Steering-by-wire control method and system based on particle swarm-sliding mode control and fuzzy radial basis function

Abstract

The invention provides a steering-by-wire control method and system based on particle swarm-sliding mode control and a fuzzy radial basis function, and the method comprises the steps: carrying out the adaptive approximation of an uncertain item and unknown disturbance of a state-space equation based on a radial basis function neural network in combination with an adaptive law, and obtaining the real-time estimation values of the uncertain item and the unknown disturbance; a sliding mode surface is obtained based on the wheel rotation angle error, the sliding mode surface is corrected and compensated based on the real-time estimation value, parameters of the sliding mode surface are optimized in combination with a particle swarm algorithm, and an optimized sliding mode surface is obtained; on the basis of a fuzzy logic controller, the optimized sliding mode surface and the change rate of the optimized sliding mode surface are converted into membership degrees of a fuzzy set for fuzzy logic reasoning, and the fuzzy set of control behaviors is obtained; obtaining a control signal based on the fuzzy set of control behaviors; and completing steering-by-wire control of the vehicle based on the control signal. According to the technical scheme, the response speed and the anti-interference capability of the steer-by-wire system can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of intelligent vehicle chassis, and particularly relates to a steer-by-wire control method and system based on particle swarm-sliding mode control and fuzzy radial basis function. Background Art

[0002] Driven by the development of vehicle intelligence and automation, steer-by-wire chassis technology has gradually become an important part of future vehicles. The steer-by-wire chassis replaces the traditional mechanical or hydraulic system with electronic signals to control the key parts of the vehicle, including steer-by-wire drive, steer-by-wire braking, and steer-by-wire steering. Its advantages lie in reducing the complexity of the mechanical structure, reducing the weight of the vehicle, and providing a strong technical foundation for future autonomous driving.

[0003] Steer-by-wire technology, as a core part of the steer-by-wire chassis system, has become a key research hotspot in the automotive field after years of continuous research and development. Compared with traditional mechanical steering, the steer-by-wire system directly controls the wheel angle through electronic signals, eliminating the mechanical connection between the steering wheel and the wheels. This technology can not only improve the performance, flexibility, and control accuracy of the vehicle, but also provide higher safety, better handling performance, and strong adaptability.

[0004] However, the existing steer-by-wire control technologies still have problems of insufficient control accuracy and stability, as well as high-frequency jitter of the system when facing the nonlinearity and uncertainty of the system dynamic behavior and external disturbances. The nonlinearity and uncertainty of vehicle dynamic behavior may lead to difficulties in designing control algorithms, affecting the stability and response speed of the system. External disturbances such as road condition changes and vehicle load changes may affect the system performance. Due to the nonlinear characteristics of the vehicle system, there is a lack of stability in the system and signal divergence, resulting in tracking deviation. In the case of high-speed driving or emergency avoidance, the system needs to respond quickly and accurately, which poses high requirements for the real-time performance of the control algorithm. Large changes may occur before the vehicle system control is stable, which will cause high-frequency oscillations in the controller output.

[0005] Therefore, from the perspectives of safety and comfort, it is urgent to improve the control algorithm. Summary of the Invention

[0006] To solve the problems of insufficient control accuracy and stability in the existing technology, the present invention provides a steer-by-wire control method and system based on particle swarm-sliding mode control and fuzzy radial basis function, which improve the response speed and anti-interference ability of the steer-by-wire system.

[0007] The steer-by-wire control method based on particle swarm-sliding mode control and fuzzy radial basis function includes:

[0008] Based on the dynamic equation of the steer-by-wire system model, obtain the state-space equation of the steer-by-wire system model;

[0009] Based on the radial basis neural network combined with the adaptive law, adaptively approximate the uncertain terms and unknown disturbances of the state-space equation to obtain real-time estimated values of the uncertain terms and unknown disturbances;

[0010] Based on the wheel angle error, obtain the sliding mode surface, correct and compensate the sliding mode surface based on the real-time estimated values, and optimize the parameters of the sliding mode surface by combining the particle swarm algorithm to obtain the optimized sliding mode surface;

[0011] Based on the fuzzy logic controller, convert the optimized sliding mode surface and the change rate of the optimized sliding mode surface into membership degrees of the fuzzy set for fuzzy logic reasoning to obtain the fuzzy set of the control behavior;

[0012] Based on the fuzzy set of the control behavior, obtain the control signal; based on the control signal, complete the steer-by-wire control of the vehicle.

