rack and pinion mass; B r is the rack and pinion damping coefficient; K kpi is the steering wheel kingpin torsional stiffness; N Li is the rack to front wheel transmission ratio; θ fwi is the steering wheel angle; i = 1, 2, corresponding to the front and rear wheels, respectively; The steering wheel system dynamics differential equation is established: In the formula, J fwi is the front wheel kingpin inertia; B kpi is the steering wheel damping coefficient; T Zi is the steering wheel rotational return moment; Linearize the dynamics model to obtain the state space equation: u = θ LQR Wherein, x is the state error vector, including state variables such as yaw rate and lateral acceleration error, u is the control input, that is, the front wheel additional angle, A is the system matrix, which describes the relationship between the state variables, B is the input matrix, which describes the influence of the control input on the state; Step 7 design LQR controller; get the state information of the steering system, including: yaw rate and lateral acceleration, respectively, subtract them from the ideal yaw rate and lateral acceleration, and the differences are denoted as e1, e2, as the input signals of the LQR controller, and the output of the LQR controller is the additional front wheel steering angle △θ LQR , the additional front wheel steering angle △θ fw is added to the initial front wheel steering angle θ fw to obtain the new vehicle front wheel steering angle θ fw , which is output to the vehicle, so that the yaw rate ω r of the vehicle better tracks the ideal yaw rate; Step 8 designs the MPC controller, predicts the vehicle state at future time instants, and further optimizes the LQR controller output additional front wheel angle LQR .

2. A stability control method for a steer-by-wire front wheel steering system according to claim 1, characterized by, In the step 1, the different intervals of the vehicle speed are set as follows: low speed area [0, 20], medium speed area [20, 70], high speed area [70, ∞].

3. The stability control method for a by-wire front wheel steering according to claim 1, characterized by, In the step 2, the fixed transmission ratio is set to 9.

6.

4. The stability control method of a by-wire front wheel steering according to claim 1, characterized by, In the step 5, the method of adopting spline interpolation method to refine and smooth the steering transmission ratio curve includes the following: Select the spline type used (cubic spline), construct a cubic polynomial for each section of data: S i (x) = a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 In order to ensure the smoothness of the spline, continuity conditions are applied at the endpoints of adjacent intervals: Function value continuous: S i (x i+1 ) = S i+1 (x i+1 ) First derivative continuous: S' i (x i+1 ) = S' i+1 (x i+1 ) Second derivative continuous: S" i (x i+1 ) = S" i+1 (x i+1 ) where S i (x) is the spline function of the i-th segment, x is the independent variable, representing the input value of the function, which can take any value within the domain, used to calculate the value of the spline function S i (x), x i is the independent variable value of the i-th known data point, representing the node of the spline function segment, a i is the constant term, representing the function value of the spline function at the start of the interval x i , b i is the first-order term coefficient, representing the slope of the spline function at the start of the interval x i , c i is the second-order term coefficient, affecting the curvature of the spline function within the interval, d i is the third-order term coefficient, further adjusting the curvature change of the spline function, making it smoother within the interval; Combine the boundary conditions of the endpoints (such as natural boundary conditions, that is, the second derivative is zero at the endpoints), form a linear equation group, solve all polynomial coefficients, and use the obtained spline function for interpolation or prediction.

5. The stability control method of a by-wire front wheel steering according to claim 1, characterized by, The implementation of the step 7 includes: The design goal of the LQR controller is to minimize a quadratic performance index, which is composed of state variables and control inputs. The performance index J is defined as: Q is the state weight matrix, R is the control weight matrix, wherein: Q is a positive definite matrix, which represents the influence degree of the corresponding state variable error on the performance index, R is a positive definite matrix, which represents the influence degree of the cost of the control input; R＝0.1； The feedback law of the LQR controller is: u=-Cx K is the feedback gain matrix; Construct a positive definite matrix P, and establish the Riccati equation as: A T P+PA-PBR -1 B T P+Q=0 Solve P by equation, calculate the optimal feedback matrix K: K = R -1 B T P Get the additional front wheel angle: Δθ fw = -Ce where e is the current state error vector, e = [el e2] T including the current yaw rate error el and the lateral acceleration error e2.

6. A stability control method for steer-by-wire front wheel steering according to claim 1, characterized by The implementation of the step 8 comprises: A linear 2DOF four-wheel vehicle model is selected as the controlled object, and the motion differential equation is as follows: where δ is the front wheel steering angle, C f and C r are the cornering stiffness of the front and rear wheels, respectively, l f and l r are the distances from the front and rear wheels to the vehicle center of mass, I z is the moment of inertia of the vehicle about the center of mass, v is the vehicle longitudinal speed, a y is the lateral acceleration, and v y is the lateral speed. The model is discretized, and a state vector x and a control input vector u are defined as follows: u = Δθ fw The vehicle model is simplified as a 2DOF model of planar motion, and is as follows: The linear continuous system is discretized into a discrete-time system by using a forward Euler method, and is as follows: X(k+1) = A k X(k) + B k U(k) where A k = AT + I, B k = TB, T is a discrete sampling time, and I is an identity matrix. The control increment is defined as follows: △U(k) = U(k) - U(k-1) The prediction model is derived; wherein, n is the number of state variables, m is the number of control variables, ξ(k) is a state vector, representing the state of the system at time step k, η(k) is an output vector, representing the output of the system at time step k; 0 m×n , 0 m denotes a 0 matrix of different dimensions, I m denotes an identity matrix; In the prediction horizon, the predicted value of the output can be calculated by the following formula: Y(k) = ψ k ξ(k) + O k ΔU(k) In the formulae, where N p is the prediction time horizon, N c is the control time horizon; A performance index (objective function) is defined to optimize the controller, which includes the weighted sum of the state deviation and the control input, and the objective function is as follows: where x k represents the state quantity at time k, x ref represents the ideal state reference value at time k, u k represents the control quantity at time k, u LQR is the ideal additional front wheel steering angle calculated by the LQR controller, Q is a state weight matrix, reflecting the influence of the deviation of the state variable on the performance, R is a control weight matrix, reflecting the cost of the control input, and N is the prediction time domain length.

7. A stability control device for a steer-by-wire front wheel steering, characterized by A processor and a memory are included, the memory stores the program code of the control method according to any one of claims 1-6, and the processor can execute the program code of the memory.

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