A method for suppressing shimmy in a dual-winding wire-controlled kingpin steer system

Abstract

The present invention discloses a method for suppressing shimmy in a dual-winding, wire-controlled kingpin steer system. The method comprises: establishing mathematical models of a four-wheel independent steering vehicle and a dual-winding kingpin steer system; subtracting the real-time yaw angular velocity of the vehicle body from the actual yaw angular velocity to obtain body shimmy data; calculating four different wheel angle values ​​in the wire-controlled kingpin steer system for suppressing body shimmy; calculating current control signals for the first set of windings of different dual-winding permanent magnet synchronous motors in the wire-controlled kingpin steer system; calculating current control signals for the second set of windings of the dual-winding permanent magnet synchronous motors; and applying the different winding current control signals to the dual-winding permanent magnet synchronous motors to achieve shimmy suppression control of the dual-winding, wire-controlled kingpin steer system. The method effectively suppresses the coupling of body and wheel-end shimmy through decoupling control between different windings, improving the efficiency of vehicle coupled shimmy suppression and enhancing the anti-interference capability and robustness of wheel angle tracking.

Description

Technical Field

[0001] The invention belongs to the technical field of automobile steering, and in particular relates to a shimmy suppression method for a dual-winding wire-controlled kingpin steering system. Background Art

[0002] As a core component of modern vehicle steering systems, the performance of steer-by-wire systems is directly related to vehicle safety and stability. Currently, most steer-by-wire systems use a single-winding permanent magnet synchronous motor as the actuator motor. When faced with vehicle body and wheel-end shimmy, these motors struggle to simultaneously control steering and suppress shimmy, resulting in poor steering stability. Furthermore, if a single winding fails, the entire steering motor ceases to function, significantly compromising the safety and stability of the steer-by-wire system. In contrast, dual-winding permanent magnet synchronous motors utilize a unique series-parallel winding reconfiguration technology, resulting in two electrically independent windings that provide superior control performance and robust fault tolerance. In actual operation, dual-winding permanent magnet synchronous motors can control different windings based on specific requirements, effectively improving the operational stability of steer-by-wire systems. This not only enhances vehicle handling in complex road conditions but also provides a certain degree of shimmy suppression.

[0003] At present, the research on the shimmy suppression of the dual-winding wire-controlled kingpin steering system is not very comprehensive. The Chinese invention patent application number is CN202211625778.2, entitled "A monitoring and control method for vehicle steering system and vehicle front wheel shimmy". By establishing a group of dynamic equations, the vehicle speed and front wheel steering angle vibration signals are collected to calculate the unstable modal frequency. Based on this and the steering angle vibration signal, the energy proportion of the shimmy main frequency is obtained, and the damper current is adjusted to suppress the shimmy. This method can effectively monitor and control the front wheel shimmy without affecting the steering performance; the Chinese invention patent application number is CN202110601543.9, entitled "A compensation method and compensation system for vehicle steering wheel shimmy In the "system", when the working conditions for steering wheel shimmy compensation are met, the suppression torque is calculated based on the hand force torque, and the compensation torque and current are determined by comparison with the threshold. The EPS motor compensation is controlled at a preset time to suppress the steering wheel shimmy; the Chinese invention patent application number is CN202210432268.7, and the name is "A method and system for suppressing wheel shimmy based on EPS". The steering system torque information is obtained to calculate the theoretical vibration frequency of the wheel shimmy, and then the steering torque time domain information is converted into frequency domain information to check the frequency. The corresponding gain is calculated according to the preset compensation current gain MAP. Finally, the steering system torque information is filtered according to the check interval, and the compensation current is calculated in combination with the gain to offset the wheel shimmy.

[0004] However, there are some common problems in existing research: none of the current technical solutions have studied the vibration suppression of the dual-winding wire-controlled kingpin steering system and the four-wheel independent steering structure characteristics, and they are insufficient in considering the complexity of the system, making it difficult to fully reflect its complex dynamic characteristics, multi-wheel steering interference and the impact of the dual-winding collaborative work; and they are also insufficient in real-time and accuracy. The complex calculation process and preset parameters are difficult to adapt to changes in system operating conditions, and the fixed calculation method does not take into account situations such as winding failures, resulting in the inability to meet the system's high requirements for real-time and accurate vibration suppression. Summary of the Invention

[0005] To address the shortcomings of the prior art, the present invention aims to provide a method for suppressing shimmy in a dual-winding, steer-by-wire kingpin steering system, addressing the shimmy problem encountered by existing vehicles with four-wheel independent steer-by-wire. Leveraging the dual-winding permanent magnet synchronous motor's two independent windings, the present invention effectively suppresses coupling shimmy between the vehicle body and the wheel ends through decoupling control between the windings. This improves the efficiency of vehicle shimmy suppression and further enhances the anti-interference capability and robustness of wheel angle tracking.

[0006] To achieve the above object, the technical solution steps adopted by the present invention are as follows:

[0007] A method for suppressing shimmy in a dual-winding, wire-controlled kingpin steering system of the present invention comprises the following steps:

[0008] 1) Establish mathematical models of a four-wheel independent steering vehicle and a dual-winding kingpin steering system, and establish the state space equation of the four-wheel independent steering vehicle system based on the mathematical models of the four-wheel independent steering vehicle;

[0009] 2) Based on the state-space equations of the four-wheel independent steering vehicle system, an unscented Kalman filter algorithm is used to establish a body yaw observer. The real-time yaw rate of the vehicle body is observed in real time and subtracted from the actual yaw rate to obtain the body yaw data.

