An improved sliding mode active disturbance rejection control method and system for a vehicle shimmy system based on an electromagnetic linear actuator

Abstract

This invention provides an improved sliding mode active disturbance rejection control (ADRC) method and system for an automotive shimmy system based on an electromagnetic linear actuator. Addressing the system's strong nonlinear characteristics and unknown external disturbances, a mathematical model of the automotive shimmy system based on the electromagnetic linear actuator is established. A nonlinear tracking differentiator is constructed to process the desired input signal of the wheel shimmy angle, rationally arrange the transient process, and synchronously extract the differential signal of the desired signal. A continuous and smooth Ifal function is constructed based on trigonometric sine and inverse proportional functions, and a novel extended state observer is designed to estimate the system's internal and external disturbances in real time. A super-helical sliding mode control law based on the hyperbolic tangent function is designed to replace the error feedback control law in the traditional ADRC, outputting a control voltage. This invention effectively estimates and compensates for the impact of vehicle state parameter changes, model uncertainties, and external disturbances on system stability, improving dynamic performance and control accuracy, and exhibiting good robustness and anti-interference capabilities.

Description

Technical Field

[0001] This invention belongs to the field of automotive chassis control technology, specifically relating to an improved sliding mode self-disturbance rejection control method and system for automotive shimmy systems based on electromagnetic linear actuators. Background Technology

[0002] Vehicle shimmy typically manifests as continuous oscillation of the steering wheel around its kingpin, accompanied by lateral vibration of the steering shaft relative to the vehicle body. Severe shimmy can increase the dynamic load on the steering mechanism and cause deviation from the desired driving trajectory. Therefore, suppressing wheel shimmy is crucial for improving steering performance and vehicle stability.

[0003] Traditional shimmy suppression methods primarily rely on passive control strategies, such as optimizing structural parameters and adding damping elements. These methods help alleviate or even eliminate shimmy phenomena during vehicle design and manufacturing. However, their suppression effect is limited by the inherent physical characteristics of the system and lacks real-time adaptability to dynamic disturbances. With the rapid development of actuators and control algorithms, active control technology, by sensing real-time state information such as wheel rotation angles, uses active actuators to apply feedback torque to actively counteract the disturbance forces causing shimmy, thereby achieving precise control of the system's dynamic behavior. Electromagnetic linear actuators are fundamental automation components that can directly convert electrical energy into mechanical energy without intermediate conversion devices. They offer advantages such as fast response, high efficiency, and high power density, and have been widely used in key fields such as aerospace, robotics, and medical equipment.

[0004] Automotive shimming systems based on electromagnetic linear actuators are typical uncertain nonlinear systems. Parameter uncertainties and external unknown disturbances can severely affect control performance. Traditional linear control methods often fail to meet system requirements due to their limitations, thus necessitating an advanced nonlinear control method capable of handling strong nonlinearity and real-time disturbance rejection. Active disturbance rejection control (ADRC) estimates and compensates for external disturbances in real time using an extended state observer (ESO), eliminating the need for precise mathematical models and effectively avoiding chattering while ensuring strong robustness. However, traditional ADRC cannot simultaneously meet the requirements of disturbance suppression performance and response speed, and the fal function is not differentiable at the inflection point, leading to system chattering and affecting control tracking accuracy.

[0005] Therefore, it is of great significance to find an advanced control method to achieve high-performance shimmy reduction control of automotive shimmy systems by solving the above problems. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides an improved sliding mode active disturbance rejection method and system for automotive shimmy systems based on electromagnetic linear actuators. This method can effectively estimate and compensate for the impact of factors such as changes in vehicle state parameters, model uncertainties, and external disturbances on system stability. It not only improves the dynamic performance and control accuracy of the system but also has good robustness and anti-interference capability, solving the problem that traditional active disturbance rejection control cannot simultaneously take into account response speed and anti-interference capability.

[0007] The present invention achieves the above-mentioned technical objectives through the following technical means.

[0008] An improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator includes the following steps:

[0009] S1: To address the strong nonlinear characteristics of the system and the unknown external disturbances, a mathematical model of the automobile swaying system based on an electromagnetic linear actuator is established.

