A shimmy suppression method for a four-wheel independent steer-by-wire system

Abstract

The application discloses a shimmy suppression method for a four-wheel independent steer-by-wire system, and comprises the following steps: establishing a wheel shimmy dynamics model of the four-wheel independent steer-by-wire system; designing an obstacle Lyapunov function to convert the shimmy amplitude constraint into a state constraint condition; designing a backstepping sliding mode controller parameter self-tuning strategy based on the shimmy frequency; designing a backstepping sliding mode controller with adaptive shimmy amplitude-frequency characteristics based on the state constraint condition; and based on the designed backstepping sliding mode controller, actively and adaptively controlling the shimmy phenomenon of the wheels with different frequencies and amplitudes, and then suppressing the shimmy phenomenon of the four-wheel independent steer-by-wire system. According to the amplitude-frequency characteristics of the shimmy phenomenon in the running process of the four-wheel independent steer-by-wire system, the shimmy phenomenon with different frequencies and amplitudes can be adaptively suppressed, and the reliable running capability of the four-wheel independent steer-by-wire system can be improved, so as to avoid the vehicle instability caused by excessive wheel shimmy.

Description

Technical Field

[0001] This invention belongs to the field of vehicle steering control, specifically relating to a method for suppressing shimmy in a four-wheel independent steer-by-wire system. Background Technology

[0002] New energy vehicles have become an important part of technological innovation and industrial upgrading in the automotive industry, fundamentally reducing energy consumption and environmental pollution. Chassis-based drive-by-wire technology is a technological development trend that meets the demands of intelligent electric vehicles for higher execution precision and faster response speeds, and is a fundamental guarantee for realizing intelligent vehicle applications and precise control.

[0003] Among them, electric vehicles with a four-wheel independent steer-by-wire system (4WIS) improve vehicle safety, handling stability, and overall energy efficiency through in-wheel motors or wheel-side motors. The four-wheel independent steer-by-wire system, employing a corner module architecture, can not only drive laterally but also rotate in place, bringing a revolutionary breakthrough to vehicle steering performance and representing a major disruptive innovation. It achieves full integration of drive, braking, steering, and suspension in distributed drive electric vehicles. Based on the coordinated control of the distributed drive system and chassis system, it significantly enhances the vehicle's maneuverability, passability, and handling stability. Four-wheel independent steer-by-wire electric vehicles are considered a key component of future intelligent transportation systems.

[0004] Currently, electric wheels used in four-wheel independent steer-by-wire systems experience increased unsprung mass due to the addition of hub motors to each wheel, leading to a wider speed range and amplitude of self-excited shimmy. Furthermore, the elimination of tie rods between the left and right wheels in four-wheel independent steer-by-wire systems makes them more prone to shimmy at high speeds due to the lack of tie rod restraint. Wheel shimmy directly affects the vehicle's safe and stable operation, easily causing excessive wheel shimmy instability and serious traffic accidents. Therefore, it is necessary to specifically suppress shimmy in four-wheel independent steer-by-wire systems.

[0005] In existing research on suppressing wheel shimmy in vehicle steering systems, for example, Chinese invention patent application number CN202310996430.2, entitled "A control method and control system for a steer-by-wire system," suppresses wheel shimmy by adjusting the real-time current value of a magnetorheological damper arranged on the output shaft of the reducer to obtain a target damping coefficient for all currently integrated electric wheels using kingpin steering; and Chinese invention patent application number CN202210432268.7, entitled "A method and system for suppressing wheel shimmy based on EPS." The Chinese invention patent application CN201010295311.7, entitled "A Method for Controlling Steering Wheel Shimmy," utilizes vehicle speed and wheel speed information from the CAN network, obtains steering system torque information through a torque sensor, calculates EPS compensation current, and uses this information to counteract wheel shimmy. The Chinese invention patent application CN202110631573.4, entitled "An Electric Vehicle Wheel with Energy Recovery and Multi-directional Vibration Reduction Functions," directly incorporates mechanical design within the wheel to achieve multi-directional vibration reduction using a single shock absorber.

[0006] However, the existing wheel shimmy suppression methods described above have the following two potential problems:

[0007] First, most of these studies are aimed at front-wheel steering or non-independent four-wheel steering systems with tie rods. However, there is currently little research on the suppression of wheel shimmy in four-wheel independent steer-by-wire systems. Considering the increased wheel instability caused by the addition of hub motors and the removal of tie rods in four-wheel independent steer-by-wire systems, these methods are not well adapted to the system and may result in poor control performance.

