A dual-objective super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system

Abstract

This invention proposes a dual-objective superspiral sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system. The method includes: establishing a dynamic model considering nonlinearity and unknown disturbances, and transforming it into a state-space model through input-output linearization; designing a dual-objective controller for the steering angle and return port pressure of the superspiral sliding mode control system under a double-saturation function; constructing a self-adjusting factor for the proportion of multivariable principal terms in the model, and using a particle swarm optimization algorithm to optimize the control parameters, thereby completing the search for the optimal control gain and further reducing the strong chattering easily generated by the existence of high-order terms in the system state equation, and enhancing robustness; establishing an evaluation method for suppressing sliding mode chattering based on the actual change amplitude-frequency value of the sliding surface function, and verifying the effectiveness of the control method. This invention aims to achieve excellent dynamic performance, improve control accuracy, suppress chattering, and ensure rapid convergence in volumetric speed-regulating electro-hydraulic steering systems for heavy vehicles, ultimately achieving high-performance steering angle tracking control.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic power steering technology for heavy vehicles, and in particular to a dual-objective super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system. Background Technology

[0002] Heavy-duty vehicles, as core equipment in large-scale transportation projects, are widely used in national economic construction and military heavy industry sectors, including the transport of large precision instruments and construction equipment, container transport in smart unmanned ports, large-scale smart agricultural harvesting and transportation, and the fixed-point transport of weapons and equipment. With the increasing complexity and variability of driving conditions and the growing trend towards green energy conservation and intelligent assisted driving, these vehicles not only need to meet the requirements of large carrying capacity but also high efficiency, energy saving, flexible and stable driving, and driving comfort and safety. Steering control technology is a key factor affecting these performance characteristics. Due to its advantages such as high power density, wide force transmission range, flexibility, and reliability, electro-hydraulic power steering systems are increasingly widely used in heavy-duty vehicles. In recent years, volumetric speed-regulating systems, which ensure both low energy consumption and good dynamic performance, have received significant attention, but their precise steering tracking control also presents greater challenges.

[0003] Existing control methods for electro-hydraulic power steering systems in heavy-duty vehicles, such as the electro-hydraulic servo steering system and control method for multi-axle vehicles with pure rolling described in patent CN104443025B, mainly rely on a throttling speed regulation system and use a PID control strategy to achieve basic multi-axle electro-hydraulic steering control effects. Another example is the neural network integral sliding mode control method for electro-hydraulic power steering systems described in patent CN109884894B, which mainly relies on a throttling speed regulation system and further improves the nonlinear control accuracy of the system by introducing an adaptive RBF neural network algorithm to optimize the sliding mode control strategy.

[0004] Existing technologies have achieved certain results in terms of high energy efficiency and high-performance dynamic control of electro-hydraulic power steering systems for heavy vehicles, but there are still areas for improvement, mainly in the following aspects:

[0005] (1) Electro-hydraulic power steering systems often use throttling speed regulation systems for steering control. This method has excellent performance in achieving high-precision steering of heavy vehicles, but its essence is to exchange high energy consumption of valve ports for precise control. In response to the global call for energy conservation and emission reduction, volumetric speed regulation systems with high efficiency, energy saving and precise response have been developed rapidly. However, due to the variable driving conditions of vehicles, unknown external disturbances, wide load fluctuation range and constant alternation of left and right steering, direct application will cause the hydraulic cylinder inlet and outlet positions to alternate frequently, and a rapid pressure relief process is easy to occur in the cavity on the return port side, which will lead to insufficient system drive stiffness and poor stability. This problem can be solved through system structure design, but the number of controlled objects and the control difficulty are also constantly increasing.

[0006] (2) In the control methods of electro-hydraulic power steering systems, the robust sliding mode control method has been widely used in engineering applications. Compared with the earliest mature PID control method, which has advantages such as simple structure and few parameters, it abandons the direct simplification of the highly nonlinear electro-hydraulic system into a linear system for control. It fully considers that the system still needs to have strong robustness under parameter uncertainty and unknown disturbances, and can further improve control accuracy. However, due to the switching characteristics of the sliding mode control method, it is easy to generate chattering, especially in systems with high-order terms in the state space expression. This will cause the bogie to continuously shake, loosen the fasteners and accelerate the fatigue damage of mechanical parts, which will also bring great danger to the driving of heavy vehicles.

[0007] (3) In the design of the control strategy, the control signal expression consists of two parts. One part is the feedforward control signal related to the physical parameters such as flow rate and pressure that have been set in the system. The other part is the feedback control signal with the deviation from the control target as input. The accuracy of the feedforward control signal mainly depends on the accuracy of the system modeling. The feedback signal is determined by the nonlinear control method. Both have an impact on the control accuracy and system stability. In the traditional nonlinear sliding mode control strategy, there are multiple control parameters that need to be set. These parameters not only affect the robustness of the system, but also the degree of chattering when the system state enters the vicinity of the sliding surface. Ultimately, they will also affect the realization of high-performance angle tracking control of the electro-hydraulic power steering system. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a dual-objective super-spiral sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system. This method overcomes the problems of insufficient drive stiffness and poor stability that easily occur when applying high-efficiency, energy-saving, and precise volumetric speed-regulating systems to electro-hydraulic power steering systems of heavy vehicles. It ensures that the system still has strong robustness under parameter uncertainty and unknown disturbances, reduces the impact of nonlinear sliding mode control chattering on steering accuracy and stability, and ensures the rapid convergence of the control system. Ultimately, it achieves high-performance angle tracking control for an energy-saving electro-hydraulic power steering system.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: a dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system, comprising the following steps:

[0010] Step S1: Considering the nonlinearity and unknown disturbances of the volumetric speed-regulating electro-hydraulic steering system, establish a dynamic model of the volumetric speed-regulating electro-hydraulic steering system;

[0011] Step S2: Transform the dynamic model of the volumetric speed-regulating electro-hydraulic steering system into a state-space expression model using the input-output linearization method;

[0012] Step S3: Construct a dual-objective controller for the electro-hydraulic steering system, consisting of a super-helical sliding mode under a double-saturation function and a normal sliding mode, for the steering angle and return port pressure;

[0013] Step S4: In the first target parameter control, the target steering angle signal of the right wheel and the actual steering angle simulation signal collected by the angle sensor are input into the controller, and the difference between the target steering angle of the right wheel of the electro-hydraulic steering system and the actual steering angle is calculated;

[0014] Step S5: Based on the difference between the target turning angle and the actual turning angle of the right wheel of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo motor pump to control it, so that the variable speed-constant displacement pump generates output flow and output pressure, thereby forming hydraulic driving force to drive the left and right steering assist hydraulic cylinder rods of the electro-hydraulic steering system to complete the extension and retraction movement and realize the wheel steering function.