[0010] S2: Construct a nonlinear tracking differentiator to process the desired input signal of the wheel sway angle, reasonably arrange the transition process, and synchronously extract the differential signal of the desired signal;

[0011] S3: Construct a continuous and smooth Ifal function based on the trigonometric sine function and the inverse proportional function, and design a novel extended state observer to estimate the internal and external disturbances of the system in real time;

[0012] S4: Design a super-helical sliding mode control law based on the hyperbolic tangent function to replace the error feedback control law in the traditional active disturbance rejection control, and output control voltage. .

[0013] In the above scheme, the Ifal function mentioned in step S3 is a piecewise function, and its expression is as follows:

[0014]

[0015] In the formula, ε is the observation error, α is the filtering factor of the Ifal function and 0 < α < 1, δ is the small error saturation threshold, η is the large error saturation threshold and η > δ, and the coefficients are... It is uniquely determined by the condition that the function is continuously differentiable at the piecewise points.

[0016] Furthermore, the coefficient Calculated using the following formula:

[0017] .

[0018] In the above scheme, the discretized expression of the novel extended state observer in step S3 is:

[0019]

[0020] In the formula, ε1 is the observation error of the left front wheel swing angle. For system output, To output the observed values ​​of y, for The differential signal, For observations of extended states, These are the adjustable gain parameters for the output observation, the output differential observation, and the extended state observation, respectively. It is the nonlinear gain of the control state variable observation channel; Controlling the nonlinear gain of the extended state observation channel, To control the gain, To control the voltage, The sampling period.

[0021] In the above scheme, the discrete error signal constructed in step S4 is:

[0022]

[0023] in, It is the tracking signal of the left front wheel sway angle. Compared with ESO observations The error between them It is the tracking signal of the left front wheel angular velocity. Compared with ESO observations The error between them To track the angular displacement signal output by the differentiator, To track the angular velocity signal output by the differentiator, The angular displacement observations output by the extended state observer. This refers to the angular velocity observation value output by the observer.

[0024] Furthermore, the superspiral sliding mode control law described in step S4 adopts a non-singular terminal sliding surface, and its expression is:

[0025]

[0026] In the formula, For swing angle tracking error, For the angular velocity tracking error of the pendulum, , , It is a positive odd number and .

[0027] Furthermore, the superspiral sliding mode control law adopts an improved reaching law based on the hyperbolic tangent function:

[0028]

[0029] In the formula, s v A1 is the first-order sliding gain coefficient of the sliding surface s, and a2 is the auxiliary state variable s. v The second-order sliding mode gain coefficient, k 01 Let k be the linear feedback gain coefficient of the sliding surface s. 02 Auxiliary state variable S v The linear feedback gain coefficient, where tanh is the hyperbolic tangent function.

[0030] Furthermore, the final control voltage It is given by the following formula:

[0031]

[0032] in, To track the angular velocity signal output by the differentiator, The estimated angular velocity output by the observer. The optimal synthesis function for fast control of the tracking differentiator is calculated using the angular acceleration signal output by the tracking differentiator. This represents the total disturbance observation.

[0033] A system for implementing the improved sliding mode active disturbance rejection control method for the automobile shimmy system based on electromagnetic linear actuators includes a mathematical model establishment module, a tracking differentiator module, an extended state observer module, and a super-helical sliding mode control law module.

[0034] The mathematical model building module is used to build a mathematical model of an automobile swaying system based on an electromagnetic linear actuator.

[0035] The tracking differentiator module is used to smooth and dynamically track the desired input signal of the wheel swing angle, and extract the differential signal.

[0036] The extended state observer module integrates a continuous smooth Ifal function constructed based on the trigonometric sine function and the inverse proportional function, which is used to estimate the internal and external disturbances of the system in real time.

[0037] The super-helical sliding mode control law module is used to replace the error feedback control law in the traditional active disturbance rejection control. It outputs control voltage to drive the electromagnetic linear actuator to generate electromagnetic force, thereby realizing active control of the wheel sway angle.

[0038] In the above scheme, the electromagnetic linear actuator is a moving-coil electromagnetic linear actuator, which outputs electromagnetic force. With control voltage satisfy:

[0039]

[0040] And this electromagnetic force is The term directly acts on the dynamic equations of the car shimmy system, where, This is the front suspension camber coefficient. The length of the lever arm.