[0013] Preferably, the method for obtaining the dynamic equation of the steer-by-wire system model includes:

[0014] Based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque exerted by the wheel on the steering motor shaft, and the torque of the motor output shaft, construct the dynamic equation of the steering motor;

[0015] Based on the dynamic equation of the steering motor, construct the dynamic equation of the steering wheel;

[0016] Based on the reduction ratio of the vehicle reducer and the dynamic equation of the steering wheel, obtain the dynamic equation of the steer-by-wire system model.

[0017] Preferably, the method for obtaining the real-time estimated values of the uncertain terms and unknown disturbances includes:

[0018] Preset the number of nodes in the hidden layer of the network, the ideal neural network weights, and the neural network approximation error, and construct a radial basis neural network through Gaussian basis functions;

[0019] Based on the minimum parameter learning method of the radial basis neural network combined with the adaptive law, obtain the estimated values of the uncertain terms and unknown disturbances of the state-space equation.

[0020] Preferably, the expression of the adaptive law is as follows:

[0021]

[0022] In the formula, φ and ξ are parameters defined by the neural network minimum parameter method, where φ = ||W|| 2, ξ = ||V|| 2 , where W and V represent the weights of the ideal neural network is an estimate of φ is an estimate of ξ represents the derivative of, γ1, γ2 represent the scalar parameters of the adaptive control gain, s represents the sliding mode surface, h represents the output of the Gaussian basis function represents the derivative of ξ, r1, r2 represent the damping coefficients of the adaptive control, r1, r2 > 0

[0023] Preferably, the expression of the sliding mode surface is as follows

[0024]

[0025] where δ ref is the desired wheel angle, c is the parameter of the sliding mode surface, δ w represents the wheel angle, e represents the system tracking error of the steer-by-wire system model, s represents the sliding mode surface

[0026] Preferably, based on the particle swarm algorithm, taking the system tracking error and the system control quantity of the steer-by-wire system model as indexes, a target function is constructed to optimize the parameters of the sliding mode surface; where the expression of the target function is as follows

[0027]

[0028] where the coefficients a and b are the weights of the system tracking error e and the system control quantity u respectively, representing the degree of emphasis on the energy consumption requirement and the error tracking requirement; t is time

[0029] The present invention also provides a steer-by-wire control system based on particle swarm-sliding mode control and fuzzy radial basis function. Applying the method includes

[0030] An equation construction module for obtaining the state space equation of the steer-by-wire system model based on the dynamic equation of the vehicle steer-by-wire system model

[0031] An estimated value acquisition module for adaptively approximating the uncertain terms and unknown disturbances of the state space equation based on the radial basis neural network combined with the adaptive law to obtain the real-time estimated values of the uncertain terms and unknown disturbances

[0032] A sliding mode surface optimization module for obtaining a sliding mode surface based on the wheel angle error, correcting and compensating the sliding mode surface based on the real-time estimated values, and optimizing the parameters of the sliding mode surface in combination with the particle swarm algorithm to obtain an optimized sliding mode surface

[0033] A fuzzy logic control module, which is used to convert the optimized sliding surface and the change rate of the optimized sliding surface into membership degrees of fuzzy sets based on a fuzzy logic controller for fuzzy logic inference to obtain a fuzzy set of control actions;

[0034] A control signal acquisition and execution module, which is used to obtain a control signal based on the fuzzy set of the control actions; and complete the steer-by-wire control of the vehicle based on the control signal.

[0035] Preferably, the equation construction module includes:

[0036] A steering motor dynamics equation construction unit, which is used to construct a dynamics equation of the steering motor based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque exerted by the wheel on the steering motor shaft, and the torque of the motor output shaft;

[0037] A steering wheel dynamics equation construction unit, which is used to construct a dynamics equation of the steering wheel based on the power equation of the steering motor;

[0038] A system model dynamics equation construction unit, which is used to obtain a dynamics equation of the steer-by-wire system model based on the reduction ratio of the vehicle reducer and the dynamics equation of the steering wheel.