[0015] Step S6: Based on the super-helical sliding mode control law under the double saturation function, construct the self-adjusting factor of the proportion of the multivariable principal terms in the model;

[0016] Step S7: In the second target parameter control, the target pressure signal of the return port of the electro-hydraulic steering system and the actual pressure simulation signal collected by the pressure sensor are input to the controller, and the difference between the target pressure and the actual pressure of the return port of the electro-hydraulic steering system is calculated.

[0017] Step S8: Based on the difference between the target pressure and the actual pressure at the return port of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo proportional valve at the return port to control it, so that the valve core of the servo proportional valve moves to adjust the valve opening size, thereby adjusting the pressure value at the return port of the electro-hydraulic steering system.

[0018] Step S9: Based on the actual amplitude and frequency values ​​of the sliding mode functions set in the controller, establish an evaluation method for the degree of chatter suppression in the volumetric speed-regulating electro-hydraulic steering system, and verify the effectiveness of the dual-objective super-helical sliding mode control method in suppressing chattering.

[0019] In a preferred embodiment, step S1 is implemented as follows: the dynamic model of the volumetric speed-regulating electro-hydraulic steering system includes a dynamic model of the mechanical subsystem and a dynamic model of the hydraulic subsystem; the method for obtaining the dynamic model of the mechanical subsystem based on the second type of Lagrange equations is as follows:

[0020]

[0021] In Equation 1, α L and α R The steering angles h represent the left and right wheels, respectively. Rγ is the distance between the left hinge point of the tie rod and the kingpin of the right wheel, m is the length of the steering knuckle arms on both sides, γ is the angle between the steering knuckle arm and the wheel axle, and H is the distance between the left hinge point and the right wheel kingpin. L B is the length of the tie rod, and B is the distance between the two kingpins of the wheel axle.

[0022]

[0023] In Equation 2, The right wheel's steering angle acceleration, F is the steering angular velocity of the right wheel. R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n θ is the distance from the asymmetric cylinder actuation point of the power steering cylinder to the kingpin. 3L ,θ 3R These are the angles between the force applied by the left and right power steering asymmetric cylinders and the velocity at the point of application, respectively, T. L T R These are the drag torques of the left and right tires, respectively, J L J is the equivalent moment of inertia of the left wheel, steering knuckle, and steering trapezoidal arm about the left kingpin. R C represents the equivalent moment of inertia of the right wheel, steering knuckle, and steering trapezoidal arm about the right kingpin. L C R These are the equivalent damping coefficients of the left and right tires and their related components, respectively.

[0024] The method for obtaining the dynamic model of the hydraulic subsystem based on the flow continuity equation is as follows:

[0025]

[0026] In Equation 3, Let U represent the left and right turning state expressions of the electro-hydraulic steering system, respectively. Assuming left turning of the wheel is forward motion, then the directional valve voltage control signal u... s-valve >0, similarly, when turning right, u s-valve <0, u stops s-valve =0;

[0027]

[0028] In Equation 4, Q p For the output flow rate of a constant displacement-variable speed pump, D p K represents the displacement of the gear pump. m u is the voltage-speed conversion factor. motor C is the input control voltage for the servo motor. p Let p1 and p2 be the internal and external leakage coefficients of the servo motor pump, and p1 and p2 be the pressures at ports A and B of the reversing valve, respectively.

[0029]

[0030] In Equation 5, This is the derivative of the back cavity pressure. β represents the derivative of the pressure in the two chambers of the power steering hydraulic cylinder, respectively. e Let A be the effective bulk modulus, A be the area of ​​the rodless chamber of the power steering hydraulic cylinder, and a be the area of ​​the rod-side chamber of the power steering hydraulic cylinder. These represent the speeds of the left and right power steering hydraulic cylinders, C. ip C ep These are the internal and external leakage coefficients of the power steering hydraulic cylinder, V. t C is the total volume of the power steering hydraulic cylinder. d Let w be the flow coefficient of the servo proportional valve at the system return port, w be the area gradient of the servo proportional valve at the system return port, ρ be the oil density, and Δp be the pressure difference across the servo proportional valve at the return port. v The displacement of the valve core of the servo proportional valve at the oil return port.

[0031] In a preferred embodiment, step S2 is implemented by defining system state variables. And the right wheel's rotation angle is α R Angular velocity of the right wheel Back cavity pressure p t The state-space representation model is as follows:

[0032]

[0033]

[0034] In Equation 7, y1 is the input variable and is set to y1 = x1. The first derivative of the input variable. For the second derivative of the input variable, F R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n The distance from the asymmetric cylinder actuation point to the kingpin in the power steering system, u motor denoted as the voltage control signal of the servo motor pump, g is a simplified expression of the auxiliary terms of the multivariable system model, f is a simplified expression of the main terms of the multivariable system model, and d is the total disturbance term of the system.

[0035] In a preferred embodiment, step S3 is implemented as follows: the dual-target controller for the system rotation angle and return port pressure composed of the super-spiral sliding mode under the double saturation function and the ordinary sliding mode consists of a first target parameter controller and a second target parameter controller; the first target parameter controller takes the difference signal between the target rotation angle and the actual rotation angle of the right wheel as input and the servo motor pump control voltage control signal as output, and achieves precise rotation angle control through the super-spiral sliding mode control method under the double saturation function; the second target parameter controller takes the difference signal between the target pressure and the actual pressure at the return port as input and the servo proportional valve voltage control signal at the return port as output, and achieves precise return port pressure control through the ordinary sliding mode control method.

[0036] In a preferred embodiment, the method for obtaining the voltage control signal output by the controller to the servo motor pump is as follows:

[0037]

[0038] In Equation 8, u motor Let be the voltage control signal of the servo motor pump, g be the simplified expression of the auxiliary terms of the multivariable system model, f be the simplified expression of the main terms of the multivariable system model, d be the total disturbance term of the system, and ξ be the total disturbance term of the system. motor These are the characteristic coefficients of the system model function. The derivative of the super-helical sliding surface function under the double-saturated function related to the wheel steering angle tracking deviation;

[0039] The method for obtaining the voltage control signal output by the controller to the return port servo proportional valve is as follows:

[0040]

[0041] In equation (9), u valve Here, C represents the control voltage signal of the return port servo proportional valve, C is a simplified expression of the multivariable terms related to the valve orifice throttling model, and H is a simplified expression of the multivariable terms related to the system pressure model. ε is the derivative of the actual displacement of the servo proportional valve spool at the return port. v1 ε v2 For adjusting the sliding mode control rate of the servo proportional valve at the oil return port, s valve For the sliding mode function related to the return port pressure tracking deviation, -(ε v1 s valve +ε v2 sgn(s valve )) is s valve The first derivative expansion, β oil This is the oil compressibility coefficient.

