Self-adaptive double-sliding-film steering wheel active return control method based on different road adhesion coefficients

Abstract

The invention discloses a self-adaptive double-sliding-mode steering wheel active return control method based on different road adhesion coefficients, and the method comprises the steps: firstly, building a steering wheel return controller and a steering angle return tracking controller based on a sliding mode control theory, and achieving the active return of a steering wheel through the cooperative control of a double-sliding-mode controller; secondly, self-adaptive parameters of a controller are designed according to different road adhesion coefficients, and the optimal values of the parameters are fitted through polynomial fitting and a BP neural network, so that the return performance of the steering system under the low-adhesion road condition is improved. Simulation experiment results show that the control method can effectively improve the return performance of the steering system under the road conditions of different road adhesion coefficients, and quick and stable return of the steering wheel and the steering wheel is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of steering control, and specifically to an adaptive dual-synovial steering wheel active return control method based on different road surface adhesion coefficients. Background Technique

[0002] Compared with traditional steering systems, the steer-by-wire system cancels the mechanical connection between the steering wheel and the steering gear, and transmits control commands through electrical signals to achieve the steering function. During the steering process of the steer-by-wire system, the return torque of the tire is transmitted to the steering wheel through the road feel motor via electrical signal simulation to assist the steering wheel in returning. However, due to factors such as the structure of the steer-by-wire system itself and system friction, there will be phenomena of overshoot during high-speed return and insufficient return during low-speed return during the vehicle return process, and the steering wheel cannot actively return to the zero position. At the same time, the return torque of the vehicle will be significantly reduced under low-adhesion road surface conditions, directly affecting the return performance of vehicle steering. And the steering return performance of the vehicle directly affects the vehicle handling stability. Poor return performance not only causes driver operation fatigue but also affects driving safety. Therefore, it is necessary to actively control the return of the steering wheel to ensure that the steering wheel can actively return to the zero position after the driver releases it, and improve the return performance of the vehicle.

[0003] Currently, the commonly used active steering wheel return control methods mainly include Proportional-Integral-Derivative (PID) control, Sliding Mode Control (SMC), Fuzzy Control (FC), and Backstepping Control, etc. PID control is a classic linear controller. Due to its excellent control performance and simple implementation method, it has become the preferred control strategy for many industrial control systems. The literature proposed an EPS active return controller based on single-neuron adaptive PID control, introducing a single neuron into the traditional PID controller to achieve the self-adaptability of the weight coefficient, and at the same time adding the feedback of the steering wheel angular velocity in the return control to improve the smoothness of active return; the literature compensated the return torque according to the vehicle speed, and at the same time designed the switching conditions of the system assist state and return state based on the feedback signals of the steering column torque and steering wheel angle to avoid sudden changes in torque; the literature proposed a fuzzy PID control scheme for steering wheel return based on absolute position, improving the return ability of the wheels under various working conditions by controlling the assist motor; the literature designed an adaptive PD return control strategy based on the road surface adhesion coefficient, improving the return performance of the vehicle on the ground adhesion road surface; although PID has a simple structure and high reliability, its effectiveness is often limited when dealing with complex systems and nonlinear phenomena. At the same time, due to the continuous accumulation of the integral term in the PID controller, it is easy to cause the control quantity to be too large, resulting in overshoot or oscillation phenomena. Based on this limitation, scholars have proposed a variety of nonlinear control strategies to improve system performance. The literature proposed an active return control strategy based on sliding mode control, which can effectively reduce the return residual angle and improve the driving stability of the vehicle. The literature proposed a nonlinear steering wheel angle control method using the self-aligning torque, estimating the self-aligning torque by introducing a high-gain disturbance observer, and designing a nonlinear controller based on backstepping control to achieve the return control of the steering wheel; the literature combined the advantages of fuzzy control and sliding mode control, and proposed a fuzzy sliding mode controller based on a two-degree-of-freedom vehicle model. The simulation test shows that the controller improves the return characteristics of the vehicle in high-speed and low-speed operating states, verifying the effectiveness of the controller. Although the nonlinear control strategy can effectively improve the robustness of the controller and improve the control stability, it does not consider the influence of low-adhesion road surface conditions on vehicle return. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an adaptive dual sliding mode steering wheel active return control method based on different road surface adhesion coefficients for the deficiencies of the above-mentioned existing technologies. First, based on the sliding mode control theory, a steering wheel return controller and an angle return tracking controller are established, and the active return of the steering wheel is realized through the coordinated control of the dual sliding mode controller. Secondly, polynomial fitting and BP neural network are used to fit the optimal parameters of the controller under different road surface conditions respectively, so as to realize the rapid and stable return of the steering wheel and the steering wheel under the road conditions of different road surface adhesion coefficients.