[0008] Secondly, while passive or semi-active control is commonly used, wheel shimmy suppression requires strong real-time performance and flexibility. Since passive control, once designed and implemented, has relatively fixed performance, it struggles to adapt to changing external conditions. Therefore, such passive or semi-active control may not meet its requirements and produce optimal results. Active control methods that can adjust control strategies in real time to adapt to constantly changing conditions are needed.

[0009] Therefore, how to fully consider the characteristics of four-wheel independent steer-by-wire systems and propose an active control method that can better cope with the strong nonlinear and time-varying characteristics of wheel shimmy, thereby avoiding the problem of wheel over-alignment and instability during the operation of four-wheel independent steer-by-wire vehicles, is a key problem that urgently needs to be solved in the current development of four-wheel independent steer-by-wire technology. Summary of the Invention

[0010] To address the shortcomings of the existing technology, the present invention aims to provide a method for suppressing wheel shimmy in a four-wheel independent steer-by-wire system. This method solves the problems in existing four-wheel independent steering systems where the lack of steering tie rod restraints and hub motor load leads to more prone self-excited vibration at low speeds and more intense forced vibration at high speeds. The method of the present invention considers the amplitude-frequency characteristics of wheel shimmy. By designing an adaptive backstepping sliding mode controller with adaptive shimmy amplitude-frequency characteristics, the amplitude of shimmy in the four-wheel independent steer-by-wire system is suppressed to avoid excessive amplitude causing controller failure and increased instability. Furthermore, by using an optimization algorithm combined with a neural network to adaptively optimize the controller parameters, wheel shimmy under different vehicle speeds and road conditions is further suppressed, improving the reliable operation of the four-wheel independent steering system and preventing excessive wheel shimmy from causing vehicle instability.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] The present invention discloses a method for suppressing shimmy in a four-wheel independent steer-by-wire system, comprising the following steps:

[0013] 1) Establish a dynamic model of wheel shimmy in a four-wheel independent steer-by-wire system;

[0014] 2) Design a barrier Lyapunov function to transform the pendulum amplitude constraint into a state constraint condition;

[0015] 3) Design a self-tuning strategy for backstepping sliding mode controller parameters based on oscillation frequency by using the gray wolf optimization algorithm and radial basis neural network fitting;

[0016] 4) Design an adaptive backstepping sliding mode controller for the amplitude-frequency characteristics of the pendulum oscillation based on the state constraints in step 2);

[0017] 5) Based on the anti-step sliding mode controller designed in step 4), the shimmy phenomenon of the wheel with different frequencies and amplitudes is actively and adaptively controlled, thereby suppressing the shimmy phenomenon of the four-wheel independent steer-by-wire system.

[0018] Furthermore, step 1) specifically includes:

[0019] 11) Establish a wheel shimmy model for a four-wheel independent steer-by-wire system using the Lagrange dynamics equations. The model considers the shimmy angle of the front wheel around the kingpin. Vertical vibration angle of the wheel about the vehicle's longitudinal axis and the rotation angle of the steering motor Three state variables;

[0020] According to Lagrange's theorem, the following exists:

[0021] (1);

[0022] In the formula, For generalized coordinates, These represent the system's kinetic energy, potential energy, and dissipated energy, respectively. Indicates time, This indicates taking the derivative with respect to time. express The generalized forces corresponding to the generalized coordinates;

[0023] The expression for the system's kinetic energy is:

[0024] (2);

[0025] In the formula, Let be the moment of inertia of the wheel about its axle. Let be the moment of inertia of the wheel assembly about the kingpin. Let be the moment of inertia of the wheel at the hinge point where it connects to the frame. The moment of inertia is the equivalent torsional angle of the steering column. For the wheel radius, For vehicle speed, These are the first derivatives of the oscillation angle, vertical vibration angle, and rotation angle of the steering motor, respectively.

[0026] The expression for the system's potential energy is:

[0027] (3);

[0028] In the formula, Let be the equivalent torsional stiffness of the wheel about the kingpin. This refers to the equivalent angular stiffness between the wheel and the suspension. The equivalent angular stiffness between the steering motor and the steering column. This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. Kingpin caster angle The effective length of the steering knuckle. This is the distance between the geometric center plane of the wheel and the kingpin;

[0029] The system dissipation energy expression is:

[0030] (4);

[0031] In the formula, Let be the equivalent angular damping coefficient of the wheel assembly about the kingpin. This is the equivalent connection angle damping coefficient between the wheel and the suspension. This is the equivalent angular damping coefficient between the steering motor and the steering column;

[0032] Considering the lateral force of the tire, the torque caused by the unbalanced mass of the wheel, and uncertain disturbances, the generalized force is as follows:

[0033] (5);