[0042] In a preferred embodiment, the method for setting the double-saturation function in the first target parameter controller is as follows:

[0043]

[0044] In Equation 10, s is the sliding surface function, δ is the boundary layer thickness coefficient, and δ > 0, then the superspiral sliding control law u δ The method to obtain it is as follows:

[0045]

[0046] In Equation 11, u δ The superspiral sliding mode control law under a double-saturation function. χ is a function expression for the sliding surface, μ1≥1,μ2≥1,k1≥1,k2≥1 are the boundary layer thicknesses, and based on the boundary conditions, the following two cases exist:

[0047] ① When |s|≥δ:

[0048]

[0049] ②When |s|<δ:

[0050]

[0051] The improved super-helical sliding mode control law model is expressed as follows:

[0052]

[0053] The improved method for obtaining the voltage signal output from the controller to the servo motor pump is summarized as follows:

[0054]

[0055] In a preferred embodiment, step S6 is implemented as follows: based on the superspiral sliding mode control law under a double-saturation function, a self-adjusting factor σ for the proportion of the multivariable principal terms in the model is constructed. FFR , 0 < σ FFR If the value is ≤1, the improved method for obtaining the voltage control signal output by the controller to the servo motor pump is as follows:

[0056]

[0057] A multi-objective intelligent optimization method based on particle swarm optimization is used to optimize the control parameters of the signal, thereby achieving the optimal control gain for the difference signal between the target steering angle and the actual steering angle of the right wheel of the search steering system. The particle swarm optimization algorithm selects a multivariate principal term proportion self-adjusting factor σ. FFR Boundary layer thickness coefficient k motor1 kmotor2 μ1, μ2, and δ are the parameter dimensions N, i.e., N = 6. Since the initial positions of these 6 particles are random, the parameter range constraints of the algorithm's input vector are as follows:

[0058]

[0059] In equation (17), P i (where i = 1, 2, 3, ..., 6) are the particles of the algorithm, i.e., the input vector expression. To limit the minimum value of the parameter range for the i-th example, Let the maximum value of the parameter range for the i-th example be defined, and let be the maximum value of the parameter range. Then its input vector P satisfies P min <P<P max ;

[0060] When optimizing the parameters in the super-spiral sliding mode control method under the double saturation function, the tracking error e of the right wheel steering angle of the steering bench is selected. a The output power P of the electro-hydraulic system power component - servo motor pump motor-pump The combination of two parameters serves as the evaluation function F of the algorithm. evalution The expression is as follows:

[0061]

[0062] In Equation 18, F evalution0 Let be the fitness function of the algorithm. The smaller the evaluation function value, the larger the fitness function value, meaning the better the optimization effect; the larger the evaluation function value, the smaller the fitness function value, meaning the worse the optimization effect.

[0063] In a preferred embodiment, step S9 is implemented by: using the sliding surface function s in the superspiral sliding mode control method under the double saturation function in the first target parameter controller. motor The changing situation, the sliding surface function s in the ordinary sliding mode control method in the second target parameter controller valve The changes were analyzed, and the sliding surface variation curves were plotted and compared with those at s=0 using a sliding surface-time coordinate graph. The chattering suppression degree of the nonlinear sliding mode control method was comprehensively evaluated by using the variance of the sliding surface function change itself. The method for obtaining the variance is as follows:

[0064] ① The sliding surface s in the superspiral sliding mode control method under the double saturation function in the first objective parameter controller motor The changes are as follows:

[0065]

[0066] In Equation 19, e motorThis is the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let be the first derivative of the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let y1 = x1 be the second derivative of the difference between the target and actual steering angles of the right wheel in the electro-hydraulic steering system, λ be the sliding surface setting coefficient, and λ > 0, and y1 = x1 be the actual steering angle value of the right wheel in the electro-hydraulic steering system. 1d This represents the target steering angle value for the right wheel of the electro-hydraulic steering system.

[0067] In the sliding surface function s motor A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. motor The maximum and minimum values ​​within the sampling time, and their sliding surface function s motor Variance of the changes It is expressed as follows:

[0068]

[0069] In Equation 20, X I-m Let Im be the sample variable, where Im = 1, 2, 3, ..., n m , n is the sample mean. m The sample size is denoted as ; where the variance is . The smaller the value, the better the sliding surface function s. motor The smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s motor The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is.

[0070] ② The sliding surface s in the ordinary sliding mode control method of the second target parameter controller valve The changes are as follows:

[0071] s valve =y3-y 3d (twenty one)

[0072] In Equation 21, y3 is the actual pressure value of the return port of the electro-hydraulic steering system, y 3d This refers to the target pressure value at the return port of the electro-hydraulic steering system.

[0073] In the sliding surface function s valve A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. valve The maximum and minimum values ​​within the sampling time, and their sliding surface function s valve Variance of the changes It is expressed as follows:

[0074]

[0075] In Equation 22, X I-v (where Iv = 1, 2, 3, ..., n) v ) is the sample variable. n is the sample mean. v The sample size is denoted as ; where the variance is . The smaller the value, the better the sliding surface function s. valve The smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s valve The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] To address the issue that direct application of volumetric speed control systems to heavy-duty vehicle steering systems can easily lead to poor stiffness and stability, a servo proportional valve is proposed to be installed at the return port. By adjusting the pressure at the return port, the aforementioned problems can be effectively avoided. Considering the number of controlled objects and control performance requirements, a novel dual-objective nonlinear control strategy for angle and pressure is proposed, enabling the system to maintain excellent dynamic performance with low energy consumption. This improves the angle tracking accuracy of the electro-hydraulic power steering system while also increasing system damping and drive stiffness.

[0078] 2. To address the issue that motor speed-angle control systems with high-order terms in their state-space expressions are more prone to chattering in sliding mode control methods, a super-helical sliding mode control strategy based on a double-saturation function is proposed. This strategy not only handles unavoidable parameter uncertainties, nonlinearities, and external disturbances, but also suppresses chattering and ensures rapid convergence. The improved control method is particularly suitable for highly nonlinear volumetric speed-regulating electro-hydraulic power steering systems. Furthermore, stability analysis of the system is conducted based on Lyapunov stability theory, and a method for evaluating the degree of chattering suppression in volumetric speed-regulating electro-hydraulic steering systems is proposed, which verifies the effectiveness of the proposed control method in suppressing chattering.