[0005] To achieve the above technical objectives, the technical solutions adopted by the present invention are as follows:

[0006] An adaptive dual sliding mode steering wheel active return control method based on different road surface adhesion coefficients, comprising:

[0007] Step 1: Collect the vehicle driving state parameters when preparing to return, including the steering wheel angle, vehicle speed, and road surface adhesion coefficient;

[0008] Step 2:

[0009] 2.1. First, after the vehicle determines to enter the return state:

[0010] The steering wheel return controller combines the steering wheel angle and vehicle speed collected in Step 1, and obtains the optimal controller parameter k through the polynomial obtained by fitting 2 ;

[0011] The steering wheel return tracking controller combines the steering wheel angle, vehicle speed, and road surface adhesion coefficient collected in Step 1, and obtains the optimal controller parameter k through the trained BP neural network t ;

[0012] 2.2. Taking the zero position of the steering wheel as the control target, the difference between it and the current real-time steering wheel angle is used as the input of the steering wheel return controller. The steering wheel return controller then combines the optimal controller parameter k 2 to calculate the sliding mode control rate, and then controls the road feel motor, continuously adjusting the torque output by the road feel motor until the steering wheel returns to the zero position;

[0013] The current real-time steering wheel angle is converted into the steering wheel angle through the transmission ratio. The difference is calculated after subtracting the converted steering wheel angle from the current real-time steering wheel angle converted into the steering actuator motor angle. This difference is used as the input of the angle return tracking controller. The angle return tracking controller then combines the optimal controller parameter k t to calculate the sliding mode control rate, and then controls the steering actuator motor to achieve the tracking control of the steering wheel by the steering wheel.

[0014] As a further improved technical solution of the present invention, the polynomial obtained by fitting in step 2.1 is:

[0015]

[0016] where δ sw is the steering wheel angle; v is the vehicle speed;

[0017] a 00 、a 10 、a 01 、a 20 、a 11 、a 02 、a 30 、a 21 、a 12 、a 03 、a 40 、a 31 、a 22 、a 13 、a 04 are the fitting parameters of k 2 .

[0018] As a further improved technical solution of the present invention, in the BP neural network of step 2.1:

[0019] Collect multiple groups of steering wheel angles, vehicle speeds, and road adhesion coefficients under different driving conditions, and simulate to obtain the corresponding optimal value of k t ;

[0020] Set the inputs of the BP neural network to the steering wheel angle, vehicle speed, and road adhesion coefficient respectively, and the output to the optimal value of k t ;

[0021] After network parameter adjustment and error comparison, finally set the parameters of the BP neural network as follows: the number of hidden layer nodes is 3, the learning rate is 0.001, the maximum number of iterations is 10,000, the activation function is Softplus, the optimizer is SGD, and the training set and test set ratios are set to 9:1 respectively.

[0022] As a further improved technical solution of the present invention, the sliding mode control rate of the steering wheel return controller in step 2.2 is:

[0023]

[0024] where k 1 、k 3 、k 4 、a, λ are all real numbers greater than zero, s 0 is the sliding mode surface of the initial state; T a is the active return torque of the steering wheel, Jsw is the moment of inertia of the steering wheel assembly, B sw is the damping coefficient of the steering wheel assembly; δ sw is the steering wheel angle; is the boundary value, sat is the saturation function, s is the sliding mode surface of the improved fast non-singular fast terminal sliding mode controller, q and p are positive odd numbers and 1 < p / q < 2; c and β are non-zero positive real numbers; e is the angle error signal, e = δ t -δ sw = -δ sw , δ t is the target angle, that is, δ t = 0, δ sw is the steering wheel angle.

[0025] As a further improved technical solution of the present invention, the sliding mode control rate of the corner return tracking controller in step 2.2 is:

[0026]

[0027] where U b is the voltage of the steering actuator motor; R b is the resistance of the steering actuator motor; I b is the current of the steering actuator motor; L b is the inductance of the steering actuator motor; k b is the back electromotive force coefficient of the steering actuator motor, c t is a non-zero positive real number, ε t is a positive real number, s t is the sliding mode surface of the corner return tracking controller: s t = c t e m + D; D is a non-zero positive real number; e m = θ r - θ f ;

[0028] where, during the return process, the acquisition process of the target angle θ r of the steering actuator motor is:

[0029] Convert the current real-time steering wheel angle to the steering wheel angle through the transmission ratio, and deduce the angle θ r of the steering actuator motor through this steering wheel angle;

[0030] where, the acquisition process of the current motor angle θ f of the steering actuator motor is:

[0031] Deduce the angle θ f of the steering actuator motor through the current real-time steering wheel angle.

[0032] The beneficial effects of the present invention are as follows:

[0033] (1) Due to the influence of the vehicle's own structure and system friction in a steer-by-wire system vehicle, problems such as overshoot during high-speed return and insufficient return during low-speed return occur when the vehicle returns to the straight-ahead position. To address this problem, a dual-sliding-mode steering wheel active return control method is proposed in this paper, which mainly consists of a steering wheel return controller and an angle return tracking controller. The steering wheel return controller mainly realizes the active return of the steering wheel by controlling the output torque of the road feel motor; the angle return tracking controller mainly realizes the return tracking of the steering wheel angle by the steering wheel through controlling the rack displacement of the steering actuator motor, ensuring the synchronous change between the steering wheel and the wheels during the steering wheel return process. At the same time, aiming at the problem that there is a significant deviation between the initial state and the target state of the steering wheel in the steering wheel return control, resulting in poor control effect of the traditional sliding mode control, a nonsingular fast terminal sliding mode steering wheel return controller is designed. In the return working condition, this controller and the steering wheel return tracking controller designed based on the traditional sliding mode are used for cooperative control to achieve the precise return of the steering wheel. The simulation test results show that compared with the traditional sliding mode controller, the designed nonsingular fast terminal sliding mode controller has a faster convergence speed, a smaller return residual angle, and higher control accuracy and control efficiency.

[0034] Note: Compared with the widely used PID controller at present, the controller designed in this paper effectively solves the problem of easy overshoot of the PID controller, and has a faster convergence speed and control accuracy.