[0041] Compared with the prior art, the beneficial effects of the present invention are:

[0042] 1. The novel continuous smooth Ifal function constructed in this invention combines the smoothing properties of the trigonometric sine function and the inverse proportional function.

[0043] With its high gain characteristic when the error is small, the Ifal function is more in line with the requirements of "small error, large gain; large error, small gain" compared to the traditional FAL function. While ensuring stability, it also has fast convergence capability and high-precision state and disturbance estimation capability.

[0044] 2. This invention introduces a superspiral sliding mode control law based on the hyperbolic tangent function to ensure that the system can quickly track the desired trajectory.

[0045] While tracking the signal, it effectively suppressed chattering, achieving an optimized balance between response speed and interference suppression capability. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of a car shimmy system based on an electromagnetic linear actuator according to an embodiment of the present invention, wherein... Figure 1 (a) is a top view. Figure 1 (b) is the front view;

[0047] Figure 2 This is a system block diagram of an improved sliding mode active disturbance rejection control method for an automobile shimmy system based on an electromagnetic linear actuator, according to an embodiment of the present invention.

[0048] Figure 3 This is a comparison chart of the characteristic curves of the Ifal function according to an embodiment of the present invention and the original fal function, wherein... Figure 3 (a) is a graph showing the characteristics of the nonlinear function. Figure 3 (b) is the error gain curve;

[0049] Figure 4 This is a diagram showing the LCO amplitude of the left front wheel sway angle with vehicle speed under different controllers according to one embodiment of the present invention. Detailed Implementation

[0050] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0051] An improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator includes the following steps:

[0052] S1: To address the strong nonlinear characteristics of the system and the unknown external disturbances, a mathematical model of the automobile swaying system based on an electromagnetic linear actuator is established.

[0053] S2: Construct a nonlinear tracking differentiator to process the desired input signal of the wheel sway angle, reasonably arrange the transition process, and synchronously extract the differential signal of the desired signal;

[0054] S3: Construct a continuous and smooth Ifal function based on the trigonometric sine function and the inverse proportional function, and design a novel extended state observer to estimate the internal and external disturbances of the system in real time;

[0055] S4: Design a super-helical sliding mode control law based on the hyperbolic tangent function to replace the error feedback control law in the traditional active disturbance rejection control, and output control voltage. .

[0056] In step S1, the dynamic differential equation of the automobile swaying system based on the electromagnetic linear actuator is:

[0057] Equation (1)

[0058] Equation (2)

[0059] Equation (3)

[0060] Equation (4)

[0061] Equation (5)

[0062] In the formula, J d J0 is the moment of inertia of the wheel about its diameter; J3 is the moment of inertia of the wheel about its axis of rotation; J4 is the moment of inertia of the steering rocker arm about its axis of rotation; k1 and k2 are the stiffnesses of the left and right steering tie rods, respectively; k3 is the angular stiffness of the steering shaft; k4 and k5 are the stiffnesses of the left and right suspensions, respectively; k b For tire vertical stiffness; k y For tire lateral stiffness; k hcc is the coefficient generated by the front suspension camber angle; c1 and c2 are the damping of the left and right steering tie rods, respectively; c3 is the equivalent angular damping of the steering shaft; c4 and c5 are the damping of the left and right front suspensions, respectively; c e The equivalent angular damping of the wheel as it rotates about its kingpin; ac The distance between the front axle and the connection point between the vehicle body and the suspension spring, i.e., l ac =l a +l c ;l b The distance from the point where the kingpin intersects the ground to the center of the tire's contact patch; d The length of the lever arm of the tie rod acting on the kingpin; f The length of the front suspension side control arm; l g γ is the lever arm length of the tie rod acting on the steering shaft; f is the coefficient of friction between the tire and the road surface; γ is the caster angle; β is the inclination angle; V is the vehicle speed; R is the tire radius; F y1 and F y2 These represent the lateral forces acting on the left and right front wheels, respectively; e represents the tire trail; F m To output electromagnetic force; equivalent moment of inertia J α =J d +ml b 2 (1+γ 2 ), J β =J d (1+γ 2 )+ml f 2 J γ =(J d +ml b l f γ, m is the mass of the wheel.