[0034] In the formula, They are respectively Generalized forces corresponding to generalized coordinates This refers to the lateral force of the tire. Tire vertical force, For dry friction torque, For unbalanced mass torque, For tire trail, The camber angle of the wheel. The disturbance torque of the unbalanced mass on the front axle;

[0035] 12) Based on the Fiala-Bridgestone tire model, the formula for tire lateral force is derived from the tire lateral force model as follows:

[0036] (6);

[0037] In the formula, The parameters are obtained from the following equation:

[0038] ;

[0039] In the formula, For tire lateral stiffness, The road surface adhesion coefficient, The vertical mass of the wheel. The system's inherent frequency, The rolling resistance coefficient, For tire vertical stiffness;

[0040] 13) Based on the Lagrange dynamics equations and simplified tire lateral forces, substitute equations (2)-(6) into equation (1) to calculate the wheel shimmy dynamics model of the four-wheel independent steer-by-wire system. Rewrite the dynamic equations in differential equation form, and we have:

[0041] (7);

[0042] (8);

[0043] (9);

[0044] In the formula, , , For the unbalanced mass of the wheel, The angular velocity of the tire. It is the distance from the intersection of the kingpin extension line and the ground to the longitudinal plane symmetrical to the wheel. The amplitude of dry friction. Pi is a constant. , Wheelbase This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. This is the overall control law of the backstepping sliding mode controller, which is the torque input of the steering motor of the four-wheel independent steer-by-wire system.

[0045] Furthermore, step 2) specifically includes:

[0046] 21) Define two state variables ,make Define the target value of the wheel rotation angle to be tracked as . Then, the steering angle tracking error of the first subsystem of the four-wheel independent steer-by-wire system can be obtained, which is the yaw amplitude value. as follows:

[0047] (10);

[0048] The Lyapunov equation defines the barrier to the first subsystem of a four-wheel independent steer-by-wire system. for:

[0049] (11);

[0050] In the formula, For an open region defined on the origin A continuous positive definite function on the open region At each point, there are continuous first-order partial derivatives, and log(·) is a logarithmic function. For the amplitude value of the variable pendulum The boundary is a positive constant, and ;

[0051] 22) Define the obstacle Lyapunov equation for the second subsystem of the four-wheel independent steer-by-wire system. for:

[0052] (12);

[0053] In the formula, , For the estimated value of an unknown normal number, The sliding surface varies with frequency. for The boundary is a positive constant, and .

[0054] Furthermore, step 3) specifically includes:

[0055] 31) The encirclement behavior of the gray wolf optimization algorithm can be represented by a mathematical model as follows:

[0056] (13);

[0057] In the formula, and These represent the optimal parameters and feasible parameters, respectively. The distance between the optimal parameters and the feasible parameters. Let A and C be the next position for enclosing behavior based on the feasible parameters and the optimal parameters, where A and C are control coefficients.

[0058] Hunting behavior can be represented by the following mathematical model:

[0059] (14);

[0060] (15);

[0061] (16);

[0062] In the formula, These are three feasible parameters and Distance with optimal parameters For different control coefficients, For the corresponding The values ​​of the three optimal parameters in the current iteration. The current parameter is determined according to the current iteration. The three candidate positions are updated by each of the three optimal parameters;

[0063] Define the objective function for:

[0064] (17);

[0065] In the formula, The total number of samples, This refers to the controller's corner tracking error.

[0066] The optimal sliding mode controller parameter dataset at different frequencies was obtained using the Grey Wolf optimization algorithm.

[0067] 32) Train a radial basis function neural network using the parameter dataset from step 31), by giving a frequency To predict the corresponding optimal control parameters;

[0068] The output expression of the radial basis function neural network is as follows:

[0069] (18);

[0070] In the formula, The output vector contains the sliding mode controller parameters. ; is the number of hidden layer neurons; h is the output layer bias term, a constant used to adjust the overall output level; For the first The weights of each hidden layer neuron; For the first Activation functions of hidden layer neurons For the first At the center of each hidden layer neuron, a Gaussian radial basis function is used, which has the following form:

[0071] (19);

[0072] In the formula, is the activation function for hidden layer neurons. For input With the center of hidden layer neurons The distance between them The width of the basis functions;

[0073] The least squares method is used to minimize the mean square error (MSE), and the output of the neural network is set as follows:

[0074] (20);

[0075] In the formula, Output the target matrix; This is the output layer weight matrix; Let be a matrix calculated from the Gaussian radial basis functions, and its elements be . ; For bias terms;

[0076] The fitting error is measured by minimizing the mean squared error (MSE), as follows:

[0077] (twenty one);

[0078] The weight matrix is ​​obtained using the following formula:

[0079] (twenty two);

[0080] After training, use a given frequency The input is a radial basis function neural network for prediction. The network output is the predicted sliding mode controller parameters, expressed as follows:

[0081] (twenty three);

[0082] In the formula, The new prediction output represents the predicted sliding mode controller parameters;

[0083] The radial basis neural network obtained by training and fitting can predict the parameters of the sliding mode controller at a given frequency.

