A neural network compensation-based adaptive robust control method for a pump-valve parallel steering system

Abstract

The application discloses a pump-valve parallel steering system adaptive robust control method based on neural network compensation, comprising: establishing a comprehensive dynamic model of a pump-valve cooperative electro-hydraulic steering system, describing an upper trapezoidal steering mechanical model, and describing a hydraulic model by means of a hydraulic cylinder power balance equation, a flow continuity equation and a servo valve flow equation. A virtual control torque is designed, an RBF neural network is designed to provide online approximation and compensation for a high-frequency dynamic compensation component of the virtual control torque. A decoupling control input is designed, a hydraulic damping coefficient is taken as an uncertain parameter, and a parameter adaptive law is constructed. The virtual control flow is linearly transformed into a control voltage of a servo motor pump and a servo proportional valve, and the steering system is adaptively and robustly controlled in real time. The application can effectively solve the problems of high-order nonlinearity, flow coupling, parameter time-varying and disturbance suppression of the system, and significantly improve the tracking accuracy, error convergence speed and complex working condition robustness of the pump-valve cooperative steering system.

Description

Technical Field

[0001] This invention relates to the field of electro-hydraulic control technology, and in particular to an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation. Background Technology

[0002] As core equipment for heavy-duty transportation, the electro-hydraulic steering system (EHSS) of heavy-duty multi-axle vehicles directly determines the mobility and safety of transportation. While traditional valve-controlled EHSS offers good control precision and stability, it suffers from inherent throttling losses and high energy consumption. Pump-controlled EHSS, although improving energy efficiency, suffers from limited dynamic response, making it difficult to adapt to the high-frequency micro-adjustment steering requirements of heavy-duty vehicles. Furthermore, mainstream steering systems cannot achieve independent wheel steering, limiting steering modes and flexibility. Therefore, a pump-valve synergy (PVC) EHSS, integrating pump-controlled flow dynamic regulation and valve-controlled symmetrical cylinder synchronous extension and retraction control, has been proposed. This system can achieve 2-DOF independent steering, balancing energy efficiency and multi-mode steering potential. Although PVC-EHSS shows significant potential in improving energy efficiency and achieving multi-mode steering, its main problem is low control precision, limiting actual steering performance, specifically in the following aspects:

[0003] The mechanical-hydraulic coupling exhibits high-order strong nonlinear characteristics and also has problems such as the flow coupling of the pump and valve subsystem, the dynamic time-varying of key parameters such as the damping coefficient of the hydraulic cylinder with the characteristics of hydraulic pressure and flow velocity, insufficient internal friction compensation of the hydraulic cylinder, and unmodeled mechanical dynamics and external disturbances caused by uneven road surface and cargo swaying, resulting in low control accuracy.

[0004] Traditional PID control is based solely on error feedback and ignores system dynamics. Under complex nonlinear conditions, the tracking error is significant. Although methods such as sliding mode control and high-gain extended state observers can suppress disturbances to a certain extent, they do not fully consider the influence of friction within the hydraulic cylinder and have limited adaptive capabilities to time-varying parameters. While adaptive control can estimate time-varying parameters online, it is difficult to quickly compensate for high-frequency unmodeled disturbances.

[0005] Radial basis function neural networks (RBFNNs) have the advantage of rapidly approximating time-varying nonlinear functions. Direct / indirect adaptive robust control (DIARC) can effectively handle high-order nonlinearity and time-varying parameter problems of the system, providing a suitable technical path for solving the control problem of PVC-EHSS, and also becoming an important technical foundation for the design of controllers by integrating related technologies in this research. Summary of the Invention

[0006] In view of this, the purpose of this invention is to provide an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation. By using radial basis function neural network (RBFNN) assistance, the tracking error is ensured to converge rapidly, providing a suitable technical path for solving the control problem of PVC-EHSS.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation, comprising:

[0008] Step 1: Establish a comprehensive dynamic model of the pump-valve coordinated electro-hydraulic steering system. The upper trapezoidal steering mechanical model is described by the Lagrange dynamic equation, and the hydraulic model is described by the hydraulic cylinder dynamic balance equation, the flow continuity equation, and the servo valve flow equation.