[0039] Preferably, the estimated value acquisition module includes:

[0040] A radial basis neural network construction unit, which is used to preset the number of nodes in the hidden layer of the network, the ideal neural network weights, and the neural network approximation error, and construct a radial basis neural network through a Gaussian basis function;

[0041] An adaptive approximation unit, which is used to obtain estimated values of the uncertain terms and unknown disturbances of the state space equation based on the minimum parameter learning method of the radial basis neural network combined with an adaptive law.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] The hybrid control algorithm (FRPS-SMC) proposed by the present invention, which combines particle swarm optimization - sliding mode control with fuzzy radial basis functions, can effectively cope with the nonlinearity and uncertainty in the steer-by-wire system, as well as the influence of external disturbances. Through the minimum parameter learning method of the radial basis neural network (RBF), the system can estimate unknown dynamics and disturbances in real time, and derive an adaptive law in combination with the Lyapunov function to ensure the global convergence and stability of the system during the control process. Therefore, this solution can achieve high-precision wheel angle tracking and ensure the control accuracy of the vehicle in various complex driving scenarios.

[0044] By introducing the Particle Swarm Optimization (PSO) algorithm, the system can dynamically optimize the sliding mode surface parameters according to the control tracking error and control rate, and update the sliding mode surface parameters in real-time through closed-loop control to adjust the control signal in a timely manner. This optimization mechanism significantly improves the response speed of the system, enabling the vehicle to respond quickly in rapidly changing driving scenarios and enhancing the real-time performance of the system.

[0045] To address the common chattering problem in the control system, the present invention designs a fuzzy logic controller. This controller takes the sliding mode surface and its rate of change as input signals by considering the system input change and its rate of change, and performs fuzzy logic reasoning using a fuzzy rule base to finally generate specific control signals. This fuzzy control mechanism can effectively reduce the high-frequency chattering in sliding mode control and enhance the smoothness and stability of the system.

[0046] By integrating the adaptive algorithm of the Radial Basis Function Neural Network (RBF), the system can estimate and compensate for unknown dynamics and external disturbances in real-time, enhancing the robustness of the system. In addition, the introduction of fuzzy logic control and the Particle Swarm Optimization algorithm enables the system to adaptively adjust control parameters according to different driving scenarios and external conditions, further enhancing the adaptability and robustness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] To more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required in the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0048] Figure 1 It is a model architecture diagram of a steer-by-wire system for a vehicle according to an embodiment of the present invention;

[0049] Figure 2 It is a flowchart of a steer-by-wire control method based on particle swarm-sliding mode control and fuzzy radial basis function according to an embodiment of the present invention;

[0050] Figure 3 It is a fuzzy membership function according to an embodiment of the present invention;

[0051] Figure 4 It is a flowchart of the particle swarm algorithm according to an embodiment of the present invention;

[0052] Figure 5 It is a schematic diagram of a sine signal according to an embodiment of the present invention; wherein, (a) is a steering angle tracking diagram; (b) is a steering angle tracking error diagram; (c) is a motor torque diagram;

[0053] Figure 6Schematic diagram of the single lane change condition of the embodiment of the present invention; among them, (a) is the corner tracking diagram; (b) is the corner tracking error diagram; (c) is the displacement tracking diagram; (d) is the displacement tracking error diagram;

[0054] Figure 7 Schematic diagram of the double lane change condition of the embodiment of the present invention; among them, (a) is the corner tracking diagram; (b) is the corner tracking error diagram; (c) is the displacement tracking diagram; (d) is the displacement tracking error diagram. Specific implementation manners

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0057] Embodiment 1

[0058] As Figure 1 、 Figure 2 shown, the steer-by-wire control method based on particle swarm-sliding mode control and fuzzy radial basis function includes:

[0059] S1: Based on the dynamic equation of the vehicle steer-by-wire system model, obtain the state space equation of the steer-by-wire system model. In this embodiment, first establish the dynamic model of the vehicle steering system and the dynamic equation of the steering wheel, and use a permanent magnet synchronous motor.