[0010] 3) Establishing a body shimmy suppression controller, using the body shimmy data from step 2) to calculate four different wheel angle values ​​in a steer-by-wire system for suppressing body shimmy;

[0011] 4) Using the wheel angle value and the desired wheel angle value in step 3), a wheel shimmy signal is calculated. Then, an improved sliding mode algorithm is used to establish a wheel-end shimmy suppression controller. Current control signals for the first winding of different dual-winding permanent magnet synchronous motors in the steer-by-wire kingpin steer system are calculated to perform body shimmy suppression control.

[0012] 5) Calculate the error between the actual wheel angle and the desired angle, and establish a kingpin steering wheel angle tracking controller using a second-order adaptive recursive terminal sliding mode algorithm. This calculates the current control signal for the second winding of the dual-winding permanent magnet synchronous motor to perform angle tracking control on different wheels.

[0013] 6) The current control signals of different windings of the dual-winding permanent magnet synchronous motor calculated in step 4) and step 5) are jointly applied to the dual-winding permanent magnet synchronous motor to complete the shimmy suppression control of the dual-winding wire-controlled kingpin steering system.

[0014] Furthermore, the mathematical model of the four-wheel independent steering vehicle and the state space equation of the four-wheel independent steering vehicle system established in step 1) are specifically:

[0015] 11) Establish the dynamic equation of the two-degree-of-freedom linear model of the vehicle, expressed as:

[0016]

[0017] Where, F Yf 、F Yr are the lateral forces of the front and rear wheels respectively; is the derivative of the vehicle's center of mass sideslip angle β; γ is the yaw rate at the vehicle's center of mass; m is the vehicle's mass; u x is the longitudinal velocity of the vehicle; a and b are the distances from the center of mass of the vehicle to the front and rear axles, respectively; I z is the moment of inertia of the vehicle around the z-axis;

[0018] 12) Considering the independent steering of the four wheels, the mathematical model of the four-wheel independent steering vehicle is modified to the 4WIS mode, considering only the lateral and yaw degrees of freedom, and establishing the dynamic model of the two-degree-of-freedom 4WIS vehicle with four control inputs as follows:

[0019]

[0020] Where C f is the cornering stiffness of the left front wheel and the right front wheel; C r is the cornering stiffness of the left and right rear wheels; δ fl , δ fr , δ rl , δ rr They are the vehicle's left front wheel angle, right front wheel angle, left rear wheel angle and right rear wheel angle respectively;

[0021] 13) The dynamic model of the two-degree-of-freedom 4WIS vehicle established in step 12) is further converted into the state space equation of the four-wheel independent steering vehicle system, which is expressed as:

[0022]

[0023] y(t)=Cx(t)+Du(t)

[0024]

[0025] Where, is the derivative of the state quantity x(t) with respect to time t; x(t) is the state quantity of the system; u(t) is the control input; A is the system matrix; B is the input matrix; C is the output matrix; and D is the direct transfer matrix.

[0026] Furthermore, the mathematical model of the dual-winding kingpin steering system established in step 1) is specifically as follows:

[0027] Select the synchronous rotating coordinate system dq, and establish the stator voltage equation and electromagnetic torque equation of the dual-winding permanent magnet synchronous motor in the dual-winding kingpin steering, which can be expressed as:

[0028]

[0029] Where u d 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; R is the stator resistance of the motor; L d , L q are the dq axis inductance components respectively; B is the viscous friction factor; is the permanent magnet flux of the motor rotor; J is the motor moment of inertia; p is the number of rotor pole pairs; δ m is the motor output shaft angle; are δ m The first and second derivatives of T L is the load torque of the reducer gear; T E is the electromagnetic torque; subscript i=1,2, respectively represents the first set of windings and the second set of windings;

[0030] The relationship between the rotation angle of the dual-winding permanent magnet synchronous motor and the wheel angle in kingpin steering is expressed as:

[0031]

[0032] Where, δ τ is the wheel angle; τ is the transmission ratio coefficient.

[0033] Furthermore, the step 2) specifically includes:

[0034] 21) The state space equation of the four-wheel independent steering vehicle system is converted into a discrete state space equation using the forward Euler method:

[0035]

[0036] C k =C

[0037] In the formula, x(k) is the state quantity of the system at time k; x(k+1) is the state quantity of the system at time k+1; y(k) is the output state quantity of the system at time k; A k is the discrete system matrix; B k is the discrete input matrix; C k is the discrete output matrix;

[0038] 22) Calculate the Sigma sampling points of the state vector x and obtain the weights of the sampling points;

[0039]

[0040] Where, is the i-th state vector at time k; is the mean of the state vector at time k; P k is the covariance of the state vector at time k; n is the dimension of the state vector; κ is a constant;

[0041] Calculate the weights of the sampling points:

[0042]