[0063] The "magic formula" nonlinear tire model is used to describe the tire's lateral characteristics, and its lateral force calculation formula is as follows:

[0064] Equation (6)

[0065] In the formula, α1 and α2 are the slip angles of the left and right tires, respectively; B, C, D and E are the stiffness factor, shape factor, peak factor and curvature factor, respectively, with B = 0.2167, C = 1.3, D = −3625.2 and E = −0.6814.

[0066] Based on tension string theory, the nonholonomic constraint equation between the left and right front wheel sway angles and the sideslip angle is:

[0067]

[0068] Equation (7)

[0069] In the formula, σ is the tire slack length; a is half the tire track length.

[0070] The active actuator employs a high-power-density moving-coil electromagnetic linear actuator, primarily composed of an outer magnetic yoke, a permanent magnet, an inner magnetic yoke, a coil, and a coil frame. The electromagnetic linear actuator is a complex system involving strong coupling of multiple fields in mechanical, electrical, and magnetic circuits. Based on Kirchhoff's laws, Lorentz's force theorem, and Newton's second law, the dynamic differential equations of the electromagnetic linear actuator can be obtained as follows:

[0071] Equation (8)

[0072] In the formula, u is the power supply voltage; i is the current through the coil; R a L represents the coil resistance and inductance; k e v is the back electromotive force constant; a The coil's velocity; N is the number of coil turns; B is the coil's magnetic flux density; l is the effective length of each coil turn in the magnetic field; k m M is the electromagnetic force coefficient; a y is the mass of the coil assembly; y is the displacement of the mover; k v F is the damping coefficient experienced by the mover in the magnetic field. f This is friction.

[0073] From equation (8), it can be seen that the control voltage The actuator generates electromagnetic force This force The term acts directly on the right side of equations (4) and (5), thereby achieving active control of the wheel sway angle.

[0074] In step S2, the specific steps of the nonlinear tracking differentiator are as follows:

[0075] Taking the left front wheel sway angle controller as an example, the state variable is defined as follows: The state-space equation of the system can then be expressed as:

[0076] Equation (9)

[0077] In the formula, f v y is the total disturbance of the system, used to uniformly characterize the uncertain effects caused by system parameter perturbations, unmodeled dynamics, and external disturbances; b0 is the adjustable control gain; u is the control voltage of the electromagnetic linear actuator; y is the output of the vehicle shimmy system, i.e., the shimmy angle of the left front wheel.

[0078] Construct a second-order discrete-form nonlinear tracking differentiator, with the specific expression as follows:

[0079] Equation (10)

[0080] In the formula, θ d Given the desired value of the left front wheel sway angle; θ v and θ w θ d The tracking signal and the differential signal; h is the discrete control period; r and h0 are the adjustable speed factor and filter factor of the fst function, respectively.

[0081] The fst function is a fast control optimal synthesis function, and its expression is:

[0082] Equation (11)

[0083] in,

[0084] Equation (12)

[0085] The design process of the novel extended state observer in step S3 is as follows:

[0086] A novel, continuous, and smooth Ifal function was designed by selecting the trigonometric sine and inverse proportional functions, which exhibit better smoothness at the origin than exponential functions. The Ifal function is a piecewise function, and its expression is as follows:

[0087] Equation (13)

[0088] In the formula, ε is the observation error, α is the filtering factor of the Ifal function and 0 < α < 1, ensuring high gain with small errors and nonlinear limiting characteristics with large errors; δ is the saturation threshold for small errors, usually a small positive number, used to balance the linear smoothness near the origin with the error amplification effect; η is the saturation threshold for large errors and η > δ, to avoid excessive control gain in the system; coefficients The parameters are uniquely determined by the condition that the function is continuously differentiable at the piecewise points. All parameters can be tuned iteratively through simulation to optimize the system's dynamic response and anti-interference performance.