[0035] (2) Since the road surface adhesion coefficient affects the return torque of the vehicle's steering wheels, there is a certain steady-state error in the controller on the road surface with a relatively low road surface adhesion coefficient. To address this problem, an adaptive dual-sliding-mode steering wheel active return control method based on different road surface adhesion coefficients is proposed in this paper. First, the operating conditions with different road surface adhesion coefficients are set through the co-simulation of CarSim and Simulink, and the optimal parameters under different working conditions are obtained by adjusting the parameters of the steering wheel return controller and the angle return tracking controller; secondly, polynomial and BP neural network are respectively used for adaptive parameter fitting to design an adaptive steering wheel return controller (Adaptive Nonsingular Fast Terminal Sliding Mode Control, ANFTSMC) and an adaptive angle tracking controller (Backpropagation-Augmented Adaptive SlidingMode Control, BPAA-SMC). The simulation results show that the adaptive dual-sliding-mode steering wheel active return control method combined with BPAA-SMC and ANFTSMC can effectively improve the return performance of the steering system under road conditions with different road surface adhesion coefficients, and achieve the fast and stable return of the steering wheel and the steering wheels. Description of the Drawings

[0036] Figure 1 It is an architecture diagram of an adaptive dual-synovial steering wheel active return control method based on different road surface adhesion coefficients.

[0037] Figure 2 It is a graph of the sat function image.

[0038] Figure 3 It is the parameter k 2 Graph of the fitting result of the optimal value

[0039] Figure 4 It is the parameter k t Graph of the optimal value result

[0040] Figure 4 In (a), it is the k obtained from 432 groups of tests t Graph of the optimal value result

[0041] Figure 4 In (b), it is the k under the condition that the steering wheel angle is 70° t Graph of the optimal value result

[0042] Figure 5 It is a graph of the BP neural network training result

[0043] Figure 5 In (a), it is a graph of the comparison result between the predicted result of the test set and the true value

[0044] Figure 5 In (b), it is the k obtained by inputting the simulation data of each operating condition into the trained fitting model t Graph of the fitting value result

[0045] Figure 6 It is a graph of the steering wheel active return test of the vehicle under different road surface conditions in the high-speed condition

[0046] Figure 6 In (a), it is a graph of the steering wheel angle return result of the vehicle with a road surface adhesion coefficient μ of 0.9 under different controller combinations in the high-speed condition

[0047] Figure 6 In (b), it is a graph of the steering wheel angle tracking result of the vehicle with a road surface adhesion coefficient μ of 0.9 under different controller combinations in the high-speed condition

[0048] Figure 6 In (c), it is a graph of the steering wheel angle return result of the vehicle with a road surface adhesion coefficient μ of 0.5 under different controller combinations in the high-speed condition

[0049] Figure 6In (d), it is the steering wheel angle tracking result diagram of the vehicle under different controller combinations in the high-speed condition when the road surface adhesion coefficient μ is 0.5.

[0050] Figure 6 In (e), it is the steering wheel angle return result diagram of the vehicle under different controller combinations in the high-speed condition when the road surface adhesion coefficient μ is 0.3.

[0051] Figure 6 In (f), it is the steering wheel angle tracking result diagram of the vehicle under different controller combinations in the high-speed condition when the road surface adhesion coefficient μ is 0.3.

[0052] Figure 7 It is the active steering wheel return test diagram of the vehicle under different road surface conditions in the low-speed condition.

[0053] Figure 7 In (a), it is the steering wheel angle return result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.9.

[0054] Figure 7 In (b), it is the steering wheel angle tracking result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.9.

[0055] Figure 7 In (c), it is the steering wheel angle return result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.5.

[0056] Figure 7 In (d), it is the steering wheel angle tracking result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.5.

[0057] Figure 7 In (e), it is the steering wheel angle return result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.3.

[0058] Figure 7 In (f), it is the steering wheel angle tracking result diagram of the vehicle under different controller combinations in the low-speed condition when the road surface adhesion coefficient μ is 0.3. Specific implementation manners

[0059] The following further describes the specific implementation manners of the present invention with reference to the drawings:

[0060] As a new type of steering system, the steer-by-wire system has greatly promoted the intelligence and ease of operation of automobiles. Aiming at the problems of overshoot during high-speed return and insufficient return during low-speed return when the vehicle returns to the straight-ahead position due to the influence of the vehicle's own structure and system friction in the steer-by-wire system, this paper proposes an adaptive double-sliding-mode steering wheel return control method based on different road surface adhesion coefficients. First, based on the sliding-mode control theory, a steering wheel return controller and a steering wheel return tracking controller are established. The return of the vehicle is achieved through the coordinated action of the double-sliding-mode controller. Secondly, the adaptive parameters of the controller are designed according to different road surface adhesion coefficients, and the optimal values of the parameters are fitted through polynomial fitting and BP neural network to improve the return performance of the steering system under low-adhesion road surface conditions. The simulation experimental results show that this control method can effectively improve the return performance of the steering system under road conditions with different road surface adhesion coefficients and achieve the rapid and stable return of the steering wheel and the steering wheel.

[0061] 1. Design of an adaptive double-sliding-mode active return control method based on different road surface adhesion coefficients:

[0062] For the steer-by-wire system, since the steering wheel and the steering wheel are controlled by a road feel motor and a steering actuator motor respectively, only controlling the road feel motor to achieve the return control of the steering wheel and ignoring the tracking control of the steering wheel by the steering wheel is likely to reduce the stability of the vehicle. Aiming at this problem, this paper designs an active return control method coordinated by a double-sliding-mode controller, which mainly cooperatively controls the return of the steering wheel through a steering wheel return controller and an angle return tracking controller. The steering wheel active return controller realizes the precise return of the steering wheel during the return condition by controlling the road feel motor, and the angle return tracking controller controls the steering wheel angle by controlling the steering actuator motor to achieve the real-time tracking control of the steering wheel angle by the steering wheel. Its architecture is as follows Figure 1 as shown.