[0060] In this embodiment, as Figure 1 shown, the steering control system (unit) receives the front wheel steering signal sent by remote control, calculates the steering torque using the controller, and then sends the torque signal to the motor control system (unit). After receiving the signal, the PMSM motor inputs the torque to the steering actuator. The torque is transmitted through the reducer and then drives the front wheels to rotate through the steering actuator. Table 1 provides the parameters of the vehicle and the steering system.

[0061] Table 1

[0062]

[0063]

[0064] A further implementation manner lies in that the method for obtaining the dynamic equation of the steer-by-wire system model includes:

[0065] Based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque exerted by the wheel on the steering motor shaft, and the torque of the motor output shaft, a dynamic equation of the steering motor is constructed; specifically, the dynamic equation of the steering motor

[0066]

[0067] ΔT represents the disturbing torque.

[0068] Based on the dynamic equation of the steering motor, a dynamic equation of the steering wheel is constructed:

[0069]

[0070] Based on the reduction ratio of the vehicle reducer and the dynamic equation of the steering wheel, the dynamic equation of the steer-by-wire system model is obtained.

[0071] In this embodiment, the reduction ratio of the reducer is:

[0072]

[0073] Thus, the dynamic equation of the steer-by-wire system is:

[0074]

[0075] The state-space equation of the steer-by-wire system can be expressed as:

[0076]

[0077] B eq represents the equivalent damping coefficient, J eq represents the equivalent moment of inertia, and g represents the transfer coefficient.

[0078] S2: Based on the radial basis neural network combined with the adaptive law, the uncertain terms and unknown disturbances of the state-space equation are adaptively approximated to obtain the real-time estimated values of the uncertain terms and unknown disturbances.

[0079] A further implementation method is that the method for obtaining the real-time estimated values of the uncertain term f(δ w ) and the unknown disturbance d(t) includes:

[0080] Preset the number of hidden layer nodes, the ideal neural network weights, and the neural network approximation error of the network, and construct a radial basis neural network through the Gaussian basis function; specifically, the RBF network algorithm is:

[0081]

[0082] d = V Th(x)+ε d , j = 1, 2, ···, m,

[0083] where x is the input signal of the network; j is the number of nodes in the hidden layer of the network.

[0084] h = [h1, h2, ···, h m T is the output of the Gaussian basis function; W is the ideal neural network weight; ε f ε d is the neural network approximation error, |ε f | ≤ ε Mf , |ε d | ≤ ε Md , f represents the unknown dynamics of the system, and d represents the unknown disturbance of the system.

[0085] The output is

[0086]

[0087] The output adopts the neural network minimum parameter method to make φ = ||W|| 2 , ξ = ||V|| 2 , W and V represent the ideal neural network weights, and φ, ξ are positive constants. is the estimate of φ, is the estimate of ξ.

[0088]

[0089] In the formula, represents the estimation deviation of the unknown dynamics, represents the estimation deviation of the unknown disturbance.

[0090] Based on the minimum parameter learning method of the radial basis neural network combined with the adaptive law, the estimated values of the uncertain terms and unknown disturbances of the state space equation are obtained.

[0091] A further implementation manner lies in that the expression of the adaptive law is as follows:

[0092]

[0093] In the formula, φ and ξ are parameters defined by the neural network minimum parameter method, where φ = ||W|| 2 , ξ = ||V|| 2 , W and V represent the ideal neural network weights, is the estimate of φ, is the estimate of ξ, represents the derivative of, γ1, γ2 represent the adaptive control gain scalar parameters, s represents the sliding mode surface, and h represents the output of the Gaussian basis function.​ represents the derivative of ξ, and r1, r2 represent the damping coefficients of the adaptive control, where r1, r2 > 0.

[0094] S3: Obtain the sliding mode surface based on the wheel angle error, correct and compensate the sliding mode surface based on the real-time estimated value, and optimize the parameters of the sliding mode surface in combination with the particle swarm algorithm to obtain the optimized sliding mode surface.