[0043] Where, ω m is the weighted mean of the sampling points; z is the scaling parameter; i is a constant; ω c is the sampling point weight covariance; α is the sampling point distribution state; υ is the weight coefficient;

[0044] 23) Establish the vehicle state parameter prediction and observation parameter prediction expressions to predict the vehicle state parameters and observation parameters. The expressions are:

[0045]

[0046] Where, is the mean of the state vector at the k+1th moment; is the weighted mean of the i-th sampling point; is the i-th observation state vector at time k; is the mean of the observed state vector at the k+1th moment;

[0047] 24) Update vehicle state parameters and state error covariance;

[0048] The calculation formula of the Kalman gain matrix is:

[0049]

[0050] Where K kis the Kalman gain matrix; P xz is the correlation covariance between the state vector and the observation value; P zz is the observed value covariance;

[0051] Update the state vector and covariance matrix, the expression is:

[0052]

[0053] Where x k+1 The predicted state of the system at the k+1th moment; y k+1 is the observed state of the system at the k+1th moment; P k+1 is the covariance matrix of the system state at the k+1th moment; P xx is the covariance matrix of the system's predicted state at the k+1th moment.

[0054] Furthermore, the vehicle body shimmy suppression controller established in step 3) can be expressed as:

[0055] 31) performing a linear transformation on the discrete state space equation of the four-wheel independent steering vehicle system obtained in step 2);

[0056] make:

[0057]

[0058] Where, ξ(k|t) is the system combined state quantity at the kth moment; ξ(k+1|t) is the system combined state vector at the k+1th moment; x(k|t) is the state quantity at the kth moment; is the new discrete system matrix; is the new discrete input matrix; u(k|t) is the input of the system at the kth moment; u(k-1|t) is the input of the system at the k-1th moment; is the new discrete output matrix; η(k|t) is the system output at the kth moment;

[0059] 32) The output equation expression of the system at the future time is:

[0060] Y(t)=ψ t (t|t)+θ t ΔU(t)

[0061]

[0062] Where, Y(t) is the system output matrix; ψ t (t|t) is the system state correlation matrix; θ t is the output influence matrix; ΔU(t) is the output variation matrix; N c is the prediction time domain; N pis the control time domain; t is the prediction time;

[0063] 33) Define the vehicle body vibration suppression evaluation function:

[0064]

[0065] Where J is the vehicle body shimmy suppression evaluation function; q1, q2, q3, q4, q5 are the weight coefficients in the evaluation function; γ is the actual shimmy angular velocity of the vehicle body; γ * The ideal vehicle body yaw angular velocity is observed by the vehicle body yaw observer;

[0066] The vehicle body shimmy suppression control evaluation function is rewritten as:

[0067]

[0068] Where H, Q, and R are positive definite matrices; E is the system output correlation matrix; g is the coefficient vector; Y d To predict the expected output value at each moment in the time domain;

[0069] 34) Define the body shimmy suppression controller to solve the constraints for suppressing body shimmy as follows:

[0070]

[0071] Where u(t+l) is the controller output; Δu(t+l) is the controller output change;

[0072] 35) Solve the body shimmy suppression controller and obtain the output sequence of the body shimmy suppression controller as follows:

[0073] u m (k)=u(k-1)+Δu * (k)

[0074] Where u m (k) is the output of the controller at the kth moment; u(k-1) is the output of the controller at the k-1th moment; Δu * (k) is the first element of the control sequence; u m =[δ fl δ fr δ rl δ rr ] T .

[0075] Furthermore, in step 4), an improved sliding mode algorithm is used to establish a wheel end shimmy suppression controller to improve angle tracking accuracy, obtain excellent dynamic performance and eliminate chattering, which is specifically expressed as follows:

[0076] 41) Define the tracking error between the actual steering angle of the wheel and the desired angle of the wheel shimmy suppression controller output to suppress the body shimmy. The expression is as follows:

[0077]

[0078] Where, e is the wheel end shimmy angle error under the influence of vehicle body shimmy, The desired angle of the wheel that suppresses the body shimmy is output by the body shimmy suppression controller; δ τ is the actual turning angle of the wheel; for The corresponding output shaft angle of the dual-winding permanent magnet synchronous motor; τ is the transmission ratio coefficient;

[0079] 42) Select the global fast terminal sliding surface so that the system converges to zero in a finite time. The expression is as follows:

[0080]

[0081] Where S is the sliding surface; α, β are constants; p, q are odd numbers, and p, q> 0;

[0082] 43) Construct the sliding mode reaching law, which is expressed as follows:

[0083]

[0084] Where, is the sliding mode reaching law; p0, q0 are odd numbers and greater than 0; φ, γ are constants and greater than 0;

[0085] 44) The control law of the wheel end shimmy suppression controller is obtained by solving the equation as follows:

[0086]

[0087] Where u vq is the control law of the improved sliding mode wheel end shimmy suppression controller, u vq =i vq It is the current control signal of the q-axis of the first set of windings of the dual-winding permanent magnet synchronous motor.