[0063] 1.1 Steering wheel return controller:

[0064] When the steering wheel enters the return state, the torque input by the driver on the steering wheel is zero, and only the return torque provided by the road feel motor exists on the steering shaft. Ignoring uncertain factors such as friction, the dynamic equation during the return process is:

[0065]

[0066] In the formula, T a is the active return torque of the steering wheel, J sw , B sw are the moment of inertia and damping coefficient of the steering wheel assembly respectively; δ sw is the steering wheel angle; u is the sliding-mode control signal.

[0067] In the steering wheel return control, the control objective is to quickly and accurately return the steering wheel from any position to the zero position. Since there may be a significant deviation between the initial state and the target state of the steering wheel, traditional sliding mode control is prone to being affected by the control effect due to the non-linear interference torque or the sudden change of the control quantity when facing such a mutation control scenario, and even the system may chatter due to parameter mismatch or disturbance. To address the above problems, a non-singular fast terminal sliding mode controller NFTSMC is proposed. By introducing non-linear terms and a dynamic sliding mode surface, the overshoot is suppressed while the convergence speed is increased, thus significantly improving the control efficiency and robustness of the active return of the steering wheel. The approach rate expression of the designed controller is:

[0068]

[0069] where k 1 , k 2 , k 3 , k 4 , a, and λ are all real numbers greater than zero; s 0 is the sliding mode surface of the initial state. At the same time, a tangent function term is introduced in this approach rate, and the convergence speed of the control system when approaching the initial state is increased by adjusting the parameter λ.

[0070] To reduce the chattering of the controller, the saturation function sat is used instead of the sign function sgn, where is the boundary value, which is a real number greater than zero. The corresponding image of the sat function is as follows Figure 2 shown, and its expression is:

[0071]

[0072] Substituting Equation (3) into Equation (2), the designed approach rate expression can be obtained as:

[0073]

[0074] The target angle is zero in the return state. Assuming that δ t is the target angle, that is, δ t = 0, and δ sw is the steering wheel angle. Thus, the angle error signal e can be expressed as:

[0075] e = δ t - δ sw = -δ sw (5);

[0076] Define the sliding mode surface of the improved fast non-singular fast terminal sliding mode controller as:

[0077]

[0078] where c and β are non-zero positive real numbers;

[0079] Deriving the derivative of it gives:

[0080]

[0081] Substituting into it gives:

[0082]

[0083] Substituting Equation (1) and Equation (8) into Equation (4), the sliding mode control law of this control system can be obtained as:

[0084]

[0085] Using Lyapunov theory to analyze the stability of the established control system, it is verified that the time for the characteristic points moving outside s = 0 to reach the sliding mode surface is convergent. When the derivative of the Lyapunov function is:

[0086]

[0087] When s≠0 and |s / φ| < 1:

[0088]

[0089] According to Lyapunov theory, it can be known that the designed controller can converge within a finite time to ensure the stability of the system.

[0090] 1.2. Steering wheel return tracking controller:

[0091] The main function of the steering wheel return tracking controller designed in this section is to convert the angular change of the steering wheel into the rack displacement change of the rack and pinion steering gear during the active return process of the vehicle steering wheel, and to achieve the return tracking control of the steering wheel by the steering wheel through controlling the rack displacement, so as to ensure the synchronous change of the steering wheel and the wheels during the return process of the steering wheel. In the steer-by-wire system, the rack displacement is mainly controlled by the steering actuator motor. Therefore, the controller is designed for the rotation angle of the steering actuator motor to achieve the angle tracking control of the steering wheel by the steering wheel during the return process.

[0092] According to Kirchhoff's law, the voltage equation of the steering actuator motor can be derived. Therefore, the control equation of the steering return tracking controller is designed as:

[0093]

[0094] Where, U b is the voltage of the steering actuator motor; R b is the resistance of the steering actuator motor; I b is the current of the steering actuator motor; Lb is the inductance of the steering actuator motor; k b is the back electromotive force coefficient of the steering actuator motor; θ f is the rotation angle of the steering actuator motor, u t is the sliding mode control signal.

[0095] The sliding mode surface of the rotation angle return tracking controller adopts a linear sliding mode surface, and its expression is:

[0096] s t = c t e m + D(13);

[0097] Assume that the target rotation angle of the steering actuator motor during the return process is θ r , and the current rotation angle of the steering actuator motor is θ f . Thus, the rotation angle error signal e m can be expressed as:

[0098] e m = θ r - θ f (14);

[0099] Among them, the process of obtaining the target rotation angle θ r of the steering actuator motor during the return process is:

[0100] Convert the current real-time steering wheel rotation angle into the steering wheel rotation angle through the transmission ratio, and deduce the rotation angle θ r of the steering actuator motor from this steering wheel rotation angle;

[0101] Among them, the process of obtaining the current motor rotation angle θ f of the steering actuator motor is:

[0102] Deduce the rotation angle θ f of the steering actuator motor from the current real-time steering wheel rotation angle.