[0009] Step 2: Design virtual control torque, and provide online approximation and compensation for its high-frequency dynamic compensation components by designing an RBF neural network; design decoupled control input, take the hydraulic damping coefficient as an uncertain parameter, construct a parameter adaptive law, and obtain virtual control flow by combining time-varying model feedforward and robust feedback;

[0010] Step 3: Linearly transform the virtual control flow into the control voltage of the servo motor pump and servo proportional valve to control the pump-valve coordinated electro-hydraulic steering system; repeat steps 1 to 3 to achieve adaptive robust real-time control of the pump-valve coordinated electro-hydraulic system; use the Lyapunov method to prove the bounded stability of the controller and the convergence of parameter estimation.

[0011] In a preferred embodiment, the comprehensive dynamic model of the pump-valve coordinated electro-hydraulic steering system in step one is as follows:

[0012]

[0013] in, and These represent the angular accelerations of the right and left wheels, respectively. and F represents the angular velocity of the right wheel and the left wheel, respectively. dR and F dL These represent the unmodeled dynamic and disturbance terms for the left and right wheels, respectively; J L and J R C represents the equivalent moments of inertia of the left and right tires, respectively; L and C R These are the equivalent damping values ​​for the left and right tires, respectively. The elastic modulus of the oil; and These represent the inlet flow rate and outlet flow rate of the electromagnetic directional valve, respectively. and These represent the displacements of the pistons in the left and right booster cylinders, respectively. and These represent the inlet and outlet oil pressures of the solenoid directional valve, respectively. and F represents the first derivative of the inlet and outlet oil pressures of the solenoid directional valve, respectively; L and F R These represent the output force of the left and right power assist cylinders, respectively; F HL and F HR These represent the output forces of the left and right chambers of the tie rod, respectively; n is the distance from the hinge point between the steering knuckle arm and the power steering cylinder to the line connecting the steering knuckle arm and the axle; m is the length of the steering knuckle arm; M L and M R These are the steering damping moments for the left and right tires, respectively; θ L and θ R These are the angles between the piston speed of the left power steering cylinder and the tangential speed of the left steering knuckle arm, and the angles between the piston speed of the right power steering cylinder and the tangential speed of the right steering knuckle arm, respectively; θ HL and θ HR These are the angles between the piston speed of the tie rod cylinder and the tangential speed of the left and right joints, respectively; A and a are the areas of the large and small chambers of the power steering cylinder, respectively; C... ip and C ep The main system internal and external leakage, V1 and V2 are the left and right main chambers of the dual booster cylinder; and These represent the displacements of the pistons in the left and right booster cylinders, respectively. p represents the speed of the piston in the tie rod cylinder. H1 and p H2 These are the inlet and outlet oil pressures of the servo proportional valve, respectively. and Take the first derivatives of the inlet and outlet oil pressures of the servo proportional valve, respectively; q H1 and q H2 These are the inlet and outlet oil flow rates through the servo proportional valve, respectively; A H C is the piston area of ​​the tie rod cylinder; Hip and C Hep These are internal and external leaks in the tie rod cylinder, respectively. The pump output flow rate; u m k m n m , These are the control voltage, dynamic gain, speed, and time constant of the servo motor, respectively; k T T is the gain due to the change in speed caused by the motor load torque; L The load torque of the servo motor is expressed as follows: D P For pump displacement, Take the first derivative of the pump output pressure; V p q represents the volume of the pump outlet oil chamber and the pipeline cavity; LP Main system load traffic; q LA To assist the system load flow; The first derivative of the servo motor's rotational speed.

[0014] In a preferred embodiment, in step two, the virtual control torque is designed as follows:

[0015]

[0016]

[0017]

[0018] Among them, F 1d and F 2d F represents the virtual control torque of the left and right wheels, respectively. 1dm1 and F 2dm1 F represents the feedforward model compensation term for the left and right wheels; 1dm2 and F 2dm2 These represent the rapid dynamic compensation terms for the left and right wheels, respectively; F 1ds1 and F 2ds1 These represent the linear feedback terms for the left and right wheels, respectively; F 1ds2 and F 2ds2 These represent the nonlinear feedback terms of the left and right wheels, respectively.