[0095] A further implementation manner is that the expression of the sliding mode surface is as follows:

[0096]

[0097] where δ ref is the desired wheel angle, c is the sliding mode surface parameter, δ w represents the wheel angle, e represents the system tracking error of the steer-by-wire system model, and s represents the sliding mode surface.

[0098] In this embodiment, the particle swarm optimization of the sliding mode surface aims to achieve fast response, high-precision tracking, and excellent steady-state performance. The particle swarm optimization process is as Figure 4 shown. The particle swarm optimization algorithm can effectively optimize the parameters of the sliding mode surface by simulating the way of group collaborative search. Through real-time feedback by closed-loop control, the system can quickly converge to the target state in a dynamic environment. This method not only enhances the response speed of the system but also improves the high-precision tracking ability of the target angle. The present invention uses the particle swarm algorithm to find the optimal parameters for the sliding mode surface coefficient c to minimize the energy consumption and tracking error of the system.

[0099] A further implementation manner is that, based on the particle swarm algorithm, taking the system tracking error and the system control quantity of the steer-by-wire system model as indicators, construct the objective function of the optimal control to optimize the parameters of the sliding mode surface; where the expression of the objective function is as follows:

[0100]

[0101] where the coefficients a and b are respectively the weights of the system tracking error e and the system control quantity u, representing the degree of emphasis on the energy consumption requirement and the error tracking requirement; t is the time.

[0102] Stability analysis

[0103] Define the Lyapunov function:

[0104]

[0105] After derivation, it is obtained that:

[0106]

[0107] Therefore, when t → ∞, At this time, the Lyapunov number is positive definite, and its derivative is semi-negative definite, proving that the by-wire system can converge stably. Q represents the constant term in the upper bound of the derivative of the Lyapunov function, and μ represents the adjustment parameter of the convergence rate of the Lyapunov function.

[0108] S4: Based on the fuzzy logic controller, convert the optimized sliding surface and the change rate of the optimized sliding surface into the membership degrees of fuzzy sets for fuzzy logic reasoning to obtain the fuzzy set of control actions.

[0109] In this embodiment, a fuzzy logic controller is introduced to dynamically adjust the control gain. Chattering is a common problem in sliding mode control, mainly caused by the high-frequency jitter brought about by discontinuous switching. Through the fuzzy logic controller, the system can intelligently adjust the control gain parameters under different working conditions, thereby reducing the amplitude and frequency of chattering and improving the smoothness and stability of control.

[0110] The system input needs to consider the change and the change rate, so choose as the system input, s is the sliding surface, is the time derivative of the sliding mode variable, reflecting the speed at which the system state deviates from the sliding surface. When the system state point is far from the sliding mode surface, the value of the sliding mode control gain η should be reduced. When the system state point is close to the sliding mode surface, the value of the sliding mode control gain η should be increased. Based on the above logic, define the input and output fuzzy sets of the system as follows:

[0111]

[0112] NB is negative large, NM is negative medium, ZO is zero, PM is positive medium, PB is positive large.

[0113] Obtain the corresponding results of the input and output according to the fuzzy rules (the fuzzy membership function is as Figure 3 shown), and the fuzzy rules are as follows:

[0114]

[0115] And estimate the upper bound Δη condition by the integral method.

[0116]

[0117] G represents the proportional scaling factor.

[0118] S5: Based on the fuzzy set of control actions, obtain the control signal; based on the control signal, complete the by-wire steering control of the vehicle.

[0119] Embodiment 2

[0120] The present invention also provides a steer-by-wire control system based on particle swarm-sliding mode control and fuzzy radial basis function, and an application method, including:

[0121] An equation construction module, configured to obtain a state space equation of the steer-by-wire system model based on the dynamic equation of the vehicle steer-by-wire system model;

[0122] An estimated value acquisition module, configured to adaptively approximate the uncertain terms and unknown disturbances of the state space equation based on a radial basis neural network combined with an adaptation law, and obtain real-time estimated values of the uncertain terms and unknown disturbances;

[0123] A sliding mode surface optimization module, configured to obtain a sliding mode surface based on the wheel angle error, correct and compensate the sliding mode surface based on the real-time estimated value, and optimize the parameters of the sliding mode surface in combination with the particle swarm algorithm to obtain an optimized sliding mode surface;

[0124] A fuzzy logic control module, configured to convert the optimized sliding mode surface and the change rate of the optimized sliding mode surface into membership degrees of a fuzzy set for fuzzy logic reasoning based on a fuzzy logic controller, and obtain a fuzzy set of control behaviors;

[0125] A control signal acquisition and execution module, configured to obtain a control signal based on the fuzzy set of control behaviors; and complete the steer-by-wire control of the vehicle based on the control signal.