[0103] Substitute Equation (12) and Equation (14) into the sliding mode surface function Equation (13), and take the derivative of it to obtain:

[0104]

[0105] This sliding mode controller adopts an exponential approach rate, which is expressed as:

[0106]

[0107] Assume that u t is the control quantity of the controller. Combining Equation (15) and Equation (16), the sliding mode control rate of this control system can be obtained as:

[0108]

[0109] The stability of the established control system is analyzed using Lyapunov theory. Substituting Equation (15) and Equation (17) gives:

[0110]

[0111] From the above Equation (18), it can be concluded that the stability condition of the above Lyapunov function is satisfied, that is, the established corner return tracking controller is stable and effective.

[0112] 1.3. Design of Adaptive Steering Wheel Return Controller:

[0113] The steering wheel return controller is mainly responsible for controlling the road feel motor to achieve the control of the steering wheel angle. The control effect of this controller is mainly affected by the steering wheel angle deviation and vehicle speed. Combining the sliding mode reaching law and control equations of this controller as shown in Equations (4) and (9), and considering that the reaching law affects the robustness and convergence speed of the sliding mode controller, the exponential reaching law coefficient k 2 in the reaching law is selected as the adaptive parameter, and an Adaptive Nonsingular Fast Terminal Sliding Mode Control (ANFTSMC) is established. k 2 is designed as a function of vehicle speed and steering wheel angle. This controller can adjust the k 2 parameter value in real time according to different driving conditions to ensure good steering wheel return performance. To determine the optimal values of the control parameters that can balance the return accuracy and return time under different conditions, a joint simulation test of active steering wheel return is carried out using CarSim and Simulink. In the simulation conditions, the vehicle speeds are set to 30 km / h, 40 km / h, 50 km / h, 60 km / h, 70 km / h, and 80 km / h, and the steering wheel angle range is set to 30° - 100°, with a step size of 10°. Taking the overshoot, residual amount, and return time of return as the judgment criteria, the k 2 parameter values with better control effects under different conditions are recorded. The simulation results are shown in Table 1.

[0114] Table 1. Optimal values of parameter k 2 Optimal values:

[0115]

[0116]

[0117] It can be seen from the table that at the same vehicle speed, the optimal value of k 2 is negatively correlated with the steering wheel angle. At the same time, at the same steering wheel angle, k 2The optimal value is negatively correlated with the vehicle speed, so k 2 has a certain linear relationship with both the steering wheel angle and the vehicle speed, and the optimal parameter k 2 can be obtained through fitting. Therefore, the curve fitting toolbox in MATLAB software is used to perform a fourth-degree polynomial fitting on the optimal k 2 values collected from the simulation, and the expression of the optimal parameter k 2 is as follows:

[0118]

[0119] where δ sw is the steering wheel angle; v is the vehicle speed; a 00 ~a 04 are the fitting parameters of k 2 , and their specific values are shown in Table 2 below.

[0120] Table 2. Parameter values of the fitting expression of k 2 :

[0121] Parameter Value Parameter Value <![CDATA[a 00 > 371.3 <![CDATA[a 12 > <![CDATA[-1.769×10 -3 > <![CDATA[a 10 > -5.99 <![CDATA[a 03 > <![CDATA[-2.776×10 -3 > <![CDATA[a 01 > -17.16 <![CDATA[a 40 > <![CDATA[6.045×10 -7 <!-- 9 -->]]> <![CDATA[a 20 > 0.0583 <![CDATA[a 31 > <![CDATA[2.258×10 -6 > <![CDATA[a 11 > 0.1682 <![CDATA[a 22 > <![CDATA[3.418×10 -6 > <![CDATA[a 02 > 0.3219 <![CDATA[a 13 > <![CDATA[6.83×10 -6 > <![CDATA[a 30 > <![CDATA[-3.104×10 -4 > <![CDATA[a 04 > <![CDATA[9.115×10 -6 > <![CDATA[a 21 > <![CDATA[-8.782×10 -4 >

[0122] Figure 3 represents the fitting result graph of the optimal value of parameter k 2 . The small black dots in the figure represent the optimal values obtained from the simulation test. It can be found that the fitting surface is relatively smooth, and the test optimal values are all on the fitting plane. At the same time, the coefficient of determination R-Square of the optimal value fitting result of k 2 is 0.995. Therefore, the error between the optimal value fitting result and the real data is small, the fitting accuracy is high, and the fitting result can be used for subsequent adaptive parameter research.

[0123] 1.4. Design of the adaptive corner return tracking controller:

[0124] The corner return tracking controller is mainly responsible for controlling the steering actuator motor to achieve the tracking control of the steering wheel angle by the steering wheel. The steering actuator motor controls the displacement of the rack and pinion to achieve the control of the steering wheel angle. The displacement of the rack and pinion is affected by the left return torque and the right return torque of the steering wheel, and the magnitude of the return torque received by the wheel is closely related to the road surface adhesion coefficient. Therefore, when designing the adaptive parameters of the corner return tracking controller, in addition to considering the steering wheel angle and the vehicle speed, the influence of the road surface adhesion coefficient on the corner return tracking effect of the steering wheel also needs to be considered.