[0084] 33) The short-time Fourier transform method is used to analyze the frequency components of the wheel sway signal received by the sensor as a function of time, and the maximum amplitude method is used to extract the main frequency in the frequency components as the instantaneous sway frequency of the system.

[0085] The segment of the oscillation signal extracted using the windowing method is represented as follows:

[0086] (twenty four);

[0087] In the formula, This is a segment of the oscillation signal. For continuous time, For window functions, This is the time offset;

[0088] For continuous time Performing a Fourier transform yields:

[0089] (25);

[0090] In the formula, The result is the short-time Fourier transform, representing the time... Location, frequency The following spectrum information; For frequency variables, For complex exponent kernel;

[0091] The dominant frequency in the frequency components is then extracted and used as the instantaneous frequency input of the radial basis neural network to update the optimal sliding mode controller parameters in real time, thus completing the self-tuning of the backstepping sliding mode controller parameters.

[0092] Further, step 4) includes:

[0093] 41) Based on the two state variables defined in 21) The differential equations of the wheel yaw dynamics model of the four-wheel independent steer-by-wire system are transformed into a low-order subsystem, expressed as:

[0094] (26);

[0095] ;

[0096] In the formula, For the linear, nonlinear and coupled parts of the system, For control coefficients, Given an unknown but bounded perturbation, and assuming... , The boundary for unknown disturbances;

[0097] Define the target value of the wheel rotation angle to be tracked as follows: Then the corner tracking error of the first subsystem can be obtained as:

[0098] (27);

[0099] Define the stable term as:

[0100] (28);

[0101] In the formula, For the stability term coefficient, The sliding surface varies with frequency;

[0102] 42) Define the virtual control variable as:

[0103] (29);

[0104] In the formula, For virtual control variables of the controller;

[0105] Use virtual control variables to replace the actual inputs of the subsystem. We can obtain:

[0106] (30);

[0107] Substituting the Lyapunov equation for the obstacle of the first subsystem of the four-wheel independent steer-by-wire system in step 21), we get:

[0108] (31);

[0109] Define the actual input The tracking error is , is represented as:

[0110] (32);

[0111] The sliding surface is designed as follows:

[0112] (33);

[0113] In the formula, The sliding surface coefficient varies with frequency;

[0114] Based on the obstacle Lyapunov equation of the second subsystem of the four-wheel independent steer-by-wire system in step 22), the equivalent control law of the four-wheel independent steer-by-wire system is designed. And adaptive law as follows:

[0115] (34);

[0116] (35);

[0117] In the formula, For smooth functions, Let be a positive integer, such that , For the estimated value of an unknown normal number, for The first derivative;

[0118] 43) Employ the exponential reaching law and use continuous functions. Replace the sign function in the original exponential reaching law The sliding mode control reaching law is expressed as:

[0119] (36);

[0120] In the formula, Let be the constant of the sliding mode reaching law. for The first derivative, It is a continuous function;

[0121] The overall control law of the backstepping sliding mode controller is:

[0122] (37).

[0123] The beneficial effects of this invention are:

[0124] This invention utilizes the Lyapunov equation for obstacles to enhance the suppression force at high speeds and reduce the impact at low speeds. It enhances suppression on bumpy roads and reduces intervention on flat roads, ensuring that the sway amplitude remains within an acceptable range under different vehicle speeds and excitation conditions, thereby reducing the risk of controller failure due to changes in sway amplitude.

[0125] This invention optimizes the backstepping sliding mode controller parameters using the gray wolf optimization algorithm and radial basis neural network, enabling the controller to be adjusted to the optimal control parameters under different vehicle speeds and external excitations, thereby reducing the poor control effect caused by changes in oscillation frequency.