[0088] Furthermore, the steps of establishing the kingpin steering wheel angle tracking controller in step 5) are as follows:

[0089] 51) Calculate the tracking error between the actual wheel angle and the desired angle. The expression is as follows:

[0090]

[0091] Where, is the wheel angle error under the influence of vehicle body shimmy; is the desired wheel angle; δ τ is the actual turning angle of the wheel; is the desired output shaft angle of the dual-winding permanent magnet synchronous motor;

[0092] 52) Establish a non-singular terminal sliding mode function σ, which is expressed as follows:

[0093]

[0094] Where λ1 and λ2 are constants; sig(x) a is a sign function; γ1 and γ2 are constants;

[0095] 53) Establish the recursive integral sliding mode function σ i , the expression is as follows:

[0096]

[0097] Where, σ i is the recursive integral sliding mode function value; is σ i The derivative of ; sgn() is the sign function; κ is a constant greater than 0;

[0098] 54) Establish the recursive integral terminal sliding surface function s, which is expressed as follows:

[0099] s=σ+λσ i

[0100] Where s is the recursive integral terminal sliding surface function; λ is a constant;

[0101] 55) The second-order adaptive recursive terminal sliding mode control output is constructed by recursive integral sliding mode function, and then the control law u of the kingpin steering wheel angle tracking controller is obtained. a , the expression is as follows:

[0102]

[0103] Where u a is the output of the sliding mode kingpin steering wheel angle tracking controller; u a =i tq is the current control signal of the second winding q-axis of the dual-winding permanent magnet synchronous motor; u equ is the equivalent control input; u int To achieve control input; is the adaptive control parameter.

[0104] Beneficial effects of the present invention:

[0105] 1. The present invention solves the problem of coupling control of different windings in a dual-winding motor. It performs decoupling control on the dual-winding motor, and can simultaneously suppress vehicle body shimmy and track wheel angles.

[0106] 2. The present invention suppresses vehicle body shimmy through a vehicle body shimmy suppression controller, and then outputs a current control signal for the first set of windings of a dual-winding permanent magnet synchronous motor through a wheel-end shimmy suppression controller. This can effectively suppress the coupling problem between vehicle body and wheel-end shimmy, thereby improving the efficiency of vehicle coupled shimmy suppression.

[0107] 3. The present invention performs wheel angle tracking by outputting a current control signal of the second set of windings of a dual-winding permanent magnet synchronous motor through a kingpin steering wheel angle tracking controller, thereby further improving the anti-interference capability and robustness of wheel angle tracking. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] Figure 1 Schematic diagram of the process of the present invention.

[0109] Figure 2 Schematic diagram of the functional relationship between the vehicle body shimmy observer and the vehicle body shimmy suppression controller in the present invention.

[0110] Figure 3 It is a schematic diagram of the functional relationship between the wheel end shimmy suppression controller and the kingpin steering wheel angle tracking controller in the present invention. DETAILED DESCRIPTION

[0111] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0112] Reference Figure 1-Figure 3 As shown, a method for suppressing shimmy of a dual-winding wire-controlled kingpin steering system of the present invention comprises the following steps:

[0113] 1) Establish mathematical models of a four-wheel independent steering vehicle and a dual-winding kingpin steering system, and establish the state space equation of the four-wheel independent steering vehicle system based on the mathematical models of the four-wheel independent steering vehicle;

[0114] The mathematical model of the four-wheel independent steering vehicle and the state space equation of the four-wheel independent steering vehicle system established in step 1) are specifically:

[0115] 11) Establish the dynamic equation of the two-degree-of-freedom linear model of the vehicle, expressed as:

[0116]

[0117] Where, F Yf 、F Yr are the lateral forces of the front and rear wheels respectively; is the derivative of the vehicle's center of mass sideslip angle β; γ is the yaw rate at the vehicle's center of mass; m is the vehicle's mass; u x is the longitudinal velocity of the vehicle; a and b are the distances from the center of mass of the vehicle to the front and rear axles, respectively; I z is the moment of inertia of the vehicle around the z-axis;

[0118] 12) Considering the independent steering of the four wheels, the mathematical model of the four-wheel independent steering vehicle is modified to the 4WIS mode, considering only the lateral and yaw degrees of freedom, and establishing the dynamic model of the two-degree-of-freedom 4WIS vehicle with four control inputs as follows:

[0119]

[0120] Where C f is the cornering stiffness of the left front wheel and the right front wheel; C r is the cornering stiffness of the left and right rear wheels; δ fl , δ fr , δ rl , δ rr They are the vehicle's left front wheel angle, right front wheel angle, left rear wheel angle and right rear wheel angle respectively;

[0121] 13) The dynamic model of the two-degree-of-freedom 4WIS vehicle established in step 12) is further converted into the state space equation of the four-wheel independent steering vehicle system, which is expressed as:

[0122]

[0123] y(t)=Cx(t)+Du(t)

[0124]

[0125]

[0126] Where, is the derivative of the state quantity x(t) with respect to time t; x(t) is the state quantity of the system; u(t) is the control input; A is the system matrix; B is the input matrix; C is the output matrix; and D is the direct transfer matrix.