[0125] Combined with the control equation of the corner return tracking controller shown in Equation (17), and considering that the reaching law affects the robustness and convergence speed of the sliding mode controller, the exponential reaching law coefficient k t is selected as the adaptive parameter, which can adjust k tParameter values ensure good steering wheel angle tracking performance. To determine the optimal parameter values that can balance control accuracy and control time under different working conditions, a combined simulation test of steering wheel active return is carried out using CarSim and Simulink. In the simulation working conditions, the vehicle speed is set to 30 - 80 km / h with a step size of 10 km / h, the steering wheel angle range is set to 30° - 100° with a step size of 10°, and the road surface adhesion coefficient range is set to 0.25 - 0.9. Taking the overshoot, residual amount, and return time of return as the judgment criteria, record the parameter k with better control effect under different working conditions t Optimal value, the results are as follows Figure 4 As shown

[0126] Figure 4 Indicates the parameter k t Optimal value result diagram, where Figure 4 (a) in represents the k t Optimal value obtained from a total of 432 groups of tests. The X, Y, and Z axes respectively represent the road surface adhesion coefficient, steering wheel angle, and vehicle speed. The dots in the figure represent the corresponding k t Optimal value under each working condition, and the dot color represents the numerical size of the optimal value; Figure 4 (b) in is the k t Optimal value result diagram under the working condition of the steering wheel angle of 70°. The k t Optimal value distribution diagram under different vehicle speed and steering wheel angle driving working conditions. It can be found from the figure that with the increase of the road surface adhesion coefficient at the same vehicle speed, the k t Optimal value first increases and then decreases. When the road surface adhesion coefficient is about 0.5, the k t Optimal value reaches the highest value.

[0127] From the k t Optimal value result diagram, there is a non - linear relationship between the k t Optimal value and vehicle speed, steering wheel angle, and road surface adhesion coefficient. When dealing with multivariate non - linear relationships by polynomial fitting, there are defects such as large errors and too many required parameters. While the Backpropagation Neural Network (BPNN) has high - efficiency non - linear fitting ability and can describe the corresponding relationship between variables in the interval in the form of an approximate function expression through training. Therefore, use the k t Optimal value data obtained from the simulation test to train the BP neural network, and establish an Adaptive Corner Return Tracking Controller (Backpropagation - Augmented Adaptive Sliding Mode Control, BPAA - SMC) to realize the adaptation of the parameter k t Of the corner return tracking controller under different working conditions, ensuring high control accuracy of the controller.

[0128] The training dataset of the BP neural network is the 432 groups of k obtained through the co - simulation of Simulink and CarSim in this section t Optimal value. Set the input layer of the network to three parameters: vehicle speed, road adhesion coefficient, and steering wheel angle, and set the output layer to one element, that is, k t Optimal value. After adjusting the network parameters and comparing the errors, finally set the parameters of the BP neural network as follows: the number of hidden layer nodes is 3, the learning rate is 0.001, the maximum number of iterations is 10000, the activation function is Softplus, the optimizer is SGD, and set the ratio of the training set to the test set to 9:1 respectively. The fitting training result of the optimal value of the BP neural network k t is as follows Figure 5 as shown

[0129] The training result of the BP neural network is as shown in the above figure, where Figure 5 (a) represents the comparison result between the predicted result of the test set and the true value. The blue dots in the figure are the target values, and the red dots are the fitted values after training the BP neural network. It can be clearly found that the k t fitted values obtained by training have high accuracy; Figure 5 (b) is the k t fitted value obtained by inputting the simulation data of each operating condition into the trained fitting model. The abscissa represents the target optimal value of k t , and the ordinate represents the fitted value. The closer the blue dots are to y = x, the closer the fitted value is to the target value. It can be clearly seen from the figure that the trained models under different operating conditions can all fit k t values with high accuracy. In addition, the coefficient of determination R - Square is selected to characterize the accuracy of the neural network fitting model. After calculation, the coefficient of determination of the training set fitted by the BP neural network reaches 0.9992, that is, the fitted model of the trained BP neural network can effectively describe the relationship between k t and vehicle speed, road adhesion coefficient, and steering wheel angle

[0130] 2. Simulation analysis:

[0131] To verify the steering wheel active return controller based on different road conditions designed in the present invention, the vehicle steering wheel release return condition is simulated through the co - simulation of CarSim and Simulink, and the high - speed return condition and the low - speed return condition are selected to conduct simulation return tests under different road adhesion coefficients

[0132] 2.1 High - speed condition steering wheel active return test:

[0133] In the high-speed condition, the vehicle conducts active return tests respectively on road conditions with road surface adhesion coefficients of 0.9, 0.5, and 0.3. The vehicle speed is 70 km / h, and the steering wheel angle is constantly input at 60°. After the vehicle travels smoothly for five seconds, the steering wheel angle input is cancelled and changed to a steering wheel torque input. At the same time, the input torque is set to 0 Nm, and the change in the steering wheel angle response during the return process is recorded. The simulation results are as Figure 6 shown. Figure 6 In it, SMC+SMC means that both the steering wheel return controller and the corner return tracking controller use the traditional sliding mode controller SMC. SMC+NFTSMC means that the steering wheel return controller uses the non-singular fast terminal sliding mode controller NFTSMC, while the corner return tracking controller uses the traditional sliding mode controller SMC. BPAA-SMC+ANFTSMC represents the adaptive dual sliding mode steering wheel return controller based on different road surface adhesion coefficients proposed in this paper.