[0079] 3. To address the impact of the weighting of feedforward and feedback components in the control signal and the setting of multiple control parameters on the system's control accuracy, stability, robustness, and chattering level, a self-adjusting factor for the proportion of multivariable principal terms in the model based on the super-helical sliding mode control law under a double saturation function is proposed. This further weakens chattering and enhances system robustness. Furthermore, a multi-objective intelligent optimization method based on particle swarm optimization is used to optimize the control parameters of the signal, thereby achieving the optimal control gain for the difference signal between the target steering angle and the actual steering angle of the right wheel in the search steering system. Ultimately, this achieves high-performance steering angle tracking control for the volumetric speed-regulating electro-hydraulic power steering system. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the hydraulic principle of the volumetric speed-regulating electro-hydraulic steering system described in a preferred embodiment of the present invention;

[0081] Figure 2 This is a schematic diagram of the volumetric speed-regulating electro-hydraulic steering system described in a preferred embodiment of the present invention;

[0082] Figure 3 This is a diagram of the dual-target superspiral sliding mode control strategy described in a preferred embodiment of the present invention;

[0083] Figure 4 This is a schematic flowchart of the dual-target superspiral sliding mode control method according to a preferred embodiment of the present invention;

[0084] Figure 5 This is a comparison diagram of the corner tracking performance of the dual-target super-helical sliding mode controller for the volumetric speed-regulating electro-hydraulic steering system of heavy vehicles described in the preferred embodiment of the present invention with PID and ordinary sliding mode control strategies;

[0085] Appendix Figure 1 In the middle section: 1. Oil tank, 2. Return port filter, 3. Servo motor, 4. One-way constant displacement-variable speed pump, 5. Return port check valve, 6. Outlet port check valve, 7. Check valve No. 1, 8. Outlet port filter, 9. Pressure sensor No. 1, 10. Relief valve No. 1, 11. Two-position two-way servo proportional valve, 12. Three-position four-way directional valve, 13. Check valve No. 2, 14. Hydraulic control check valve No. 1, 15. Relief valve No. 2, 16. Revolver, 17. Pressure sensor No. 2, 18. Bracket 19. Steering power assist asymmetric cylinder No. 1; 20. Left trapezoidal arm; 21. Tie rod; 22. Right trapezoidal arm; 23. Right wheel; 24. Steering power assist asymmetric cylinder No. 2; 25. Angle sensor; 26. Pressure sensor No. 3; 27. Relief valve No. 3; 28. Hydraulic control check valve No. 2; 29. ​​Check valve No. 3; 30. Two-position three-way directional valve; 31. Hydraulic valve actuator; 32. Relief valve No. 4; 33. System controller; 34. Check valve No. 4; 35. Servo motor actuator. Detailed Implementation

[0086] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0087] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0088] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations according to this application; as used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise; furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0089] As attached Figure 1 As shown, a dual-objective super-spiral sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system is disclosed for heavy vehicle steering. The volumetric speed-regulating electro-hydraulic steering system includes:

[0090] Mechanical Sub-section P3: Left wheel 16, bracket 18, left trapezoidal arm 20, tie rod 21, right trapezoidal arm 22, right wheel 23; Electro-hydraulic Sub-section: Two-position two-way servo proportional valve 11, three-position four-way directional valve 12, No. 1 power steering asymmetric cylinder 19, No. 2 power steering asymmetric cylinder 24; Power Sub-section P1: Oil tank 1, return oil filter 2, servo motor 3, one-way constant displacement-variable speed pump 4, return oil check valve 5, outlet oil check valve 6, outlet oil filter 8; Safety Circuit and Locking Sub-section: No. 1 One-way valve 7, relief valve 10, one-way valve 2 13, hydraulically controlled one-way valve 14, relief valve 2 15, relief valve 3 27, hydraulically controlled one-way valve 28, one-way valve 3 29, two-position three-way directional valve 30, relief valve 4 32, one-way valve 4 34; Data acquisition sub-section: pressure sensor 1 9, pressure sensor 2 17, angle sensor 25, pressure sensor 3 26; Intelligent control sub-section P2: hydraulic valve actuator 31, system controller 33, servo motor actuator 35;

[0091] As attached Figure 2 As shown, in this embodiment, taking a certain type of heavy-duty vehicle electro-hydraulic power steering system as an example, its relevant parameters are as follows:

[0092]

[0093] Preferably, in this embodiment, the target steering angle curve y of the right wheel is set. d The cyclic steering condition with a turning angle of 20sin(0.14πt) has a turning angle amplitude of ±20°.

[0094] As attached Figure 4 As shown, a dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system includes the following steps:

[0095] Step S1: Considering that the system still needs to have strong robustness under parameter uncertainty and unknown disturbances, a dynamic model of a volumetric speed-regulating electro-hydraulic steering system is established.

[0096] Step S2: Transform the dynamic model of the volumetric speed-regulating electro-hydraulic steering system into a state-space expression model using the input-output linearization method;

[0097] Step S3: Construct a dual-objective controller for the electro-hydraulic steering system, consisting of a super-helical sliding mode under a double-saturation function and a normal sliding mode, for the steering angle and return port pressure;

[0098] Step S4: In the first target parameter control, the target steering angle signal of the right wheel and the actual steering angle simulation signal collected by the angle sensor are input into the controller, and the difference between the target steering angle of the right wheel of the electro-hydraulic steering system and the actual steering angle is calculated;

[0099] Step S5: Based on the difference between the target turning angle and the actual turning angle of the right wheel of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo motor pump to control it, so that the variable speed-constant displacement pump generates output flow and output pressure, thereby forming hydraulic driving force to drive the left and right steering assist hydraulic cylinder rods of the electro-hydraulic steering system to complete the extension and retraction movement and realize the wheel steering function.

[0100] Step S6: Based on the super-helical sliding mode control law under the double saturation function, construct the model multivariate principal term proportion self-adjustment factor to further weaken the strong chattering phenomenon that is more likely to occur due to the existence of higher-order terms in the system state equation, and enhance the robustness of the control system.

[0101] Step S7: In the second target parameter control, the target pressure signal of the return port of the electro-hydraulic steering system and the actual pressure simulation signal collected by the pressure sensor are input to the controller, and the difference between the target pressure and the actual pressure of the return port of the electro-hydraulic steering system is calculated.

[0102] Step S8: Based on the difference between the target pressure and the actual pressure at the return port of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo proportional valve at the return port to control it, so that the valve core of the servo proportional valve moves to adjust the valve opening size, thereby adjusting the pressure value at the return port of the electro-hydraulic steering system.

[0103] Step S9: Based on the actual amplitude and frequency values ​​of the sliding mode functions set in the controller, establish an evaluation method for the degree of chatter suppression in the volumetric speed-regulating electro-hydraulic steering system, and verify the effectiveness of the dual-objective super-helical sliding mode control method in suppressing chattering.

[0104] Furthermore, the implementation method of step S1 is as follows: the dynamic model of the volumetric speed-regulating electro-hydraulic steering system mainly includes two parts: one is the dynamic model of the mechanical subsystem, and the other is the dynamic model of the hydraulic subsystem; the method for obtaining the dynamic model of the mechanical subsystem based on the second type of Lagrange equations is as follows:

[0105]

[0106] In Equation 1, α L and α R The steering angles h represent the left and right wheels, respectively. R γ is the distance between the left hinge point of the tie rod and the kingpin of the right wheel, m is the length of the steering knuckle arms on both sides, γ is the angle between the steering knuckle arm and the wheel axle, and H is the distance between the left hinge point and the right wheel kingpin. L B is the length of the tie rod, and B is the distance between the two kingpins of the wheel axle.