[0126] This invention can adaptively suppress shimmy phenomena of different frequencies and amplitudes based on the amplitude-frequency characteristics of shimmy phenomena that occur during the operation of a four-wheel independent steer-by-wire system, thereby improving the reliable operation capability of the four-wheel independent steer-by-wire system and avoiding vehicle instability caused by excessive wheel shimmy. Attached Figure Description

[0127] Figure 1 This is a schematic diagram of the method of the present invention;

[0128] Figure 2 This is a structural diagram of the four-wheel independent steer-by-wire system in this invention;

[0129] Figure 3 This is a schematic diagram of the backstepping design process in this invention;

[0130] Figure 4 This is a schematic diagram of the gray wolf optimization algorithm flow in this invention;

[0131] Figure 5 This is a schematic diagram of the radial basis neural network process in this invention. Detailed Implementation

[0132] To facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and accompanying drawings. The content mentioned in the embodiments is not intended to limit the present invention.

[0133] Reference Figures 1 to 5As shown, this invention discloses a method for suppressing shimmy in a four-wheel independent steer-by-wire system. In this method, the housings of the steering motor controller 1 and the steering motor 2 are integrated. The steering motor controller 1 receives steering angle commands from the vehicle control unit (VCU) and controls the motor 2 to rotate in the desired direction and angle. The output shaft of the steering motor 2 is connected to a first-stage planetary gear reduction mechanism 3, which is connected to a second-stage worm gear reduction mechanism 4. The second-stage worm gear reduction mechanism 4 is connected to a clearance adaptive adjustment module 5, enabling dynamic adjustment of the meshing clearance between the mechanisms to compensate for the backlash caused by mechanical wear. The output end of the clearance adaptive adjustment module 5 is rigidly connected to the upper end of the steering arm column 6, forming a stable torque transmission path. The steering angle transmission... The inner ring of sensor 7 is fixed to the upper end of steering arm column 6 to collect steering angle data in real time and realize closed-loop steering control; the lower end of steering arm column 6 is rigidly connected to the upper end of steering column 8 to transmit the output torque of steering motor 2 to steering knuckle 10 to realize the steering function of the wheel; the center of steering knuckle 10 is connected to brake disc assembly 9, hub motor 11 and wheel 12 respectively. Brake disc assembly 9 is used for vehicle braking control, hub motor 11 realizes independent drive function, and wheel 12 completes the final steering and driving task; upper wishbone 13 and lower wishbone 14 are connected to the upper and lower arms of steering knuckle 10 through ball joints respectively, and shock absorber 14 is connected to lower wishbone 15 through a hinge, so that the shock absorber can have a certain swing space when the wheel bounces up and down, thereby playing the role of vibration reduction and vehicle body support;

[0134] The method steps are as follows:

[0135] 1) Establish a dynamic model of wheel shimmy in a four-wheel independent steer-by-wire system;

[0136] Specifically, step 1) includes:

[0137] 11) Establish a wheel shimmy model for a four-wheel independent steer-by-wire system using the Lagrange dynamics equations. The model considers the shimmy angle of the front wheel around the kingpin. Vertical vibration angle of the wheel about the vehicle's longitudinal axis and the rotation angle of the steering motor Three state variables;

[0138] According to Lagrange's theorem, the following exists:

[0139] (1);

[0140] In the formula, For generalized coordinates, These represent the system's kinetic energy, potential energy, and dissipated energy, respectively. Indicates time, This indicates taking the derivative with respect to time. express The generalized forces corresponding to the generalized coordinates;

[0141] The expression for the system's kinetic energy is:

[0142] (2);

[0143] In the formula, Let be the moment of inertia of the wheel about its axle. Let be the moment of inertia of the wheel assembly about the kingpin. Let be the moment of inertia of the wheel at the hinge point where it connects to the frame. The moment of inertia is the equivalent torsional angle of the steering column. For the wheel radius, For vehicle speed, These are the first derivatives of the oscillation angle, vertical vibration angle, and rotation angle of the steering motor, respectively.

[0144] The expression for the system's potential energy is:

[0145] (3);

[0146] In the formula, Let be the equivalent torsional stiffness of the wheel about the kingpin. This refers to the equivalent angular stiffness between the wheel and the suspension. The equivalent angular stiffness between the steering motor and the steering column. This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. Kingpin caster angle The effective length of the steering knuckle. This is the distance between the geometric center plane of the wheel and the kingpin;

[0147] The system dissipation energy expression is:

[0148] (4);

[0149] In the formula, Let be the equivalent angular damping coefficient of the wheel assembly about the kingpin. This is the equivalent connection angle damping coefficient between the wheel and the suspension. This is the equivalent angular damping coefficient between the steering motor and the steering column;

[0150] Considering the lateral force of the tire, the torque caused by the unbalanced mass of the wheel, and uncertain disturbances, the generalized force is as follows:

[0151] (5);

[0152] In the formula, They are respectively Generalized forces corresponding to generalized coordinates This refers to the lateral force of the tire. Tire vertical force, For dry friction torque, For unbalanced mass torque, For tire trail, The camber angle of the wheel. The disturbance torque of the unbalanced mass on the front axle;