[0134] Figure 6 It represents the active return test of the steering wheel of the vehicle under different road surface conditions in the high-speed condition. Figure 6 In (b), (d), and (f) of it are the corner tracking result diagrams of the steering wheel. It can be seen from the figures that the designed controller can track the steering wheel angle well and has strong stability. Figure 6Among them, (a), (c), and (e) are the steering wheel angle return results diagrams. It can be seen from the diagrams that for the vehicle without a steering wheel return controller, the steering wheel cannot return to the zero position on the road surfaces with a road adhesion coefficient of 0.9, 0.5, and 0.3. There is an overshoot phenomenon during the return process, and at the same time, the change gradient of the steering wheel angle is relatively large, which easily leads to the problem of low vehicle driving stability caused by the steering wheel jitter. In the driving condition of the vehicle on the road surface with a road adhesion coefficient of 0.9, after using the combined double traditional sliding mode controllers, the overshoot of the steering wheel return is significantly reduced. At the same time, the change of the steering wheel angle is relatively gentle, preventing the steering wheel jitter caused by the sharp change of the angle during the return process. However, the steering wheel return time is relatively long, with an average return time of 2.6 s. After replacing the steering wheel return controller with the NFTSMC controller, compared with the traditional sliding mode controller, it has a faster convergence speed. During the return process, the change of the steering wheel angle is stable, and the return time is shorter, with an average return time of 1.06 s, and the return residual angle is less than 0.1°. However, as the road adhesion coefficient decreases, the controller accuracy significantly decreases. When the road adhesion coefficient is 0.3, there is a steady-state error of about 4° for the steering wheel, and the return performance is poor. By introducing adaptive adjustment parameters into the steering wheel active return controller and the steering wheel return tracking controller respectively, that is, the adaptive double sliding mode steering wheel active return controller combined with BPAA - SMC and ANFTSMC can ensure the return speed and significantly improve the problem of large steady-state error under different road adhesion coefficient conditions. The steady-state error is about 0.03°, improving the overshoot phenomenon of the steering wheel return in the high-speed driving condition of the vehicle, and having high stability and accuracy.

[0135] 2.1.2. Active Return Test of Steering Wheel under Low-Speed Condition:

[0136] Under the low-speed condition, the vehicle conducts active return tests on the road surfaces with road adhesion coefficients of 0.9, 0.5, and 0.3 respectively. The vehicle speed is 40 km / h, the steering wheel angle is constantly input at 90°, and the vehicle returns after driving smoothly for five seconds. The other settings are the same as those in the high-speed condition return simulation test. The simulation results are as Figure 7 shown.

[0137] Figure 7 It shows the active return test of the steering wheel of the vehicle under different road conditions in the low-speed condition. Figure 7 Among them, (b), (d), and (f) are the steering wheel angle tracking result diagrams. It can be seen from the diagrams that the designed controller can well track the steering wheel angle and has strong stability. Figure 7Among them, (a), (c), and (e) are the steering wheel angle return results diagrams. It can be found from the diagrams that for the vehicle without a steering wheel return controller, the steering wheel cannot return to the zero position on the road surfaces with a road adhesion coefficient of 0.9, 0.5, and 0.3, showing insufficient return. The same as in the high-speed condition, the steering wheel return gradient is relatively large, which easily leads to problems such as steering wheel jitter. In the driving condition of the vehicle on the road surface with a road adhesion coefficient of 0.9, after using the combination of two traditional sliding mode controllers, the insufficient return amount of the steering wheel is significantly reduced, the change of the steering wheel angle is relatively gentle, and the residual return angle is about 0.12°. However, the steering wheel return time is still relatively long, with an average return time of 2.7 s. After replacing the steering wheel return controller with the NFTSMC controller, compared with the traditional sliding mode controller, it has a faster convergence speed. During the return process, the steering wheel angle changes smoothly and has a faster convergence speed, with an average return time of 1.4 s, and the residual return angle is less than 0.1°. However, as the road adhesion coefficient decreases, the controller accuracy decreases significantly. When the road adhesion coefficient is 0.3, the steering wheel has a steady-state error of about 5.4°, and the return performance is poor. By introducing adaptive adjustment parameters into the steering wheel active return controller and the steering wheel return tracking controller respectively, that is, the adaptive dual sliding mode steering wheel active return controller combined with BPAA-SMC and ANFTSMC can ensure the return speed and significantly improve the problem of large steady-state error under different road adhesion coefficient conditions. The steady-state error is about 0.01°, improving the overshoot phenomenon of the steering wheel return in the low-speed condition of the vehicle, and having high stability and accuracy.

[0138] From the above simulation tests, it can be obtained that the designed adaptive dual sliding mode steering wheel return controller based on road adhesion coefficient has the characteristics of fast convergence speed, high return accuracy, and smooth change of the steering wheel angle during return. It can effectively improve the return performance of the steering system under different road conditions, ensuring that the steer-by-wire system can achieve normal return on road surfaces with different adhesion coefficients and under different working conditions.

[0139] 3. Conclusion:

[0140] Combined with the sliding mode control principle, polynomial fitting, and BP neural network fitting model, this paper proposes an adaptive dual sliding mode steering wheel return control method based on different road adhesion coefficients. According to the theoretical analysis and simulation test results, the following conclusions are obtained:

[0141] (1)A dual-sliding-mode steering wheel active return control method is proposed, which mainly conducts collaborative control of the steering wheel return through a steering wheel return controller and an angle return tracking controller. At the same time, aiming at the problem that there is a significant deviation between the initial state and the target state of the steering wheel in the steering wheel return control, resulting in poor traditional sliding-mode control effect, a non-singular fast terminal sliding-mode steering wheel return controller NFTSMC is designed. In the return working condition, this controller conducts collaborative control with the steering wheel return tracking controller designed based on the traditional sliding mode to achieve precise return of the steering wheel. The simulation results show that the designed dual-sliding-mode steering wheel active return control method can effectively achieve the return control of the steering wheel under different vehicle speed conditions.