[0019] The feedforward compensation term and linear feedback term of the virtual control torque model are as follows:

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where e1 and e3 represent the tracking errors of the right and left wheels of the pump-valve coordinated electro-hydraulic steering system, respectively; ; and These represent the turning angles of the right and left wheels, respectively. They represent and The target value; They represent and The first derivative of the target value; x2 and x4 represent the angular velocities of the right and left wheels, respectively; x 2eq and x 4eqLet x2 and x4 represent the target values ​​respectively, P1 and P2 represent the synovial membrane amounts on both sides respectively, and k1 and k4 both represent the positive definite coefficients of the synovial membrane amounts; This represents the feedforward model compensation term for the left wheel. This represents the equivalent moment of inertia of the right tire. This represents the first derivative of the target value of x2. This indicates the steering damping torque of the right tire. This represents the equivalent damping of the right tire. This represents the estimated values ​​of the unmodeled dynamics and disturbance terms of the right wheel; This represents the feedforward model compensation term for the right wheel. This represents the equivalent moment of inertia of the left tire. This represents the first derivative of the target value of x4. This indicates the steering damping torque of the left tire. This represents the equivalent damping of the left tire. This represents the estimated values ​​of the unmodeled dynamics and disturbance terms of the revolver. , Both represent the proportional gain of linear robust feedback.

[0026] In a preferred embodiment, in step two, the high-frequency dynamic compensation component is specifically designed using an RBF neural network as follows:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032]

[0033] Where d1 and d2 represent static compensation components, , Represented as high-frequency dynamic compensation components; O1 and O2 serve as the network input vectors for the left and right wheels, respectively; and F dR and F dL The error value; P1 and P2 represent the amount of synovial membrane on both sides, respectively; Represents a 5-dimensional real vector space; Let represent the radial basis function of the j-th hidden layer neuron; Represented as a vector of hidden layer basis functions; This represents the input vector of the neural network; represents the center vector of the j-th Gaussian kernel function; j represents the index of the hidden layer neuron; i represents the number of hidden layer neuron nodes in the RBF neural network, where i=5; denoted as the width parameter of the RBF neural network; p and q represent the index of the hidden layer neurons; Let represent the center vectors of the Gaussian radial basis functions corresponding to the p-th neuron and the q-th neuron; M represents the total number of unique center pairs. Indicates the discontinuous projection operator; This represents the weight estimate of the j-th neuron; This is expressed as the adaptive weight update law; where >0 indicates the learning rate; > 0 is used as the weight decay factor; T represents transpose; e2 and e4 represent the errors between the virtual control torque of the left and right wheels and the backstep target value, respectively; e1 and e3 represent the tracking errors of the right and left wheels of the pump-valve coordinated electro-hydraulic steering system, respectively; P1 and P2 represent the quasi-slippery amount on both sides, respectively; P1 and P2 represent the quasi-slippery amount on both sides, respectively. and These represent the inlet and outlet oil pressures of the solenoid directional valve, respectively.

[0034] The fast dynamics compensation term and the nonlinear feedback term are as follows:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] Among them, F 1dm2 and F 2dm2 These represent the rapid dynamic compensation terms for the left and right wheels, respectively; , Represented as the predicted value of the static compensation component; and express and The first derivative; This represents a pre-set estimated value; and They represent The upper and lower boundaries; and It is represented as a positive constant; The functional relationship representing the projection mapping; , Represented as high-frequency dynamic compensation components; and They represent RBF for and Online estimation; and These represent the error values ​​of the left and right wheels approximated by the neural network, respectively. and This represents the system state variable, which is the network input vector mentioned earlier. / ; and All positive numbers >0 are arbitrarily small positive numbers; and y1 and y2 represent the parameter estimation errors of the static disturbance components of the right and left wheels, respectively; y1 and y2 both represent bounded upper bound functions of the system uncertainty. and These represent the transposes of the weight estimates for the first neuron and the transposes of the weight estimates for the second neuron, respectively. , F represents the hidden layer output vector of a neural network. 1ds2 and F 2ds2 These represent the nonlinear feedback terms of the left and right wheels, respectively.

[0043] In a preferred embodiment, in step two, the virtual control traffic is specifically as follows:

[0044]

[0045]

[0046]

[0047] Among them, Q 1d and Q 2d These represent the virtual control flow of the left and right wheels, respectively; Q 1dm1 and Q 2dm1 This represents the feedforward model compensation term; Q 1dm2 and Q 2dm2 These represent its fast dynamic compensation term; Q 1ds1 and Q 2ds1 These represent its linear feedback term; Q 1ds2 and Q 2ds2 These represent their nonlinear feedback terms;

[0048] The feedforward compensation term and linear feedback term of the virtual control flow model are as follows:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057]

[0058]