[0153] 12) Based on the Fiala-Bridgestone tire model, the formula for tire lateral force is derived from the tire lateral force model as follows:

[0154] (6);

[0155] In the formula, The parameters are obtained from the following equation:

[0156] ;

[0157] In the formula, For tire lateral stiffness, The road surface adhesion coefficient, The vertical mass of the wheel. The system's inherent frequency, The rolling resistance coefficient, For tire vertical stiffness;

[0158] 13) Based on the Lagrange dynamics equations and simplified tire lateral forces, substitute equations (2)-(6) into equation (1) to calculate the wheel shimmy dynamics model of the four-wheel independent steer-by-wire system. Rewrite the dynamic equations in differential equation form, and we have:

[0159] (7);

[0160] (8);

[0161] (9);

[0162] In the formula, , , For the unbalanced mass of the wheel, The angular velocity of the tire. It is the distance from the intersection of the kingpin extension line and the ground to the longitudinal plane symmetrical to the wheel. The amplitude of dry friction. Pi is a constant. , Wheelbase This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. This is the overall control law of the backstepping sliding mode controller, which is the torque input of the steering motor of the four-wheel independent steer-by-wire system.

[0163] 2) Design a barrier Lyapunov function to transform the pendulum amplitude constraint into a state constraint condition; specifically including:

[0164] 21) Define two state variables ,make Define the target value of the wheel rotation angle to be tracked as . Then, the steering angle tracking error of the first subsystem of the four-wheel independent steer-by-wire system can be obtained, which is the yaw amplitude value. as follows:

[0165] (10);

[0166] The Lyapunov equation defines the barrier to the first subsystem of a four-wheel independent steer-by-wire system. for:

[0167] (11);

[0168] In the formula, For an open region defined on the origin A continuous positive definite function on the open region At each point, there are continuous first-order partial derivatives, and log(·) is a logarithmic function. For the amplitude value of the variable pendulum The boundary is a positive constant, and ;

[0169] 22) Define the obstacle Lyapunov equation for the second subsystem of the four-wheel independent steer-by-wire system. for:

[0170] (12);

[0171] In the formula, , For the estimated value of an unknown normal number, The sliding surface varies with frequency. for The boundary is a positive constant, and .

[0172] 3) Design a self-tuning strategy for the backstepping sliding mode controller parameters based on the oscillation frequency using the gray wolf optimization algorithm and radial basis function neural network fitting; specifically including:

[0173] 31) The encirclement behavior of the gray wolf optimization algorithm can be represented by a mathematical model as follows:

[0174] (13);

[0175] In the formula, and These represent the optimal parameters and feasible parameters, respectively. The distance between the optimal parameters and the feasible parameters. Let A and C be the next position for enclosing behavior based on the feasible parameters and the optimal parameters, where A and C are control coefficients.

[0176] Hunting behavior can be represented by the following mathematical model:

[0177] (14);

[0178] (15);

[0179] (16);

[0180] In the formula, These are three feasible parameters and Distance with optimal parameters For different control coefficients, For the corresponding The values ​​of the three optimal parameters in the current iteration. The current parameter is determined according to the current iteration. The three candidate positions are updated by each of the three optimal parameters;

[0181] Define the objective function for:

[0182] (17);

[0183] In the formula, The total number of samples, This refers to the controller's corner tracking error.

[0184] The optimal sliding mode controller parameter dataset at different frequencies was obtained using the Grey Wolf optimization algorithm.

[0185] 32) Train a Radial Basis Function Neural Network (RBFNN) using the parameter dataset from step 31), by giving a frequency To predict the corresponding optimal control parameters;

[0186] The output expression of the radial basis function neural network is as follows:

[0187] (18);

[0188] In the formula, The output vector contains the sliding mode controller parameters. ; is the number of hidden layer neurons; h is the output layer bias term, a constant used to adjust the overall output level; For the first The weights of each hidden layer neuron; For the first Activation functions of hidden layer neurons For the first At the center of each hidden layer neuron, a Gaussian radial basis function is used, which has the following form:

[0189] (19);

[0190] In the formula, is the activation function for hidden layer neurons. For input With the center of hidden layer neurons The distance between them The width of the basis functions;

[0191] The least squares method is used to minimize the mean square error (MSE), and the output of the neural network is set as follows:

[0192] (20);

[0193] In the formula, Output the target matrix; This is the output layer weight matrix; Let be a matrix calculated from the Gaussian radial basis functions, and its elements be . ; For bias terms;

[0194] The fitting error is measured by minimizing the mean squared error (MSE), as follows:

[0195] (twenty one);

[0196] The weight matrix is ​​obtained using the following formula:

[0197] (twenty two);

[0198] After training, use a given frequency The input is a radial basis function neural network for prediction. The network output is the predicted sliding mode controller parameters, expressed as follows:

[0199] (twenty three);

[0200] In the formula, The new prediction output represents the predicted sliding mode controller parameters;

[0201] The radial basis neural network obtained by training and fitting can predict the parameters of the sliding mode controller at a given frequency.