[0089] To ensure that the Ifal function is continuous and differentiable at the piecewise points, the function value and derivative must be the same on both sides of the piecewise point, i.e.:

[0090] Equation (14)

[0091] Solving for the given information, we get:

[0092] Equation (15)

[0093] The discretized expression for the novel extended state observer based on the Ifal function in step S3 is:

[0094] Equation (16)

[0095] In the formula, ε1 is the observation error of the left front wheel swing angle. For system output, To output the observed values ​​of y, for The differential signal, For observations of extended states, These are the adjustable gain parameters for the output observation, the output differential observation, and the extended state observation, respectively. It is the nonlinear gain of the control state variable observation channel; Controlling the nonlinear gain of the extended state observation channel, To control the gain, To control the voltage, The sampling period is specified. Different filter factors are used in the observer for state error and extended state. and To optimize the performance of state estimation and perturbation estimation respectively.

[0096] The design process of the super-spiral sliding mode control law in step S4 is as follows:

[0097] Given the left front wheel swing angle tracking output signal θ v θ w Based on the output observations z1 and z2 of the state observer, the discrete error signal of the left front wheel sway angle of the car shimmy system is constructed as follows:

[0098] Equation (17)

[0099] in, It is the tracking signal of the left front wheel sway angle. Compared with ESO observations The error between them It is the tracking signal of the left front wheel angular velocity. Compared with ESO observations The error between them To track the angular displacement signal output by the differentiator, To track the angular velocity signal output by the differentiator, The angular displacement observations output by the extended state observer. This refers to the angular velocity observation value output by the observer.

[0100] Taking into account the sliding modes, the superhelical sliding mode control law adopts a non-singular terminal sliding surface, and its expression is:

[0101] Equation (18)

[0102] In the formula, A constant greater than 0 , It is a positive odd number and .

[0103] Differentiating with respect to the sliding surface, we get:

[0104] Equation (19)

[0105] Traditional exponential reaching laws exhibit significant chattering near the sliding surface. To balance convergence speed and chattering, this invention introduces a hyperbolic tangent function to replace the sign function in the traditional superspiral sliding mode control algorithm, and further superimposes a linear feedback term to construct an improved superspiral sliding mode reaching law. This improved reaching law is based on the hyperbolic tangent function.

[0106] Equation (20)

[0107] In the formula, s v A1 is the first-order sliding gain coefficient of the sliding surface s, and a2 is the auxiliary state variable s. v The second-order sliding mode gain coefficient, k 01 Let k be the linear feedback gain coefficient of the sliding surface s. 02 Auxiliary state variable S v The linear feedback gain coefficient is used to enhance the damping characteristics of the system and improve the convergence speed in the neighborhood of the sliding surface; tanh is the hyperbolic tangent function.

[0108] Combining equations (19) and (20), the output control quantity, i.e., the control voltage, of the improved sliding mode active disturbance rejection controller can finally be obtained. It is given by the following formula:

[0109] Equation (21)

[0110] in, To track the angular velocity signal output by the differentiator, The estimated angular velocity output by the observer. The optimal synthesis function for fast control of the tracking differentiator is given, which tracks the angular acceleration signal output by the differentiator. This represents the total disturbance observation.

[0111] like Figure 1 As shown, Figure 1 (a) is a top view. Figure 1(b) is a front view. The vehicle shimmy system based on the electromagnetic linear actuator contains five degrees of freedom: the shimmy angle θ1 of the left front wheel around its kingpin, the shimmy angle θ2 of the right front wheel around its kingpin, the shimmy angle θ3 of the steering rocker arm in the steering system, the shimmy angle φ1 of the left front wheel axle around its shimmy center, and the shimmy angle φ2 of the right front wheel axle around its shimmy center. The electromagnetic linear actuator, as an active control unit, is integrated into the front suspension system. One end is rigidly connected to the steering tie rod, and the other end is fixed to the frame and arranged in parallel with the suspension elastic or damping elements. When shimmy is induced by road surface excitation, tire nonlinear characteristics, or system parameter perturbations during vehicle operation, the control system collects the aforementioned state variables in real time and dynamically adjusts the driving voltage applied to the electromagnetic linear actuator based on the improved sliding mode self-disturbance rejection control strategy proposed in this invention, thereby precisely controlling the magnitude and direction of its output electromagnetic force. This electromagnetic force is transmitted through the lever arm length l between its point of application and the kingpin axis. ac This is converted into an equivalent control torque around the kingpin to counteract harmful shimmy, thereby achieving active control of the wheel sway angle. Simultaneously, the reaction force generated by the electromagnetic linear actuator on the suspension system during the output of electromagnetic force is considered. This reaction force is transmitted through the suspension-vehicle connection structure and is absorbed or attenuated by the suspension's elastic and damping elements, thus avoiding adverse effects on other degrees of freedom of the system and not altering its original degree-of-freedom characteristics.