[0127] The mathematical model of the dual-winding kingpin steering system established in step 1) is specifically as follows:

[0128] Select the synchronous rotating coordinate system dq, and establish the stator voltage equation and electromagnetic torque equation of the dual-winding permanent magnet synchronous motor in the dual-winding kingpin steering, which can be expressed as:

[0129]

[0130] Where ud 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; R is the stator resistance of the motor; L d 、L q are the dq axis inductance components respectively; B is the viscous friction factor; is the permanent magnet flux of the motor rotor; J is the motor moment of inertia; p is the number of rotor pole pairs; δ m is the motor output shaft angle; are δ m The first and second derivatives of T L is the load torque of the reducer gear; T E is the electromagnetic torque; subscript i=1,2, respectively represents the first set of windings and the second set of windings;

[0131] The relationship between the rotation angle of the dual-winding permanent magnet synchronous motor and the wheel angle in kingpin steering is expressed as:

[0132]

[0133] Where, δ τ is the wheel angle; τ is the transmission ratio coefficient.

[0134] 2) Based on the state-space equations of the four-wheel independent steering vehicle system, an unscented Kalman filter algorithm is used to establish a body yaw observer. The real-time yaw rate of the vehicle body is observed in real time and subtracted from the actual yaw rate to obtain the body yaw data. Specifically, the following steps are involved:

[0135] 21) The state space equation of the four-wheel independent steering vehicle system is converted into a discrete state space equation using the forward Euler method:

[0136]

[0137]

[0138] C k =C

[0139] In the formula, x(k) is the state quantity of the system at time k; x(k+1) is the state quantity of the system at time k+1; y(k) is the output state quantity of the system at time k; A k is the discrete system matrix; B k is the discrete input matrix; C k is the discrete output matrix;

[0140] 22) Calculate the Sigma sampling points of the state vector x and obtain the weights of the sampling points;

[0141]

[0142] Where, is the i-th state vector at time k; is the mean of the state vector at time k; P k is the covariance of the state vector at time k; n is the dimension of the state vector; κ is a constant;

[0143] Calculate the weights of the sampling points:

[0144]

[0145] Where, ω m is the weighted mean of the sampling points; z is the scaling parameter; i is a constant; ω c is the sampling point weight covariance; α is the sampling point distribution state; υ is the weight coefficient;

[0146] 23) Establish the vehicle state parameter prediction and observation parameter prediction expressions to predict the vehicle state parameters and observation parameters. The expressions are:

[0147]

[0148] Where, is the mean of the state vector at the k+1th moment; is the weighted mean of the i-th sampling point; is the i-th observation state vector at time k; is the mean of the observed state vector at the k+1th moment;

[0149] 24) Update vehicle state parameters and state error covariance;

[0150] The calculation formula of the Kalman gain matrix is:

[0151]

[0152] Where K k is the Kalman gain matrix; P xz is the correlation covariance between the state vector and the observation value; P zz is the observed value covariance;

[0153] Update the state vector and covariance matrix, the expression is:

[0154]

[0155] Where x k+1 The predicted state of the system at the k+1th moment; y k+1 is the observed state of the system at the k+1th moment; P k+1 is the covariance matrix of the system state at the k+1th moment; Pxx is the covariance matrix of the system's predicted state at the k+1th moment.

[0156] 3) Establishing a body shimmy suppression controller, using the body shimmy data from step 2) to calculate four different wheel angle values ​​in a steer-by-wire system for suppressing body shimmy;

[0157] The vehicle body shimmy suppression controller established in step 3) can be expressed as:

[0158] 31) performing a linear transformation on the discrete state space equation of the four-wheel independent steering vehicle system obtained in step 2);

[0159] make:

[0160]

[0161] Where, ξ(k|t) is the system combined state quantity at the kth moment; ξ(k+1|t) is the system combined state vector at the k+1th moment; x(k|t) is the state quantity at the kth moment; is the new discrete system matrix; is the new discrete input matrix; u(k|t) is the input of the system at the kth moment; u(k-1|t) is the input of the system at the k-1th moment; is the new discrete output matrix; η(k|t) is the system output at the kth moment;

[0162] 32) The output equation expression of the system at the future time is:

[0163] Y(t)=ψ t (t|t)+θ t ΔU(t)

[0164]

[0165] Where, Y(t) is the system output matrix; ψ t (t|t) is the system state correlation matrix; θ t is the output influence matrix; ΔU(t) is the output variation matrix; N c is the prediction time domain; N p is the control time domain; t is the prediction time;

[0166] 33) Define the vehicle body vibration suppression evaluation function:

[0167]

[0168] Where J is the vehicle body shimmy suppression evaluation function; q1, q2, q3, q4, q5 are the weight coefficients in the evaluation function; γ is the actual shimmy angular velocity of the vehicle body; γ *The ideal vehicle body yaw angular velocity is observed by the vehicle body yaw observer;

[0169] The vehicle body shimmy suppression control evaluation function is rewritten as:

[0170]

[0171] Where H, Q, and R are positive definite matrices; E is the system output correlation matrix; g is the coefficient vector; Y d To predict the expected output value at each moment in the time domain;

[0172] 34) Define the body shimmy suppression controller to solve the constraints for suppressing body shimmy as follows:

[0173]

[0174] Where u(t+l) is the controller output; Δu(t+l) is the controller output change;

[0175] 35) Solve the body shimmy suppression controller and obtain the output sequence of the body shimmy suppression controller as follows:

[0176] u m (k)=u(k-1)+Δu * (k)

[0177] Where u m (k) is the output of the controller at the kth moment; u(k-1) is the output of the controller at the k-1th moment; Δu * (k) is the first element of the control sequence; u m =[δ fl δ fr δ rl δ rr ] T .