[0059] in, and Both represent adaptive regression vectors; Indicates parameters and The estimated vector; Don't represent parameters and The estimated vector; This represents the online estimate of the viscous damping coefficient of the right main steering cylinder; This represents the online estimate of the viscous damping coefficient of the right main steering cylinder; V1 and V2 represent the online estimated value of the viscous damping coefficient of the tie rod cylinder; V1 and V2 are the left and right total volumes of the dual-boost cylinder. and These represent the displacements of the pistons in the left and right booster cylinders, respectively; A H Here, e1 represents the piston area of ​​the tie rod cylinder; e2 and e4 represent the errors between the virtual control torques of the left and right wheels and the target values ​​of the backstepping, respectively. and These represent the equivalent driving torques of the right-wheel and left-wheel steering mechanisms, respectively. and They represent and The estimated value; B represents the acceleration of the piston in the tie rod cylinder. R B L BH These represent the damping coefficients of the right, left, and tie rod hydraulic cylinders, respectively; f1~f4 and g1~g4 are Q... 1dm1 and Q 2dm1 The linearization coefficients simplify the model structure;

[0060] The fast dynamic compensation term and nonlinear feedback term of the virtual control flow are as follows:

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] and Both represent positive linear feedback gain coefficients; d3 and d4 represent the static terms of rapid compensation in the hydraulic model, respectively. , These are respectively represented as the high-frequency dynamic components of rapid compensation; and These represent the tracking deviations of the dynamic changes in the equivalent driving torque target of the right-wheel and left-wheel steering mechanisms, respectively. and These represent the online estimates of low-frequency static disturbances d3 and d4, respectively. and These represent the update rates of parameters d3 and d4, respectively. and It is represented as a positive constant; The functional relationship representing the projection mapping; and y3 and y4 represent the estimation errors of d3 and d4, respectively; y3 and y4 both represent bounded upper bound functions of the system uncertainty. and All numbers greater than 0 are arbitrarily small positive numbers.

[0067] In a preferred embodiment, step two, which involves constructing the parameter adaptive law, is as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075]

[0076]

[0077] in, This refers to the total torque of the power assist cylinder and the tie rod cylinder; The kinematic transfer matrix represents the damping force; This represents the model's uncertainty and external disturbances; Represents the vector of unknown parameters to be estimated; express Online matrix estimation; Q(s) is represented as a first-order filter; Y R Defined as a computable observation signal. This is expressed as the error between the observed value and the estimated value; Represents a saturation function; Represents the slowly varying parameter matrix of the system The derivative of the parameter estimation matrix; Indicates that the input is Projective mapping functions; Indicates the forgetting factor; This represents the linear regression matrix used in online squared estimation of a nonlinear dynamic model. This indicates the maximum preset parameter update rate; Represents an input vector; Represents the feasible parameter set The boundary, s represents The external unit normal vector at that location.

[0078] In a preferred embodiment, in step three, the virtual control flow of the left and right wheels is linearly transformed into the control voltage of the servo motor pump and the servo proportional valve, as follows:

[0079]

[0080] Wherein, the coupling matrix coefficients are

[0081] in, This indicates the actual input control voltage of the servo motor pump. This indicates the control voltage of the directional valve in the pump control circuit; This represents the actual input control voltage of the servo proportional valve. and The target flow rates of the right and left wheel master steering cylinders are represented respectively; Q represents the virtual control flow rate; and L represents the mapping relationship between the virtual control flow rate Q and the actual input control voltage u of the proportional valve of the pump-valve coordinated steering system. Indicates pump control input Right wheel flow The influence coefficient; Indicates valve-controlled input Right wheel flow The influence coefficient; Indicates pump control input For left wheel flow The influence coefficient; Indicates valve-controlled input For left wheel flow The influence coefficient; This indicates the flow coefficient of the solenoid valve. Indicates the valve opening gain; Represents a symbolic function; This represents the pump control dynamic coefficient of the right wheel master cylinder; This indicates the valve-controlled dynamic system of the right wheel tie rod cylinder; This represents the pump control dynamic coefficient of the left wheel master cylinder; This represents the valve control dynamic coefficient of the left wheel tie rod cylinder.

[0082] The present invention also provides an electronic device, comprising: a memory and a processor coupled to each other, wherein the memory stores program data, and the processor invokes the program data to execute an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation as described above.

[0083] The present invention also provides a computer-readable storage medium storing program data thereon, which, when executed by a processor, implements an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation as described above.