[0126] A further implementation manner lies in that the equation construction module includes:

[0127] A steering motor dynamic equation construction unit, configured to construct a dynamic equation of the steering motor based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque applied by the wheel to the steering motor shaft, and the torque of the motor output shaft;

[0128] A steering wheel dynamic equation construction unit, configured to construct a dynamic equation of the steering wheel based on the dynamic equation of the steering motor;

[0129] A system model dynamic equation construction unit, configured to obtain a dynamic equation of the steer-by-wire system model based on the reduction ratio of the vehicle reducer and the dynamic equation of the steering wheel.

[0130] A further implementation manner lies in that the estimated value acquisition module includes:

[0131] A radial basis neural network construction unit, configured to preset the number of nodes in the network hidden layer, the ideal neural network weights, and the neural network approximation error, and construct a radial basis neural network through a Gaussian basis function;

[0132] An adaptive approximation unit, which is used to obtain the estimated values of the uncertainties and unknown disturbances of the state-space equation based on the minimum parameter learning method of the radial basis neural network combined with the adaptive law.

[0133] Embodiment III

[0134] In terms of verifying the effectiveness of the proposed control method, three representative test scenarios were constructed through the co-simulation platform of CarSim and MATLAB / Simulink. These scenarios include the sine signal tracking of the front wheel steering angle, single-lane lane change maneuver, and double lane change maneuver. The design of these test scenarios aims to simulate the complex road conditions that may be encountered in actual driving to comprehensively evaluate the performance of the control strategy.

[0135] In the experiment, for the vehicle model, its detailed data (key parameters of the steer-by-wire system and permanent magnet synchronous motor) are listed in Table 2.

[0136] Table 2

[0137] Parameter Value k 60 <![CDATA[J sm (kg·m 2 )]]> 0.000828 <![CDATA[J w (kg·m 2 )]]> 1.829 <![CDATA[B sm (Nms / rad)]]> 6 <![CDATA[B w (Nms / rad)]]> 0.008 <![CDATA[C f (kN / rad)]]> 14 <![CDATA[l f (m)]]> 1.05

[0138] Meanwhile, in order to ensure the real-time performance and effectiveness of the control strategy, the sampling time of the controller is accurately set to T = 0.001 s. In the comparative analysis, the proposed control algorithm is compared with two algorithms, namely sliding mode control (SMC) and fault-tolerant sliding mode predictive control (SMPC). Through this comparison, the superiority of the proposed algorithm in different test scenarios can be comprehensively evaluated.

[0139] Sine signal: It can be seen from Figure 5 (a) the steering angle tracking diagram and Figure 5 (b) the tracking error diagram that there are relatively high errors and instability in the tracking of the SMC steering angle, and there are problems in terms of control accuracy or stability. Both SMPC and FRPS-SMC can track the steering angle signal well, but compared with FRPS-SMC, SMPC is slightly insufficient in terms of response speed and overshoot. FRPS-SMC shows a faster response speed and the smallest overshoot, and the tracking effect is also the best.

[0140] Figure 5 (c) In terms of torque control, it can be clearly seen that there is strong oscillation in SMC, SMPC performs well but there is still range oscillation. The FRPS-SMC controller can effectively reduce the motor torque fluctuation when the steering angle enters the steady state, which is more in line with the actual application of motor control.

[0141] Single lane change condition: Figure 6 (a) and Figure 6It can be seen from (b) that there are always high oscillations in the SMC control algorithm during the response process. In contrast, the oscillations of the SMPC control algorithm gradually weaken at about 2.2 seconds, indicating its certain adaptive ability in adapting to the changes in the front wheel steering angle. FRPS-SMC starts to maintain stable tracking at 0.5 seconds according to the estimation and adaptive mechanism compensation for disturbances and system uncertainties, and maintains high-precision tracking.