[0202] 33) The short-time Fourier transform (STFT) method is used to analyze the frequency components of the wheel sway signal received by the sensor as a function of time, and the maximum amplitude method is used to extract the main frequency in the frequency components as the instantaneous sway frequency of the system.

[0203] The segment of the oscillation signal extracted using the windowing method is represented as follows:

[0204] (twenty four);

[0205] In the formula, This is a segment of the oscillation signal. For continuous time, For window functions, This is the time offset;

[0206] For continuous time Performing a Fourier transform yields:

[0207] (25);

[0208] In the formula, The result is the short-time Fourier transform, representing the time... Location, frequency The following spectrum information; For frequency variables, For complex exponent kernel;

[0209] The dominant frequency in the frequency components is then extracted and used as the instantaneous frequency input of the radial basis neural network to update the optimal sliding mode controller parameters in real time, thus completing the self-tuning of the backstepping sliding mode controller parameters.

[0210] 4) Design an adaptive backstepping sliding mode controller for the amplitude-frequency characteristics of the pendulum oscillation based on the state constraints in step 2); specifically including:

[0211] 41) Based on the two state variables defined in 21) The differential equations of the wheel yaw dynamics model of the four-wheel independent steer-by-wire system are transformed into a low-order subsystem, expressed as:

[0212] (26);

[0213] ;

[0214] In the formula, For the linear, nonlinear and coupled parts of the system, For control coefficients, Given an unknown but bounded perturbation, and assuming... , The boundary for unknown disturbances;

[0215] Define the target value of the wheel rotation angle to be tracked as follows: Then the corner tracking error of the first subsystem can be obtained as:

[0216] (27);

[0217] Define the stable term as:

[0218] (28);

[0219] In the formula, For the stability term coefficient, The sliding surface varies with frequency;

[0220] 42) Define the virtual control variable as:

[0221] (29);

[0222] In the formula, For virtual control variables of the controller;

[0223] Use virtual control variables to replace the actual inputs of the subsystem. We can obtain:

[0224] (30);

[0225] Substituting the Lyapunov equation for the obstacle of the first subsystem of the four-wheel independent steer-by-wire system in step 21), we get:

[0226] (31);

[0227] Define the actual input The tracking error is , is represented as:

[0228] (32);

[0229] The sliding surface is designed as follows:

[0230] (33);

[0231] In the formula, The sliding surface coefficient varies with frequency;

[0232] Based on the obstacle Lyapunov equation of the second subsystem of the four-wheel independent steer-by-wire system in step 22), the equivalent control law of the four-wheel independent steer-by-wire system is designed. And adaptive law as follows:

[0233] (34);

[0234] (35);

[0235] In the formula, For smooth functions, Let be a positive integer, such that , For the estimated value of an unknown normal number, for The first derivative;

[0236] 43) Employ the exponential reaching law and use continuous functions. Replace the sign function in the original exponential reaching law The sliding mode control reaching law is expressed as:

[0237] (36);

[0238] In the formula, Let be the constant of the sliding mode reaching law. for The first derivative, It is a continuous function;

[0239] The overall control law of the backstepping sliding mode controller is:

[0240] (37).

[0241] 5) Based on the anti-step sliding mode controller designed in step 4), the shimmy phenomenon of the wheel with different frequencies and amplitudes is actively and adaptively controlled, thereby suppressing the shimmy phenomenon of the four-wheel independent steer-by-wire system.

[0242] This invention has many specific applications. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for suppressing shimmy in a four-wheel independent steer-by-wire system, characterized in that, The steps are as follows: 1) Establish a dynamic model of wheel shimmy in a four-wheel independent steer-by-wire system; 2) Design a barrier Lyapunov function to transform the pendulum amplitude constraint into a state constraint condition; 3) Design a self-tuning strategy for backstepping sliding mode controller parameters based on oscillation frequency by using the gray wolf optimization algorithm and radial basis neural network fitting; 4) Design an adaptive backstepping sliding mode controller for the amplitude-frequency characteristics of the pendulum oscillation based on the state constraints in step 2); 5) Based on the anti-step sliding mode controller designed in step 4), the shimmy phenomenon of the wheel with different frequencies and amplitudes is actively and adaptively controlled, thereby suppressing the shimmy phenomenon of the four-wheel independent steer-by-wire system.