[0107]

[0108] In Equation 2, The right wheel's steering angle acceleration, F is the steering angular velocity of the right wheel. R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n θ is the distance from the asymmetric cylinder actuation point of the power steering cylinder to the kingpin. 3L ,θ 3R These are the angles between the force applied by the left and right power steering asymmetric cylinders and the velocity at the point of application, respectively, T. L T R These are the drag torques of the left and right tires, respectively, J L J is the equivalent moment of inertia of the left wheel, steering knuckle, and steering trapezoidal arm about the left kingpin. R C represents the equivalent moment of inertia of the right wheel, steering knuckle, and steering trapezoidal arm about the right kingpin. L C R These are the equivalent damping coefficients of the left and right tires and their related components, respectively.

[0109] The method for obtaining the dynamic model of the hydraulic subsystem based on the flow continuity equation is as follows:

[0110]

[0111] In Equation 3, Let U represent the left and right turning state expressions of the electro-hydraulic steering system, respectively. Assuming left turning of the wheel is forward motion, then the directional valve voltage control signal u... s-valve >0, similarly, when turning right, u s-valve <0, u stops s-valve =0;

[0112]

[0113] In Equation 4, Q p For the output flow rate of a constant displacement-variable speed pump, D p Where D is the displacement of the gear pump, and p =1.6×10 -5 m3 / r;K m Here is the voltage-speed conversion factor, and K m =200 / 60, meaning 1V voltage corresponds to 200r / min; u motor C is the input control voltage for the servo motor. p Let p1 and p2 be the internal and external leakage coefficients of the servo motor pump, and p1 and p2 be the pressures at ports A and B of the reversing valve, respectively.

[0114]

[0115] In Equation 5, This is the derivative of the back cavity pressure. β represents the derivative of the pressure in the two chambers of the power steering hydraulic cylinder, respectively. e Let A be the effective bulk modulus, A be the area of ​​the rodless chamber of the power steering hydraulic cylinder, and a be the area of ​​the rod-side chamber of the power steering hydraulic cylinder. These represent the speeds of the left and right power steering hydraulic cylinders, C. ip C ep These are the internal and external leakage coefficients of the power steering hydraulic cylinder, V. t C is the total volume of the power steering hydraulic cylinder. d Let w be the flow coefficient of the servo proportional valve at the system return port, w be the area gradient of the servo proportional valve at the system return port, ρ be the oil density, and Δp be the pressure difference across the servo proportional valve at the return port. v The displacement of the valve core of the servo proportional valve at the oil return port.

[0116] Furthermore, step S2 is implemented by defining system state variables. And the right wheel's rotation angle is α R Angular velocity of the right wheel Back cavity pressure p t The state-space representation model is as follows:

[0117]

[0118]

[0119] In Equation 7, y1 is the input variable and is set to y1 = x1. The first derivative of the input variable. For the second derivative of the input variable, F R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n The distance from the asymmetric cylinder actuation point to the kingpin in the power steering system, u mo t ordenoted as , where is the voltage control signal for the servo motor pump; 'g' is a simplified expression of the auxiliary terms of the multivariable system model; 'f' is a simplified expression of the main terms of the multivariable system model; and 'd' is the total disturbance term of the system. Where:

[0120]

[0121]

[0122] In equation (9), u valve Here, C represents the control voltage signal of the return port servo proportional valve, C is a simplified expression of the multivariable terms related to the valve orifice throttling model, and H is a simplified expression of the multivariable terms related to the system pressure model. ε is the derivative of the actual displacement of the servo proportional valve spool at the return port. v1 ε v2 For adjusting the sliding mode control rate of the servo proportional valve at the oil return port, s valve For the sliding mode function related to the return port pressure tracking deviation, -(ε v1 s valve +ε v2 sgn(s valve )) is s valve The first derivative expansion, β oil This is the oil compressibility coefficient.

[0123]

[0124] Define the input variable y2 = x3, and take the second derivative to obtain:

[0125]

[0126] In Equation 11, u valve Here, C represents the control voltage signal of the return port servo proportional valve, C is a simplified expression of the multivariable terms related to the valve port throttling model, H is a simplified expression of the multivariable terms related to the system pressure model, and β... oil is the oil compressibility coefficient. Where:

[0127]

[0128]

[0129]

[0130] As attached Figure 3As shown, a dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system is described. Step S3 is implemented as follows: The dual-target controller for the system's steering angle and return port pressure, composed of the super-helical sliding mode under a dual-saturation function and a conventional sliding mode, consists of two parts. The first part is a first target parameter controller, which takes the difference signal between the target steering angle and the actual steering angle of the right wheel as input and the servo motor pump control voltage control signal as output, thereby achieving precise steering angle control through the super-helical sliding mode control method under a dual-saturation function. The second part is a second target parameter controller, which takes the difference signal between the target pressure and the actual pressure at the return port as input and the return port servo proportional valve voltage control signal as output, thereby achieving precise return port pressure control through the conventional sliding mode control method.

[0131] Furthermore, the method for setting the double-saturation function in the first target parameter controller is as follows:

[0132]

[0133] In Equation 15, s is the sliding surface function, δ is the boundary layer thickness coefficient, and δ > 0, then the superspiral sliding control law u δ The method to obtain it is as follows:

[0134]

[0135] In equation (16), u δ The superspiral sliding mode control law under a double-saturation function. χ is a function expression for the sliding surface, μ1≥1,μ2≥1,k1≥1,k2≥1 are the boundary layer thicknesses, and based on the boundary conditions, the following two cases exist:

[0136] ① When |s|≥δ:

[0137]

[0138] ②When |s|<δ:

[0139]

[0140] The improved super-helical sliding mode control law model is expressed as follows:

[0141]

[0142] Furthermore, the angle control error e is defined. motor for:

[0143] e motor =y1-y 1d (20)

[0144] Construct a sliding mode function s related to the corner tracking error.motor s motor =0 is the sliding surface, and the state is made to converge to the sliding surface s by designing conditions. motor If the value is equal to 0, then the corner tracking error e can be guaranteed. motor It also converges to 0, and the sliding surface is as follows:

[0145]

[0146] In Equation 21, n is the system order. According to the linearized expression of the input-output of the corner control, n = 3, therefore:

[0147]

[0148] In Equation 22, λ > 0. Taking the derivative with respect to the sliding surface yields the dynamics of the sliding surface:

[0149]

[0150] Based on the input-output relationship of motor speed and rotation angle, establish the sliding surface s motor With controller input u motor Relationship:

[0151]

[0152] In Equation 24, Substitution and sorting We can obtain:

[0153]

[0154] The control law is derived as follows:

[0155]

[0156] In equation (26), u motor Let be the voltage control signal of the servo motor pump, g be the simplified expression of the auxiliary terms of the multivariable system model, f be the simplified expression of the main terms of the multivariable system model, d be the total disturbance term of the system, and ξ be the total disturbance term of the system. motor These are the characteristic coefficients of the system model function. This is the derivative of the superspiral sliding mode function under the double-saturated function related to the wheel steering angle tracking deviation.

[0157] The following is an analysis of system stability:

[0158] A) When s≠0

[0159] Since the set double saturation function has two cases, proving the global convergence of sliding mode dynamics requires analyzing both cases.