[0142] From Figure 6 (c) and Figure 6 (d), it can be seen that due to the slow response speed and high oscillations of the SMC control algorithm for the steering angle, there is a relatively high deviation of SMC compared with other control algorithms. The SMPC and FRPS-SMC control algorithms achieve high-precision displacement tracking.

[0143] Double lane change condition: In the Figure 7 (a) and Figure 7 In the analysis of the steering angle tracking performance shown in (b), it can be observed that there is a significant delay in the response speed of the SMC algorithm. The SMPC algorithm has a good tracking effect during the control process but has slight oscillations. The FRPS-SMC algorithm shows excellent stability and robustness in the tracking performance. With the rapid change of the front wheel steering angle, the performance of the three control algorithms in terms of the stable error at the steering angle peak is as follows: the error of the SMC algorithm is 1.897 degrees, the error of the SMPC algorithm is 0.781 degrees, and the error of the FRPS-SMC algorithm is only 0.296 degrees.

[0144] From Figure 7 (c) and Figure 7 (d), it can be seen that in the double lane change maneuver scenario, the SMC control algorithm becomes unstable and cannot achieve high-precision displacement tracking. The performance of the SMPC control algorithm will decline after 150m in path tracking. It can be seen that in the face of continuous external disturbances and system uncertainties, the real-time estimation feedback and adaptive regulation ability of FRPS-SMC have advantages.

[0145] In order to quantitatively evaluate the performance of the steering controller, the present invention introduces the mean absolute error (MAE) to evaluate the front wheel steering angle tracking performance under the condition that the system is disturbed. As shown in Table 3.

[0146] Table 3

[0147] MAE SMC SMPC FRPS-SMC Sin 1.116 0.435 0.111 DYX 0.354 0.160 0.039 SYX 0.585 0.261 0.074

[0148] The designed control algorithm was tested and verified on an experimental vehicle equipped with a steer-by-wire system under the sine steering condition and the mixed steering condition. Compared with

[0149] For the SMC and SMPC controllers, the MAE values of the FRPS-SMC controller are reduced by 90.05% and 74.48% respectively under the sine steering condition. For the single-lane change vehicle, the MAE values of the FRPS-SMC controller are reduced by 88.98% and 75.62% respectively under the sine steering condition.

[0150] For the double lane change maneuver, the MAE values of the FRPS-SMC controller are reduced by 87.36% and 71.65% respectively under the sine steering condition.

[0151] The experimental results show that the FRPS-SMC algorithm designed in the present invention can effectively handle the system uncertainties and unknown disturbances, can avoid oscillations effectively while responding quickly, and can achieve high-precision tracking of the whole vehicle.

[0152] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention shall fall within the protection scope determined by the claims of the present invention.

Claims

1. A wire-controlled steering control method based on particle swarm-sliding mode control and fuzzy radial basis function, characterized in that, Including: Based on the dynamic equation of the steer-by-wire system model, obtain the state-space equation of the steer-by-wire system model; Based on the radial basis neural network combined with the adaptive law, adaptively approximate the uncertain terms and unknown disturbances of the state-space equation to obtain real-time estimated values of the uncertain terms and unknown disturbances; Based on the wheel angle error, obtain the sliding mode surface, correct and compensate the sliding mode surface based on the real-time estimated value, and optimize the parameters of the sliding mode surface by combining the particle swarm algorithm to obtain the optimized sliding mode surface; Based on the fuzzy logic controller, convert the optimized sliding mode surface and the change rate of the optimized sliding mode surface into the membership degrees of the fuzzy set for fuzzy logic reasoning to obtain the fuzzy set of control actions; Based on the fuzzy set of control actions, obtain the control signal; Based on the control signal, complete the steer-by-wire control of the vehicle.

2. The method according to claim 1, characterized in that, The method for obtaining the dynamic equation of the steer-by-wire system model includes: Based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque applied by the wheel to the steering motor shaft, and the torque of the motor output shaft, construct the dynamic equation of the steering motor; Based on the dynamic equation of the steering motor, construct the dynamic equation of the steering wheel; Based on the reduction ratio of the vehicle reducer and the dynamic equation of the steering wheel, obtain the dynamic equation of the steer-by-wire system model.