[0142] (2)Since the low road surface adhesion coefficient affects the return torque of the vehicle's steering wheels, there is a certain steady-state error in the controller on the road surface with a low road surface adhesion coefficient. Aiming at this problem, the present invention proposes an adaptive dual-sliding-mode steering wheel return control method based on different road surface adhesion coefficients. First, the operating conditions with different road surface adhesion coefficients are set through the co-simulation of CarSim and Simulink, and the optimal parameters under different conditions are obtained by adjusting the parameters of the dual-sliding-mode steering wheel active return controller. Secondly, the adaptive parameter fitting is carried out through polynomials and BP neural networks respectively, and an adaptive steering wheel return controller ANFTSMC and an adaptive angle tracking controller BPAA-SMC are designed. The simulation results show that the adaptive dual-sliding-mode steering wheel active return controller combined with BPAA-SMC and ANFTSMC can effectively improve the return performance of the steering system under road conditions with different road surface adhesion coefficients, and achieve the fast and stable return of the steering wheel and the steering wheels.

[0143] The protection scope of the present invention includes but is not limited to the above embodiments. The protection scope of the present invention is subject to the claims, and any substitutions, deformations, and improvements that are easily conceivable by those skilled in the art to this technology fall within the protection scope of the present invention.

Claims

1. An adaptive dual-film steering wheel active return control method based on different road adhesion coefficients, characterized in that: include: Step 1: Collect the vehicle driving state parameters when preparing to return to the center position, including steering wheel angle, vehicle speed and road adhesion coefficient; Step 2 2.

1. First, after the vehicle is determined to enter the return state: The steering wheel return controller combines the steering wheel angle and vehicle speed collected in step 1, and obtains the optimal controller parameter k2 through the fitted polynomial; The steering cycle positive tracking controller combines the steering wheel angle, vehicle speed and road adhesion coefficient collected in step 1, and obtains the optimal controller parameter k through the trained BP neural network. t ; 2.

2. Taking the steering wheel zero position as the control target, the difference between the steering wheel zero position and the current real-time steering wheel angle is used as the input of the steering wheel return controller. The steering wheel return controller then calculates the sliding mode control rate in combination with the optimal controller parameter k2, and then controls the road sense motor, and continuously adjusts the torque output by the road sense motor until the steering wheel returns to zero position; The current real-time steering wheel angle is converted into the steering wheel angle through the transmission ratio, and the steering wheel angle and the current real-time steering wheel angle are converted into the steering execution motor angle, and the difference is taken as the input of the angle return tracking controller. The angle return tracking controller is combined with the optimal controller parameter k t The sliding mode control rate is calculated, and then the steering actuator motor is controlled to achieve tracking control of the steering wheel by the steering wheel.

2. The adaptive dual-film steering wheel active return control method based on different road adhesion coefficients according to claim 1, characterized in that: The polynomial fitted in step 2.1 is: Among them, δ sw is the steering wheel angle; v is the vehicle speed; a 00 、a 10 、a 01 、a 20 、a 11 、a 02 、a 30 、a 21 、a 12 、a 03 、a 40 、a 31 、a 22 、a 13 、a 04 is the fitting parameter k2.

3. The adaptive dual-film steering wheel active return control method based on different road adhesion coefficients according to claim 1, characterized in that: In the BP neural network of step 2.1: Collect multiple sets of steering wheel angles, vehicle speeds, and road adhesion coefficients under different driving conditions, and simulate to obtain the corresponding k t Optimal value; The BP neural network input is set as the steering wheel angle, vehicle speed and road contact coefficient, and the output is set as k t Optimal value; After network parameter adjustment and error comparison, the parameters of the BP neural network are finally set as follows: the number of hidden layer nodes is 3, the learning rate is 0.001, the maximum number of iterations is 10000, the activation function is Softplus, the optimizer is SGD, and the ratio of the training set to the test set is set to 9:

1.

4. The adaptive dual-film steering wheel active return control method based on different road adhesion coefficients according to claim 2, characterized in that: The sliding mode control rate of the steering wheel return controller in step 2.2 is: where k1, k3, k4, a, and λ are all real numbers greater than zero, and s0 is the sliding mode surface in the initial state; T a is the active return-to-center torque of the steering wheel, and J sw is the moment of inertia of the steering wheel assembly, and B sw is the damping coefficient of the steering wheel assembly; δ sw is the steering wheel angle; is the boundary value, sat is the saturation function, s is the sliding mode surface of the improved fast non-singular fast terminal sliding mode controller, q and p are positive odd numbers and 1 < p / q < 2; c and β are non-zero positive real numbers; e is the angle error signal, e = δ t -δ sw = -δ sw , δ t is the target angle, that is, δ t = 0, δ sw is the steering wheel angle.

5. The adaptive dual-sliding membrane steering wheel active return control method according to claim 3, characterized in that: The sliding mode control rate of the steering angle return tracking controller in step 2.2 is: Among them, U b is the voltage of the steering actuator motor; R b The resistance of the steering actuator motor; I b L is the current of the steering actuator motor; b is the inductance of the steering actuator motor; k b is the back electromotive force coefficient of the steering actuator motor, c t is a non-zero positive real number, ε t is a positive real number, s t is the sliding surface of the corner return tracking controller: t =c t e m +D; D is a non-zero positive real number; e m =θ r -θ f ; Among them, the target angle of the steering motor during the return process is θ r The acquisition process is: The current real-time steering wheel angle is converted into the steering wheel angle through the transmission ratio, and the steering execution motor angle θ is derived from the steering wheel angle r ; Among them, the current motor angle θ of the steering actuator motor f The acquisition process is: The steering wheel angle is used to calculate the steering motor angle θ. f .

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