[0160] Case I:

[0161] As can be seen from Formula 15, when |s|≥δ, the saturation function always behaves as a sign function; definition The model is as follows:

[0162]

[0163] make and

[0164] The Lyapunov function is constructed as follows:

[0165]

[0166] Since matrix R is a positive definite symmetric matrix, the function is positive definite, continuous, and differentiable everywhere.

[0167] Taking the derivative of the Lyapunov time function, we can obtain

[0168]

[0169] And make

[0170]

[0171]

[0172] Due to the matrix All the leading principal minors are greater than zero, which indicates that: This proves that the system is convergent when |s|≥δ.

[0173] Situation II:

[0174] As can be seen from Equation 15, when |s| < δ, the saturation function always behaves as follows:

[0175]

[0176] definition The model is as follows:

[0177]

[0178] Construct the following Lyapunov function:

[0179] V = ζ T Pζ (34)

[0180] make and

[0181] Therefore, the function V(ζ) is positive definite, continuous, and differentiable everywhere.

[0182] The first derivative of ζ is as follows:

[0183]

[0184] in, Differentiating the Lyapunov time function, we get:

[0185]

[0186]

[0187] A real symmetric matrix M is positive definite if and only if all its eigenvalues ​​are greater than zero, that is, all its principal minors are greater than zero. M satisfies this condition, indicating that:

[0188] Based on the proofs for cases I and II, it can be shown that ζ will converge to zero, i.e., s. It can converge to zero, further illustrating e. If all values ​​converge to zero, the system state reaches the desired value and the system is stable. Therefore, the sliding surface has global convergence.

[0189] B) When s = 0:

[0190] We know that s = 0, And the matrix also satisfies When s≠0, it forces s to deviate from zero, thus triggering case A.

[0191] Furthermore, the implementation method of step S6 is as follows: based on the super-spiral sliding mode control law under the double saturation function, construct the self-adjusting factor σ of the proportion of the multivariable principal terms in the model. FFR (0<σ FFR If ≤1), then the improved method for obtaining the voltage control signal output by the controller to the servo motor pump is as follows:

[0192]

[0193] Furthermore, the method for obtaining the voltage control signal output by the controller to the return port servo proportional valve is as follows:

[0194]

[0195] In equation (39), u valve Here, C represents the control voltage signal of the return port servo proportional valve, C is a simplified expression of the multivariable terms related to the valve orifice throttling model, and H is a simplified expression of the multivariable terms related to the system pressure model. s is the derivative of the actual displacement of the servo proportional valve spool at the return port. valve For the sliding mode function related to the return port pressure tracking deviation, -(ε v1s valve +ε v2 sgn(s valve )) is s valve The first derivative expansion, β oil This is the oil compressibility coefficient.

[0196] The following analysis of system stability is performed, and the following Lyapunov function is designed:

[0197]

[0198] Differentiating, we get:

[0199]

[0200] This indicates that its control system is asymptotically convergent.

[0201] As attached Figure 3 As shown, a dual-objective super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system employs a multi-objective intelligent optimization method based on particle swarm optimization to optimize the control parameters of the signal. This achieves optimal control gain for the difference signal between the target right wheel steering angle and the actual steering angle of the steering system. The particle swarm optimization algorithm selects a multivariate principal term proportion self-adjusting factor σ. FFR Boundary layer thickness coefficient k motor1 k motor2 μ1, μ2, and δ are the parameter dimensions N, i.e., N = 6. Since the initial positions of these 6 particles are random, the parameter range constraints of the algorithm's input vector are as follows:

[0202]

[0203] In equation (42), P i (where i = 1, 2, 3, ..., 6) are the particles of the algorithm, i.e., the input vector expression. To limit the minimum value of the parameter range for the i-th example, Let the maximum value of the parameter range for the i-th example be defined, and let be the maximum value of the parameter range. Then its input vector P satisfies P min <P<P max ;

[0204] When optimizing the parameters in the super-spiral sliding mode control method under the double saturation function, the tracking error e of the right wheel steering angle of the steering bench is selected. a The output power P of the electro-hydraulic system power component - servo motor pump motor-pump The combination of two parameters serves as the evaluation function F of the algorithm. evalution The expression is as follows:

[0205]

[0206] In equation (43), F evalution0 Let be the fitness function of the algorithm. The smaller the evaluation function value, the larger the fitness function value, that is, the better the optimization effect, and vice versa.

[0207] Furthermore, the implementation method of step S9 is as follows: based on the sliding surface function s in the super-spiral sliding mode control method under the double saturation function in the first target parameter controller. motor The changing situation, the sliding surface function s in the ordinary sliding mode control method in the second target parameter controller valve The changes were analyzed, and the sliding surface variation curves were plotted and compared with those at s=0 using a sliding surface-time coordinate graph. The chattering suppression degree of the nonlinear sliding mode control method was comprehensively evaluated by using the variance of the sliding surface function change itself. The method for obtaining the variance is as follows:

[0208] ① The sliding surface s in the superspiral sliding mode control method under the double saturation function in the first objective parameter controller motor The changes are as follows:

[0209]

[0210] In equation (44), e motor This is the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let be the first derivative of the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let y1 = x1 be the second derivative of the difference between the target and actual steering angles of the right wheel in the electro-hydraulic steering system, λ be the sliding surface setting coefficient, and λ > 0, and y1 = x1 be the actual steering angle value of the right wheel in the electro-hydraulic steering system. 1d This represents the target steering angle value for the right wheel of the electro-hydraulic steering system.

[0211] In the sliding surface function s motor A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. motor The maximum and minimum values ​​within the sampling time, and their sliding surface function s motor Variance of the changes It is expressed as follows:

[0212]

[0213] In equation (45), X I-m (where Im = 1, 2, 3, ..., n) m ) is the sample variable. n is the sample mean. m The sample size is denoted as ; where the variance is . The smaller the value, the better the sliding surface function s. motorThe smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s motor The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is.

[0214] ② The sliding surface s in the ordinary sliding mode control method of the second target parameter controller valve The changes are as follows:

[0215] s valve =y3-y 3d (46)

[0216] In equation (46), y3 is the actual pressure value of the return port of the electro-hydraulic steering system, y 3d This refers to the target pressure value at the return port of the electro-hydraulic steering system.

[0217] In the sliding surface function s valve A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. valve The maximum and minimum values ​​within the sampling time, and their sliding surface function s valve Variance of the changes It is expressed as follows:

[0218]

[0219] In equation (47), X I-v (where Iv = 1, 2, 3, ..., n) v ) is the sample variable. n is the sample mean. v The sample size is denoted as ; where the variance is . The smaller the value, the better the sliding surface function s. valve The smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s valve The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is.