[0112] A system for implementing the improved sliding mode active disturbance rejection control method for the automobile shimmy system based on electromagnetic linear actuators includes a mathematical model establishment module, a tracking differentiator module, an extended state observer module, and a super-helical sliding mode control law module.

[0113] The mathematical model building module is used to build a mathematical model of an automobile swaying system based on an electromagnetic linear actuator.

[0114] The tracking differentiator module is used to smooth and dynamically track the desired input signal of the wheel swing angle, and extract the differential signal.

[0115] The extended state observer module integrates a continuous smooth Ifal function constructed based on the trigonometric sine function and the inverse proportional function, which is used to estimate the internal and external disturbances of the system in real time.

[0116] The super-helical sliding mode control law module is used to replace the error feedback control law in the traditional active disturbance rejection control. It outputs control voltage to drive the electromagnetic linear actuator to generate electromagnetic force, thereby realizing active control of the wheel sway angle.

[0117] The electromagnetic linear actuator is a moving-coil electromagnetic linear actuator, which outputs electromagnetic force. With control voltage satisfy:

[0118]

[0119] And this electromagnetic force is The term directly acts on the dynamic equations of the car shimmy system, where, This is the front suspension camber coefficient. The length of the lever arm.

[0120] like Figure 2 As shown, the improved sliding mode active disturbance rejection controller mainly consists of three parts: a tracking differentiator, an extended state observer, and a super-helical sliding mode control law. First, the tracking differentiator determines the desired swing angle θ of the left front wheel of the oscillating system. d Tracking is performed, and a transition process is arranged for the desired value. High-frequency noise in the command is filtered out by adjusting the filtering parameters, thereby improving control performance. An extended state observer estimates the disturbance signal in the control system and performs dynamic feedback compensation. The super-helical sliding mode control law replaces the state error feedback law in the traditional active disturbance rejection control, overcoming the defects of complex parameters and difficulty in tuning in the state error feedback control law, and enhancing the dynamic response and robustness of the control system.

[0121] Table 1 shows the relevant parameters of the vehicle sway system in this embodiment. The parameters were selected based on the design specifications, industry standards and typical engineering experience of general mid-sized passenger vehicles to ensure that the parameters meet the actual vehicle application.

[0122] Table 1 Structural parameters of automotive shimmy system

[0123] c parameter numerical values unit parameter numerical values unit <![CDATA[J0]]> 8 <![CDATA[kg∙m 2 ]]> <![CDATA[l c ]]> 0.16 m <![CDATA[J d ]]> 6 <![CDATA[kg∙m 2 ]]> <![CDATA[l d ]]> 0.126 m <![CDATA[J3]]> 3 <![CDATA[kg∙m 2 ]]> <![CDATA[l f ]]> 0.612 m <![CDATA[k1, k2]]> 1900 kN / m <![CDATA[l g ]]> 0.1 m <![CDATA[k3]]> 55 kN∙m / rad <![CDATA[l h ]]> 0.4 m <![CDATA[k4, k5]]> 30 kN / m M 1248 kg <![CDATA[k b ]]> 360 kN / m m 60 kg <![CDATA[k y ]]> 68 kN / m f 0.015 / <![CDATA[c1, c2]]> 630 N∙s / m γ 0.06 rad <![CDATA[c3]]> 80 N∙m∙s / rad β 0.08 rad <![CDATA[c4, c5]]> 2500 N∙s / m R 0.4 m <![CDATA[c e ]]> 44 N∙m∙s / rad e 0.07 m <![CDATA[l a ]]> 0.14 m <![CDATA[a t ]]> 0.2 m <![CDATA[l b ]]> 0.2 m σ 0.65 m

[0124] The control method of this invention (ISTSM-ADRC) is compared with traditional PID control, traditional active disturbance rejection controller (ADRC), and traditional sliding mode active disturbance rejection controller (SM-ADRC). Both ADRC and SM-ADRC use the traditional ESO. Regarding the control law, ADRC uses the traditional state error feedback control law u0=β1fal(e1, α1, δ1)+β2fal(e2, α2,δ2), while SM-ADRC uses s=c 01 e1+ c 02 e2's sliding surface and proportionality approach law ṡ=−k 01 s− k 02 sign(s).