[0178] 4) Using the wheel angle value and the desired wheel angle value in step 3), a wheel shimmy signal is calculated. Then, an improved sliding mode algorithm is used to establish a wheel-end shimmy suppression controller. Current control signals for the first winding of different dual-winding permanent magnet synchronous motors in the steer-by-wire kingpin steer system are calculated to perform body shimmy suppression control.

[0179] In step 4), an improved sliding mode algorithm is used to establish a wheel end shimmy suppression controller to improve angle tracking accuracy, obtain excellent dynamic performance, and eliminate chattering, which is specifically expressed as follows:

[0180] 41) Define the tracking error between the actual steering angle of the wheel and the desired angle of the wheel shimmy suppression controller output to suppress the body shimmy. The expression is as follows:

[0181]

[0182] Where, e is the wheel end shimmy angle error under the influence of vehicle body shimmy, The desired angle of the wheel that suppresses the body shimmy is output by the body shimmy suppression controller; δ τ is the actual turning angle of the wheel; for The corresponding output shaft angle of the dual-winding permanent magnet synchronous motor; τ is the transmission ratio coefficient;

[0183] 42) Select the global fast terminal sliding surface so that the system converges to zero in a finite time. The expression is as follows:

[0184]

[0185] Where S is the sliding surface; α, β are constants; p, q are odd numbers, and p, q> 0;

[0186] 43) Construct the sliding mode reaching law, which is expressed as follows:

[0187]

[0188] Where, is the sliding mode reaching law; p0, q0 are odd numbers and greater than 0; φ, γ are constants and greater than 0;

[0189] 44) The control law of the wheel end shimmy suppression controller is obtained by solving the equation as follows:

[0190]

[0191] Where u vq is the control law of the improved sliding mode wheel end shimmy suppression controller, u vq =i vq It is the current control signal of the q-axis of the first set of windings of the dual-winding permanent magnet synchronous motor.

[0192] 5) Calculate the error between the actual wheel angle and the desired angle, and establish a kingpin steering wheel angle tracking controller using a second-order adaptive recursive terminal sliding mode algorithm. This calculates the current control signal for the second winding of the dual-winding permanent magnet synchronous motor to perform angle tracking control on different wheels.

[0193] The steps of establishing the kingpin steering wheel angle tracking controller in step 5) are as follows:

[0194] 51) Calculate the tracking error between the actual wheel angle and the desired angle. The expression is as follows:

[0195]

[0196] Where, is the wheel angle error under the influence of vehicle body shimmy; is the desired wheel angle; δ τ is the actual turning angle of the wheel; is the desired output shaft angle of the dual-winding permanent magnet synchronous motor;

[0197] 52) Establish a non-singular terminal sliding mode function σ, which is expressed as follows:

[0198]

[0199] Where λ1 and λ2 are constants; sig(x) a is a sign function; γ1 and γ2 are constants;

[0200] 53) Establish the recursive integral sliding mode function σ i , the expression is as follows:

[0201]

[0202] Where, σ i is the recursive integral sliding mode function value; is σ i The derivative of ; sgn() is the sign function; κ is a constant greater than 0;

[0203] 54) Establish the recursive integral terminal sliding surface function s, which is expressed as follows:

[0204] s=σ+λσ i

[0205] Where s is the recursive integral terminal sliding surface function; λ is a constant;

[0206] 55) The second-order adaptive recursive terminal sliding mode control output is constructed by recursive integral sliding mode function, and then the control law u of the kingpin steering wheel angle tracking controller is obtained. a , the expression is as follows:

[0207]

[0208] Where u a is the output of the sliding mode kingpin steering wheel angle tracking controller; u a =i tq is the current control signal of the second winding q-axis of the dual-winding permanent magnet synchronous motor; u equ is the equivalent control input; u int To achieve control input; is the adaptive control parameter.

[0209] 6) The current control signals of different windings of the dual-winding permanent magnet synchronous motor calculated in step 4) and step 5) are jointly applied to the dual-winding permanent magnet synchronous motor to complete the shimmy suppression control of the dual-winding wire-controlled kingpin steering system.

[0210] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be considered as the scope of protection of the present invention.

Claims

1. A method for suppressing shimmy in a dual-winding, wire-controlled kingpin steering system, characterized in that: Here are the steps: Step 1: Establish a mathematical model of a four-wheel independent steering vehicle and a mathematical model of a dual-winding kingpin steering system, and establish a state space equation of the four-wheel independent steering vehicle system through the mathematical model of the four-wheel independent steering vehicle; Step 2: Based on the state-space equations of the four-wheel independent steering vehicle system, an unscented Kalman filter algorithm is used to establish a body yaw observer. The real-time yaw rate of the vehicle body is observed in real time and subtracted from the actual yaw rate to obtain the body yaw data. Step 3: Establish a body shimmy suppression controller, and use the body shimmy data from step 2) to calculate four different wheel angle values ​​in the steer-by-wire system for suppressing body shimmy; Step 4: Calculate the wheel shimmy signal using the wheel angle value and the desired wheel angle value from step 3. Then, use the improved sliding mode algorithm to establish a wheel-end shimmy suppression controller. Calculate the current control signal for the first winding of different dual-winding permanent magnet synchronous motors in the steer-by-wire kingpin system to perform body shimmy suppression control. Step 5: Calculate the error between the actual wheel angle and the desired angle, and use a second-order adaptive recursive terminal sliding mode algorithm to establish a kingpin steering wheel angle tracking controller. This calculates the current control signal for the second set of windings in the dual-winding permanent magnet synchronous motor to perform angle tracking control for different wheels. Step 6: The current control signals of different windings of the dual-winding permanent magnet synchronous motor calculated in steps 4 and 5 are applied to the dual-winding permanent magnet synchronous motor to complete the shimmy suppression control of the dual-winding wire-controlled kingpin steer system.

2. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 1, characterized in that: The mathematical model of the four-wheel independent steering vehicle and the state space equation of the four-wheel independent steering vehicle system established in step 1 are specifically: Step 11: Establish the dynamic equation of the two-degree-of-freedom linear model of the vehicle, expressed as: Where, F Yf 、F Yr are the lateral forces of the front and rear wheels respectively; is the derivative of the vehicle's center of mass sideslip angle β; γ is the yaw rate at the vehicle's center of mass; m is the vehicle's mass; u x is the longitudinal velocity of the vehicle; a and b are the distances from the center of mass of the vehicle to the front and rear axles, respectively; I z is the moment of inertia of the vehicle around the z-axis; Step 12: Considering the independent steering of the four wheels, the mathematical model of the four-wheel independent steering vehicle is modified to the 4WIS mode, considering only the lateral and yaw degrees of freedom, and establishing the dynamic model of the two-degree-of-freedom 4WIS vehicle with four control inputs as follows: Where C f is the cornering stiffness of the left front wheel and the right front wheel; C r is the cornering stiffness of the left and right rear wheels; δ fl , δ fr , δ rl , δ rr They are the vehicle's left front wheel angle, right front wheel angle, left rear wheel angle and right rear wheel angle respectively; Step 13: The dynamic model of the two-degree-of-freedom 4WIS vehicle established in step 12 is further transformed into the state space equation of the four-wheel independent steering vehicle system, which is expressed as: Where, is the derivative of the state quantity x(t) with respect to time t; x(t) is the state quantity of the system; u(t) is the control input; A is the system matrix; B is the input matrix; C is the output matrix; and D is the direct transfer matrix.

3. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 2, characterized in that: The mathematical model of the dual-winding kingpin steering system established in step 1 is specifically as follows: Select the synchronous rotating coordinate system dq, and establish the stator voltage equation and electromagnetic torque equation of the dual-winding permanent magnet synchronous motor in the dual-winding kingpin steering, which can be expressed as: Where u d 、u q are the stator voltages of the d and q axes respectively; i d 、i q are the stator currents of the d and q axes respectively; R is the stator resistance of the motor; L d , L q are the dq axis inductance components respectively; B is the viscous friction factor; is the permanent magnet flux of the motor rotor; J is the motor moment of inertia; p is the number of rotor pole pairs; δ m is the motor output shaft angle; are δ m The first and second derivatives of T L is the load torque of the reducer gear; T E is the electromagnetic torque; subscript i=1,2, respectively represents the first set of windings and the second set of windings; The relationship between the rotation angle of the dual-winding permanent magnet synchronous motor and the wheel angle in kingpin steering is expressed as: Where, δ τ is the wheel angle; τ is the transmission ratio coefficient.

4. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 3, characterized in that: The step 2 specifically includes: Step 21: Convert the state space equation of the four-wheel independent steering vehicle system into a discrete state space equation using the forward Euler method: In the formula, x(k) is the state quantity of the system at time k; x(k+1) is the state quantity of the system at time k+1; y(k) is the output state quantity of the system at time k; A k is the discrete system matrix; B k is the discrete input matrix; C k is the discrete output matrix; Step 22: Calculate the Sigma sampling points of the state vector x and obtain the weights of the sampling points; Where, is the i-th state vector at time k; is the mean of the state vector at time k; P k is the covariance of the state vector at time k; n is the dimension of the state vector; κ is a constant; Calculate the weights of the sampling points: Where, ω m is the weighted mean of the sampling points; z is the scaling parameter; i is a constant; ω c is the sampling point weight covariance; α is the sampling point distribution state; υ is the weight coefficient; Step 23: Establish the vehicle state parameter prediction and observation parameter prediction expressions to predict the vehicle state parameters and observation parameters. The expressions are: Where, is the mean of the state vector at the k+1th moment; is the weighted mean of the i-th sampling point; is the i-th observation state vector at time k; is the mean of the observed state vector at the k+1th moment; Step 24: Update vehicle state parameters and state error covariance; The calculation formula of the Kalman gain matrix is: Where K k is the Kalman gain matrix; P xz is the correlation covariance between the state vector and the observation value; P zz is the observed value covariance; Update the state vector and covariance matrix, the expression is: Where x k+1 The predicted state of the system at the k+1th moment; y k+1 is the observed state of the system at the k+1th moment; P k+1 is the covariance matrix of the system state at the k+1th moment; P xx is the covariance matrix of the system's predicted state at the k+1th moment.

5. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 4, characterized in that: The vehicle body shimmy suppression controller established in step 3 can be expressed as: Step 31: linearly transform the discrete state space equation of the four-wheel independent steering vehicle system obtained in step 2; make: Where, ξ(k|t) is the system combined state quantity at the kth moment; ξ(k+1|t) is the system combined state vector at the k+1th moment; x(k|t) is the state quantity at the kth moment; is the new discrete system matrix; is the new discrete input matrix; u(k|t) is the input of the system at the kth moment; u(k-1|t) is the input of the system at the k-1th moment; is the new discrete output matrix; η(k|t) is the system output at the kth moment; Step 32: Establish the output equation expression of the system at the future time: Y(t)=ψ t (t|t)+θ t ΔU(t) Where, Y(t) is the system output matrix; ψ t (t|t) is the system state correlation matrix; θ t is the output influence matrix; ΔU(t) is the output variation matrix; N c is the prediction time domain; N p is the control time domain; t is the prediction time; Step 33: Define the vehicle body vibration suppression evaluation function: Where J is the vehicle body shimmy suppression evaluation function; q1, q2, q3, q4, q5 are the weight coefficients in the evaluation function; γ is the actual shimmy angular velocity of the vehicle body; γ * The ideal vehicle body yaw angular velocity is observed by the vehicle body yaw observer; The vehicle body shimmy suppression control evaluation function is rewritten as: Where H, Q, and R are positive definite matrices; E is the system output correlation matrix; g is the coefficient vector; Y d To predict the expected output value at each moment in the time domain; Step 34: Define the body shimmy suppression controller to solve the constraints for suppressing body shimmy as follows: Where u(t+l) is the controller output; Δu(t+l) is the controller output change; Step 35: Solve the body shimmy suppression controller and obtain the output sequence of the body shimmy suppression controller as follows: at m (k)=u(k-1)+Δu * (k) Where u m (k) is the output of the controller at the kth moment; u(k-1) is the output of the controller at the k-1th moment; Δu * (k) is the first element of the control sequence; u m =[δ fl δ fr δ rl δ rr ] T .

6. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 5, characterized in that: In step 4, an improved sliding mode algorithm is used to establish a wheel end shimmy suppression controller to improve angle tracking accuracy, obtain excellent dynamic performance, and eliminate chattering. Specifically, it is expressed as follows: Step 41: Define the tracking error between the actual steering angle of the wheel and the output of the wheel shimmy suppression controller to suppress the desired angle of the wheel in vehicle body shimmy. The expression is as follows: Where, e is the wheel end shimmy angle error under the influence of vehicle body shimmy, The desired angle of the wheel that suppresses the body shimmy is output by the body shimmy suppression controller; δ τ is the actual turning angle of the wheel; for The corresponding output shaft angle of the dual-winding permanent magnet synchronous motor; τ is the transmission ratio coefficient; Step 42: Select the global fast terminal sliding surface so that the system converges to zero in a finite time. The expression is as follows: Where S is the sliding surface; α, β are constants; p, q are odd numbers, and p, q> 0; Step 43: Construct the sliding mode reaching law, which is expressed as follows: Where, is the sliding mode reaching law; p0, q0 are odd numbers and greater than 0; φ, γ are constants and greater than 0; Step 44: Solve and obtain the control law of the wheel-end shimmy suppression controller. The calculation expression is as follows: Where u vq is the control law of the improved sliding mode wheel end shimmy suppression controller, u vq =i vq It is the current control signal of the q-axis of the first set of windings of the dual-winding permanent magnet synchronous motor.

7. The method for suppressing shimmy of a dual-winding, wire-controlled kingpin steer system according to claim 6, characterized in that: The steps of establishing the kingpin steering wheel angle tracking controller in step 5 are as follows: Step 51: Calculate the tracking error between the actual wheel angle and the desired angle. The expression is as follows: Where, is the wheel angle error under the influence of vehicle body shimmy; is the desired wheel angle; δ τ is the actual turning angle of the wheel; is the desired output shaft angle of the dual-winding permanent magnet synchronous motor; Step 52: Establish a non-singular terminal sliding mode function σ, which is expressed as follows: Where λ1 and λ2 are constants; sig(x) a is a sign function; γ1 and γ2 are constants; Step 53: Establish the recursive integral sliding mode function σ i , the expression is as follows: Where, σ i is the recursive integral sliding mode function value; is σ i The derivative of ; sgn() is the sign function; κ is a constant greater than 0; Step 54: Establish the recursive integration terminal sliding surface function s, which is expressed as follows: s=σ+λσ i Where s is the recursive integral terminal sliding surface function; λ is a constant; Step 55: Construct the second-order adaptive recursive terminal sliding mode control output by recursively integrating the sliding mode function, and then obtain the control law u of the kingpin steering wheel angle tracking controller a , the expression is as follows: Where u a is the output of the sliding mode kingpin steering wheel angle tracking controller; u a =i tq is the current control signal of the second winding q-axis of the dual-winding permanent magnet synchronous motor; u equ is the equivalent control input; u int To achieve control input; is the adaptive control parameter.

Images