[0220] Finally, the experimental results of the volumetric speed-regulating electro-hydraulic steering system are attached. Figure 5 As shown, sub Figure 1 This is a diagram showing the angle tracking under a PID control strategy. Figure 2 This is a rotation tracking diagram under a common sliding mode control strategy. Figure 4The diagram shows the angle tracking under the control strategy described in this patent. It can be seen that the dual-objective superspiral sliding mode controller for heavy-duty vehicle volumetric speed-regulating electro-hydraulic steering systems designed in this invention enables the system to maintain excellent dynamic performance with low energy consumption. It can also handle unavoidable parameter uncertainties, nonlinearities, and external disturbances, suppress chattering, ensure fast convergence, and achieve high-performance angle tracking control. Furthermore, compared to the angle tracking diagrams of PID and ordinary sliding mode control strategies, the heavy-duty vehicle volumetric speed-regulating electro-hydraulic steering system exhibits the smallest steady-state angle tracking error and the best tracking effect under the designed dual-objective superspiral sliding mode control. These experimental results demonstrate that the control method designed in this invention has superior transient response and better system robustness.

[0221] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A dual-target superspiral sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system, characterized in that, Includes the following steps: Step S1: Considering the nonlinearity and unknown disturbances of the volumetric speed-regulating electro-hydraulic steering system, establish a dynamic model of the volumetric speed-regulating electro-hydraulic steering system; Step S2: Transform the dynamic model of the volumetric speed-regulating electro-hydraulic steering system into a state-space expression model using the input-output linearization method; Step S3: Construct a dual-objective controller for the electro-hydraulic steering system, consisting of a super-helical sliding mode under a double-saturation function and a normal sliding mode, for the steering angle and return port pressure; Step S4: In the first target parameter control, the target steering angle signal of the right wheel and the actual steering angle simulation signal collected by the angle sensor are input into the controller, and the difference between the target steering angle of the right wheel of the electro-hydraulic steering system and the actual steering angle is calculated; Step S5: Based on the difference between the target turning angle and the actual turning angle of the right wheel of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo motor pump to control it, so that the variable speed-constant displacement pump generates output flow and output pressure, thereby forming hydraulic driving force to drive the left and right steering assist hydraulic cylinder rods of the electro-hydraulic steering system to complete the extension and retraction movement and realize the wheel steering function. Step S6: Based on the super-helical sliding mode control law under the double saturation function, construct the self-adjusting factor of the proportion of the multivariable principal terms in the model; Step S7: In the second target parameter control, the target pressure signal of the return port of the electro-hydraulic steering system and the actual pressure simulation signal collected by the pressure sensor are input to the controller, and the difference between the target pressure and the actual pressure of the return port of the electro-hydraulic steering system is calculated. Step S8: Based on the difference between the target pressure and the actual pressure at the return port of the electro-hydraulic steering system, the controller outputs a voltage control signal to the servo proportional valve at the return port to control it, so that the valve core of the servo proportional valve moves to adjust the valve opening size, thereby adjusting the pressure value at the return port of the electro-hydraulic steering system. Step S9: Based on the actual amplitude and frequency values ​​of the sliding mode functions set in the controller, establish an evaluation method for the degree of chatter suppression in the volumetric speed-regulating electro-hydraulic steering system, and verify the effectiveness of the dual-objective super-helical sliding mode control method in suppressing chattering. The implementation method of step S3 is as follows: the dual-target controller for the rotation angle and return port pressure of the system composed of the super spiral sliding mode under the double saturation function and the ordinary sliding mode consists of a first target parameter controller and a second target parameter controller; the first target parameter controller takes the difference signal between the target rotation angle and the actual rotation angle of the right wheel as input and the servo motor pump control voltage control signal as output, and achieves precise rotation angle control through the super spiral sliding mode control method under the double saturation function; the second target parameter controller takes the difference signal between the target pressure and the actual pressure of the return port as input and the return port servo proportional valve voltage control signal as output, and achieves precise return port pressure control through the ordinary sliding mode control method; The method for setting the double saturation function in the first target parameter controller is as follows: In Equation 10, s is the sliding surface function, δ is the boundary layer thickness coefficient, and δ > 0, then the superspiral sliding control law u δ The method to obtain it is as follows: In Equation 11, u δ The superspiral sliding mode control law under a double-saturation function. χ is a function expression for the sliding surface, μ1≥1,μ2≥1,k1≥1,k2≥1 are the boundary layer thicknesses, and based on the boundary conditions, the following two cases exist: ① When |s|≥δ: ②When |s|<δ: The improved super-helical sliding mode control law model is expressed as follows: The improved method for obtaining the voltage signal output from the controller to the servo motor pump is summarized as follows:

2. The dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system according to claim 1, characterized in that, The implementation method of step S1 is as follows: the dynamic model of the volumetric speed-regulating electro-hydraulic steering system includes the dynamic model of the mechanical subsystem and the dynamic model of the hydraulic subsystem; the method for obtaining the dynamic model of the mechanical subsystem based on the second type of Lagrange equations is as follows: In Equation 1, α L and α R The steering angles h represent the left and right wheels, respectively. R γ is the distance between the left hinge point of the tie rod and the kingpin of the right wheel, m is the length of the steering knuckle arms on both sides, γ is the angle between the steering knuckle arm and the wheel axle, and H is the distance between the left hinge point and the right wheel kingpin. L B is the length of the tie rod, and B is the distance between the two kingpins of the wheel axle. In Equation 2, The right wheel's steering angle acceleration, F is the steering angular velocity of the right wheel. R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n θ is the distance from the asymmetric cylinder actuation point of the power steering cylinder to the kingpin. 3L θ 3R These are the angles between the force applied by the left and right power steering asymmetric cylinders and the velocity at the point of application, respectively, T. L T R These are the drag torques of the left and right tires, respectively, J L J is the equivalent moment of inertia of the left wheel, steering knuckle, and steering trapezoidal arm about the left kingpin. R C represents the equivalent moment of inertia of the right wheel, steering knuckle, and steering trapezoidal arm about the right kingpin. L C R These are the equivalent damping coefficients of the left and right tires and their related components, respectively. The method for obtaining the dynamic model of the hydraulic subsystem based on the flow continuity equation is as follows: In Equation 3, Let U represent the left and right turning state expressions of the electro-hydraulic steering system, respectively. Assuming left turning of the wheel is forward motion, then the directional valve voltage control signal u... s-valve >0, similarly, when turning right, u s-valve <0, u stops s-valve =0; In Equation 4, Q p For the output flow rate of a constant displacement-variable speed pump, D p K represents the displacement of the gear pump. m u is the voltage-speed conversion factor. motor C is the input control voltage for the servo motor. p Let p1 and p2 be the internal and external leakage coefficients of the servo motor pump, and p1 and p2 be the pressures at ports A and B of the reversing valve, respectively. In Equation 5, This is the derivative of the back cavity pressure. β represents the derivative of the pressure in the two chambers of the power steering hydraulic cylinder, respectively. e Let A be the effective bulk modulus, A be the area of ​​the rodless chamber of the power steering hydraulic cylinder, and a be the area of ​​the rod-side chamber of the power steering hydraulic cylinder. These represent the speeds of the left and right power steering hydraulic cylinders, C. ip C ep These are the internal and external leakage coefficients of the power steering hydraulic cylinder, V. t C is the total volume of the power steering hydraulic cylinder. d Let w be the flow coefficient of the servo proportional valve at the system return port, w be the area gradient of the servo proportional valve at the system return port, ρ be the oil density, and Δp be the pressure difference across the servo proportional valve at the return port. v The displacement of the valve core of the servo proportional valve at the oil return port.