3. The method according to claim 1, wherein The method for obtaining the real-time estimated values of the uncertain terms and unknown disturbances includes: Preset the number of nodes in the hidden layer of the network, the ideal neural network weights, and the neural network approximation error, and construct a radial basis neural network through Gaussian basis functions; Based on the least parameter learning method of the radial basis neural network combined with the adaptive law, obtain the estimated values of the uncertain terms and unknown disturbances of the state-space equation.

4. The method according to claim 3, wherein The expression of the adaptive law is as follows: where φ and ξ are parameters defined by the neural network minimum parameter method, where φ = ||W|| 2 , ξ = ||V|| 2 , W and V represent the ideal neural network weights, is the estimate of φ, is the estimate of ξ, represents the derivative of, γ1, γ2 represent the adaptive control gain scalar parameters, s represents the sliding mode surface, h represents the output of the Gaussian basis function, represents the derivative of ξ, r1, r2 represent the damping coefficients of the adaptive control, r1, r2 >

0.

5. The method according to claim 3, characterized in that, The expression of the sliding mode surface is as follows: where δ ref is the desired wheel angle, c is the sliding mode surface parameter, δ w represents the wheel angle, e represents the system tracking error of the steer-by-wire system model, and s represents the sliding mode surface.

6. The method according to claim 5, wherein Based on the particle swarm algorithm, use the system tracking error and the system control quantity of the steer-by-wire system model as indicators to construct an objective function and optimize the parameters of the sliding mode surface; where the expression of the objective function is as follows: Where the coefficients a and b are the weights of the system tracking error e and the system control quantity u respectively, representing the degree of emphasis on the energy consumption requirement and the error tracking requirement; t is time.

7. A steer-by-wire control system based on particle swarm-sliding mode control and fuzzy radial basis function, applying the method according to any one of claims 1-6, characterized in that Including: An equation construction module for obtaining the state-space equation of the steer-by-wire system model based on the dynamic equation of the steer-by-wire system model; An estimated value acquisition module for adaptively approximating the uncertain terms and unknown disturbances of the state-space equation based on the radial basis neural network combined with the adaptive law to obtain real-time estimated values of the uncertain terms and unknown disturbances; A sliding mode surface optimization module for obtaining the sliding mode surface based on the wheel angle error, correcting and compensating the sliding mode surface based on the real-time estimated value, and optimizing the parameters of the sliding mode surface by combining the particle swarm algorithm to obtain the optimized sliding mode surface; A fuzzy logic control module for converting the optimized sliding mode surface and the change rate of the optimized sliding mode surface into the membership degrees of the fuzzy set for fuzzy logic reasoning based on the fuzzy logic controller to obtain the fuzzy set of control actions; A control signal acquisition and execution module, configured to obtain a control signal based on the fuzzy set of the control behavior; Based on the control signal, complete the steer-by-wire control of the vehicle.

8. The system according to claim 7, wherein The equation construction module includes: A steering motor dynamics equation construction unit, configured to construct a dynamics equation of the steering motor based on the moment of inertia of the steering motor rotor, the steering angle of the motor output shaft, the viscous friction coefficient of the steering motor rotor, the torque applied by the wheel to the steering motor shaft, and the torque of the motor output shaft; A steering wheel dynamics equation construction unit, configured to construct a dynamics equation of the steering wheel based on the power equation of the steering motor; A system model dynamics equation construction unit, configured to obtain a dynamics equation of the steer-by-wire system model based on the reduction ratio of the vehicle reducer and the dynamics equation of the steering wheel.

9. The system according to claim 7, wherein The estimated value acquisition module includes: A radial basis neural network construction unit, configured to preset the number of nodes in the network hidden layer, the ideal neural network weights, and the neural network approximation error, and construct a radial basis neural network through a Gaussian basis function; An adaptive approximation unit, configured to obtain an estimated value of the uncertain term and the unknown disturbance of the state space equation based on the minimum parameter learning method of the radial basis neural network combined with the adaptive law.

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