[0125] To ensure fairness in the controller comparison analysis, the parameters of the active disturbance rejection controllers used were kept consistent during the parameter tuning process. It is worth noting that the parameters of the aforementioned controllers were all based on theoretical analysis and underwent multiple rounds of adjustment to ensure that each controller has a fast response speed and no overshoot.

[0126] The parameters of the control method of this invention are as follows: in the tracking differentiator, h=0.0001, r=300, h0=0.01; in the extended state observer, β 01 =300, β 02 =6×10 5 , β 03 =1.2×10 5 α 01 =0.5, α 02 =0.25, δ=0.001, η=0.05; In the improved superspiral sliding mode control law, c 01 =10, c 02 =2, p=13, q=11, a1=30, a2=0.5, k 01 =k 02 =0.1. k in the PID controller p =5000, k i = 200, k d = 10.

[0127] like Figure 3 The image shows a comparison of the characteristic curves of the improved Ifal function and the original Ifal function under a set of typical parameter conditions (α=0.25, δ=0.2, η=0.5). Figure 3 (a) shows that the fal function has a distinct inflection point at the piecewise points, where it is non-differentiable, while the Ifal function is continuous and smooth. From Figure 3 (b) It can be seen that when |ε| > η, the Ifal function exhibits a smaller error gain, avoiding overshoot; when the error is near zero, the error gain of the Ifal function is significantly greater than that of the fal function, greatly improving the system's response speed. In summary, the improved Ifal function better reflects the characteristics of "small error, large gain; large error, small gain," while overcoming the jitter problem at the piecewise ±δ points, thus improving the anti-interference capability of the control system.

[0128] To verify the ISTSM-ADRC's effectiveness in suppressing shimmy in unstable regions, the variation curves of the left front wheel sway angle and vehicle speed under different control algorithms were analyzed, such as... Figure 4 As shown in the figure. The results show that the LCO amplitude of the left front wheel sway angle under all four controllers is less than 0.0005 rad at full speed, and the unstable region is completely eliminated. Compared with PID, ADRC and SM-ADRC, ISTSM-ADRC significantly reduces the maximum LCO amplitude, verifying the effectiveness and advantages of ISTSM-ADRC.

[0129] This invention establishes a mathematical model of a car shimmy system based on an electromagnetic linear actuator; constructs a nonlinear tracking differentiator to smooth and dynamically track the desired wheel shimmy angle command signal, effectively avoiding high-frequency chattering; constructs a continuously smooth improved fal function (Ifal) based on the fusion of trigonometric sine and inverse proportional functions, and designs a novel extended state observer to estimate the system's internal and external disturbances in real time; designs a super-helical sliding mode control law based on the hyperbolic tangent function to improve control accuracy and enhance the system's ability to suppress internal and external disturbances. This invention integrates active disturbance rejection control with a super-helical sliding mode strategy, fully leveraging the advantages of both in disturbance suppression and dynamic response, effectively solving the problem of decreased control performance of traditional control methods under strongly nonlinear and multi-disturbance conditions.

[0130] It should be understood that although this specification is described according to various embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

[0131] The detailed descriptions listed above are merely specific illustrations of feasible embodiments of the present invention and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. An improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator, characterized in that, Includes the following steps: S1: To address the strong nonlinear characteristics of the system and the unknown external disturbances, a mathematical model of the automobile swaying system based on an electromagnetic linear actuator is established. S2: Construct a nonlinear tracking differentiator to process the desired input signal of the wheel sway angle, reasonably arrange the transition process, and synchronously extract the differential signal of the desired signal; S3: Construct a continuous and smooth Ifal function based on the trigonometric sine function and the inverse proportional function, and design a novel extended state observer to estimate the internal and external disturbances of the system in real time; S4: Design a super-helical sliding mode control law based on the hyperbolic tangent function to replace the error feedback control law in the traditional active disturbance rejection control, and output control voltage. .

2. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 1, characterized in that, The Ifal function mentioned in step S3 is a piecewise function, and its expression is as follows: In the formula, ε is the observation error, α is the filtering factor of the Ifal function and 0 < α < 1, δ is the small error saturation threshold, η is the large error saturation threshold and η > δ, and the coefficients are... It is uniquely determined by the condition that the function is continuously differentiable at the piecewise points.

3. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 2, characterized in that, The coefficient Calculated using the following formula: 。 4. The improved sliding mode active disturbance rejection control method for automobile shimmy system based on electromagnetic linear actuator according to claim 1, characterized in that, The discretized expression of the novel extended state observer described in step S3 is: In the formula, ε1 is the observation error of the left front wheel swing angle. For system output, To output the observed values ​​of y, for The differential signal, For observations of extended states, These are the adjustable gain parameters for the output observation, the output differential observation, and the extended state observation, respectively. It is the nonlinear gain of the control state variable observation channel; Controlling the nonlinear gain of the extended state observation channel, To control the gain, To control the voltage, The sampling period.

5. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 1, characterized in that, The discrete error signal constructed in step S4 is: in, It is the tracking signal of the left front wheel sway angle. Compared with ESO observations The error between them It is the tracking signal of the left front wheel angular velocity. Compared with ESO observations The error between them To track the angular displacement signal output by the differentiator, To track the angular velocity signal output by the differentiator, The angular displacement observations output by the extended state observer. This refers to the angular velocity observation value output by the observer.

6. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 5, characterized in that, The superspiral sliding mode control law described in step S4 uses a non-singular terminal sliding surface, and its expression is: In the formula, , , It is a positive odd number and .

7. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 6, characterized in that, The superspiral sliding mode control law adopts an improved reaching law based on the hyperbolic tangent function: In the formula, s v A1 is the first-order sliding gain coefficient of the sliding surface s, and a2 is the auxiliary state variable s. v The second-order sliding mode gain coefficient, k 01 Let k be the linear feedback gain coefficient of the sliding surface s. 02 Auxiliary state variable S v The linear feedback gain coefficient, where tanh is the hyperbolic tangent function.

8. The improved sliding mode active disturbance rejection control method for an automotive shimmy system based on an electromagnetic linear actuator according to claim 7, characterized in that, Final control voltage It is given by the following formula: in, To track the angular velocity signal output by the differentiator, The estimated angular velocity output by the observer. To track the fast control optimal synthesis function of the differentiator, This represents the total disturbance observation.

9. A system for implementing the improved sliding mode active disturbance rejection control method for an automobile shimmy system based on an electromagnetic linear actuator as described in any one of claims 1-8, characterized in that, It includes a mathematical model building module, a tracking differentiator module, an extended state observer module, and a super-helical sliding mode control law module; The mathematical model building module is used to build a mathematical model of an automobile swaying system based on an electromagnetic linear actuator. The tracking differentiator module is used to smooth and dynamically track the desired input signal of the wheel swing angle, and extract the differential signal. The extended state observer module integrates a continuous smooth Ifal function constructed based on the trigonometric sine function and the inverse proportional function, which is used to estimate the internal and external disturbances of the system in real time. The super-helical sliding mode control law module is used to replace the error feedback control law in the traditional active disturbance rejection control. It outputs control voltage to drive the electromagnetic linear actuator to generate electromagnetic force, thereby realizing active control of the wheel sway angle.

10. The system of the improved sliding mode active disturbance rejection control method for automobile shimmy system based on electromagnetic linear actuator according to claim 9, characterized in that, The electromagnetic linear actuator is a moving-coil electromagnetic linear actuator, which outputs electromagnetic force. With control voltage satisfy: And this electromagnetic force is The term directly acts on the dynamic equations of the car shimmy system, where, This is the front suspension camber coefficient. The length of the lever arm.

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