3. The dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system according to claim 1, characterized in that, The implementation method for step S2 is as follows: Define system state variables. And the right wheel's rotation angle is α R Angular velocity of the right wheel Back cavity pressure p t The state-space representation model is as follows: In Equation 7, y1 is the input variable and is set to y1 = x1. The first derivative of the input variable. For the second derivative of the input variable, F R For the thrust of the right steering assist asymmetric cylinder, F L For the thrust of the left steering assist asymmetric cylinder, h n The distance from the asymmetric cylinder actuation point to the kingpin in the power steering system, u motor denoted as the voltage control signal of the servo motor pump, g is a simplified expression of the auxiliary terms of the multivariable system model, f is a simplified expression of the main terms of the multivariable system model, and d is the total disturbance term of the system.

4. The dual-target superspiral sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system according to claim 1, characterized in that, The method for obtaining the voltage control signal output by the controller to the servo motor pump is as follows: In Equation 8, u motor Let be the voltage control signal of the servo motor pump, g be the simplified expression of the auxiliary terms of the multivariable system model, f be the simplified expression of the main terms of the multivariable system model, d be the total disturbance term of the system, and ξ be the total disturbance term of the system. motor These are the characteristic coefficients of the system model function. The derivative of the super-helical sliding surface function under the double-saturated function related to the wheel steering angle tracking deviation; The method for obtaining the voltage control signal output by the controller to the return port servo proportional valve is as follows: In equation (9), u valve Here, C represents the control voltage signal of the return port servo proportional valve, C is a simplified expression of the multivariable terms related to the valve orifice throttling model, and H is a simplified expression of the multivariable terms related to the system pressure model. ε is the derivative of the actual displacement of the servo proportional valve spool at the return port. v1 ε v2 For adjusting the sliding mode control rate of the servo proportional valve at the oil return port, s valve For the sliding mode function related to the return port pressure tracking deviation, -(ε v1 s valve +ε v2 sgn(s valve )) is s valve The first derivative expansion, β oil This is the oil compressibility coefficient.

5. The dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system according to claim 1, characterized in that, The implementation method of step S6 is as follows: Based on the super-spiral sliding mode control law under the double saturation function, construct the self-adjusting factor σ of the proportion of the multivariable principal terms in the model. FFR 0<σ FFR If the value is ≤1, the improved method for obtaining the voltage control signal output by the controller to the servo motor pump is as follows: A multi-objective intelligent optimization method based on particle swarm optimization is used to optimize the control parameters of the signal, thereby achieving the optimal control gain for the difference signal between the target steering angle and the actual steering angle of the right wheel of the search steering system. The particle swarm optimization algorithm selects a multivariate principal term proportion self-adjusting factor σ. FFR Boundary layer thickness coefficient k motor1 k motor2 μ1, μ2, and δ are the parameter dimensions N, i.e., N = 6. Since the initial positions of these 6 particles are random, the parameter range constraints of the algorithm's input vector are as follows: In equation (17), P i Let i be the particles in the algorithm, where i = 1, 2, 3, ..., 6, i.e., the input vector expression. To limit the minimum value of the parameter range for the i-th example, Let the maximum value of the parameter range for the i-th example be defined, and let be the maximum value of the parameter range. Then its input vector P satisfies P min <P<P max ; When optimizing the parameters in the super-spiral sliding mode control method under the double saturation function, the tracking error e of the right wheel steering angle of the steering bench is selected. a The output power P of the electro-hydraulic system power component - servo motor pump motor-pump The combination of two parameters serves as the evaluation function F of the algorithm. evalution The expression is as follows: In Equation 18, F evalution0 Let be the fitness function of the algorithm. The smaller the evaluation function value, the larger the fitness function value, meaning the better the optimization effect; the larger the evaluation function value, the smaller the fitness function value, meaning the worse the optimization effect.

6. The dual-target super-helical sliding mode control method for a volumetric speed-regulating electro-hydraulic steering system according to claim 1, characterized in that, The implementation method of step S9 is as follows: based on the sliding surface function s in the super-spiral sliding mode control method under the double saturation function in the first target parameter controller. motor The changing situation, the sliding surface function s in the ordinary sliding mode control method in the second target parameter controller valve The changes were analyzed, and the sliding surface variation curves were plotted and compared with those at s=0 using a sliding surface-time coordinate graph. The chattering suppression degree of the nonlinear sliding mode control method was comprehensively evaluated by using the variance of the sliding surface function change itself. The method for obtaining the variance is as follows: ① The sliding surface s in the superspiral sliding mode control method under the double saturation function in the first objective parameter controller motor The changes are as follows: In Equation 19, e motor This is the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let be the first derivative of the difference between the target steering angle and the actual steering angle of the right wheel in the electro-hydraulic steering system. Let y1 = x1 be the second derivative of the difference between the target and actual steering angles of the right wheel in the electro-hydraulic steering system, λ be the sliding surface setting coefficient, and λ > 0, and y1 = x1 be the actual steering angle value of the right wheel in the electro-hydraulic steering system. 1d This represents the target steering angle value for the right wheel of the electro-hydraulic steering system. In the sliding surface function s motor A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. motor The maximum and minimum values ​​within the sampling time, and their sliding surface function s motor Variance of the changes It is expressed as follows: In Equation 20, X I-m Let Im be the sample variable, where Im = 1, 2, 3, ..., n m , n is the sample mean. m The sample size is denoted as ; where the variance is denoted as . The smaller the value, the better the sliding surface function s. motor The smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s motor The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is. ② The sliding surface s in the ordinary sliding mode control method of the second target parameter controller valve The changes are as follows: s valve =y3-y 3d (21) In Equation 21, y3 is the actual pressure value of the return port of the electro-hydraulic steering system, y 3d This refers to the target pressure value at the return port of the electro-hydraulic steering system. In the sliding surface function s valve A suitable number of chatter suppression evaluation sample points are selected from the variation curve, including but not limited to the sliding surface function s. valve The maximum and minimum values ​​within the sampling time, and their sliding surface function s valve Variance of the changes It is expressed as follows: In Equation 22, X I-v Let Iv be the sample variable, where Iv = 1, 2, 3, ..., n v , n is the sample mean. v The sample size is denoted as ; where the variance is denoted as . The smaller the value, the better the sliding surface function s. valve The smaller the fluctuation of the change around the sample mean, i.e., the smaller the sliding mode surface function s valve The more stable the changes, the closer the sample mean is to s=0, the more obvious the flutter suppression is.

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