2. The method for suppressing shimmy in a four-wheel independent steer-by-wire system according to claim 1, characterized in that, Step 1) specifically includes: 11) Establish a wheel shimmy model for a four-wheel independent steer-by-wire system using the Lagrange dynamics equations. The model considers the shimmy angle of the front wheel around the kingpin. Vertical vibration angle of the wheel about the vehicle's longitudinal axis and the rotation angle of the steering motor Three state variables; According to Lagrange's theorem, the following exists: （1）； In the formula, For generalized coordinates, These represent the system's kinetic energy, potential energy, and dissipated energy, respectively. Indicates time, This indicates taking the derivative with respect to time. express The generalized forces corresponding to the generalized coordinates; The expression for the system's kinetic energy is: （2）； In the formula, Let be the moment of inertia of the wheel about its axle. Let be the moment of inertia of the wheel assembly about the kingpin. Let be the moment of inertia of the wheel at the hinge point where it connects to the frame. The moment of inertia is the equivalent torsional angle of the steering column. For the wheel radius, For vehicle speed, These are the first derivatives of the oscillation angle, vertical vibration angle, and rotation angle of the steering motor, respectively. The expression for the system's potential energy is: （3）； In the formula, Let be the equivalent torsional stiffness of the wheel about the kingpin. This refers to the equivalent angular stiffness between the wheel and the suspension. The equivalent angular stiffness between the steering motor and the steering column. This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. Kingpin caster angle The effective length of the steering knuckle. This is the distance between the geometric center plane of the wheel and the kingpin; The system's energy dissipation expression is: （4）； In the formula, Let be the equivalent angular damping coefficient of the wheel assembly about the kingpin. This represents the equivalent connection angle damping coefficient between the wheel and the suspension. This is the equivalent angular damping coefficient between the steering motor and the steering column; Considering the lateral force of the tire, the torque caused by the unbalanced mass of the wheel, and uncertain disturbances, the generalized force is as follows: （5）； In the formula, They are respectively Generalized forces corresponding to generalized coordinates This refers to the lateral force of the tire. Tire vertical force, For dry friction torque, For unbalanced mass torque, For tire trail, The camber angle of the wheel. The disturbance torque of the unbalanced mass on the front axle; 12) Based on the Fiala-Bridgestone tire model, the formula for tire lateral force is derived from the tire lateral force model as follows: （6）； In the formula, The parameters are obtained from the following equation: ； In the formula, For tire lateral stiffness, The road surface adhesion coefficient, The vertical mass of the wheel, For the system's inherent frequency, The rolling resistance coefficient, For tire vertical stiffness; 13) Based on the Lagrange dynamics equations and simplified tire lateral forces, substitute equations (2)-(6) into equation (1) to calculate the wheel shimmy dynamics model of the four-wheel independent steer-by-wire system. Rewrite the dynamic equations in differential equation form, and we have: （7）； （8）； （9）； In the formula, , , For the unbalanced mass of the wheel, The angular velocity of the tire. It is the distance from the intersection of the kingpin extension line and the ground to the longitudinal plane symmetrical to the wheel. The amplitude of dry friction. Pi is a constant. , Wheelbase This represents the equivalent stiffness of the wheel and steering knuckle along the Y-axis. This represents the equivalent stiffness of the wheel and steering knuckle along the Z-axis. This is the overall control law of the backstepping sliding mode controller, which is the torque input of the steering motor of the four-wheel independent steer-by-wire system.

3. The method for suppressing shimmy in a four-wheel independent steer-by-wire system according to claim 2, characterized in that, Step 2) specifically includes: 21) Define two state variables ,make Define the target value of the wheel rotation angle to be tracked as . Then, the steering angle tracking error of the first subsystem of the four-wheel independent steer-by-wire system can be obtained, which is the yaw amplitude value. as follows: （10）； The Lyapunov equation defines the barrier to the first subsystem of a four-wheel independent steer-by-wire system. for: （11）； In the formula, For an open region defined on the origin A continuous positive definite function on the open region At each point, there are continuous first-order partial derivatives, and log(·) is a logarithmic function. For the amplitude value of the variable pendulum The boundary is a positive constant, and ; 22) Define the obstacle Lyapunov equation for the second subsystem of the four-wheel independent steer-by-wire system. for: （12）； In the formula, , For the estimated value of an unknown normal number, The sliding surface varies with frequency. for The boundary is a positive constant, and , It is a positive number.

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