[0084] Compared with the prior art, the present invention has the following beneficial effects: the present invention can effectively solve the problems of high-order nonlinearity, flow coupling, time-varying parameters and disturbance suppression in the system, and significantly improve the tracking accuracy, error convergence speed and robustness under complex working conditions of the pump-valve coordinated steering system. Attached Figure Description

[0085] Figure 1 This is a schematic diagram of the pump-valve coordinated electro-hydraulic steering system of the present invention;

[0086] Figure 2 This is a block diagram of the adaptive robust control system of the pump-valve coordinated electro-hydraulic steering system of the present invention;

[0087] Figure 3 This is a simulation curve of the left wheel's steering angle error in the adaptive robust controller of the pump-valve coordinated electro-hydraulic steering system of the present invention.

[0088] Figure 4 This is a simulation curve of the right wheel's steering angle error in the adaptive robust controller of the pump-valve coordinated electro-hydraulic steering system of the present invention. Detailed Implementation

[0089] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0090] 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.

[0091] 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.

[0092] like Figure 1 As shown, the pump-valve coordinated electro-hydraulic steering system of the present invention includes an upper mechanical system and a hydraulic system:

[0093] (1) Mechanical system: The system consists of a two-degree-of-freedom trapezoidal steering mechanism composed of left and right steering knuckle arms 2, 6, left and right tie rods 3, 5, tie rod cylinder 4, left and right power steering cylinders 8, 9, and axle 10, and left and right tires 1, 7. It is worth mentioning that the two-degree-of-freedom trapezoidal steering mechanism converts the linear motion of the left and right power steering cylinders into the steering motion of the left and right tires through the left and right steering knuckle arms. The variable tie rod composed of the left and right tie rods and tie rod cylinders is a two-force bar element inside the steering mechanism, which plays the role of transmitting steering drive torque and correcting the steering angle of the left wheel.

[0094] (2) Hydraulic System: Composed of an electromagnetic directional valve 11, a servo proportional valve 12, a servo motor 13, a fixed displacement pump 14, a relief valve 15, and an oil tank 16. The servo pump control unit, composed of the servo motor and the fixed displacement pump, is the sole power source of the steering system and the control element of the dual-power-assist cylinder steering unit; the electromagnetic directional valve only has opening and closing actions, used to change the steering direction of the tires; the servo proportional valve is the control element of the tie rod cylinder, and adjusting the valve core opening can control the linear motion of the tie rod cylinder and adjust the tie rod length; the relief valve provides safety protection for the circuit, and the oil tank is used to store and cool the oil. At the same time, according to the different contributions of each part to the steering, the servo pump control unit, the electromagnetic directional valve, and the dual-power-assist cylinder are classified as the main system, and the servo proportional valve and the tie rod cylinder are classified as the auxiliary system. Therefore, the complete steering system is called a pump-valve main-auxiliary electro-hydraulic steering system, hereinafter referred to as the steering system.

[0095] The working principle is as follows: The servo motor 13, based on the right wheel steering command signal and the right wheel steering status, drives the fixed displacement pump 14 to draw hydraulic oil from the oil tank 16 and directly deliver it to the left and right power steering cylinders 8 and 9, driving the left and right tires to steer simultaneously. The solenoid valve opens its valve core according to the steering direction command, changing the tire steering direction. The servo proportional valve 14 adjusts the valve core opening in real time according to the left wheel steering command and the left wheel steering status, branching a flow from the fixed displacement pump outlet to supply the tie rod cylinder 4. While maintaining the tie rod cylinder tension, it finely adjusts the tie rod cylinder length to correct the left wheel steering angle. Thus, through the close cooperation of the three control components—servo motor, servo proportional valve, and solenoid directional valve—simultaneous servo steering of the left and right tires can be achieved, releasing the degree of freedom of the single-axle steering system and improving the overall vehicle maneuverability; it also fully utilizes the energy-saving advantages of pump-controlled volumetric speed regulation control, reducing the overall vehicle steering energy consumption.

[0096] Establishing a dynamic model of the pump-valve coordinated electro-hydraulic steering system, including the upper mechanical system and the hydraulic system, includes the following steps:

[0097] Using the rotation angles of the left and right wheels as the generalized coordinates of the left and right tires respectively, the Lagrange dynamic equations of the trapezoidal mechanism are established:

[0098]

[0099]

[0100] In the formula, and These are the left and right tire turning angles, respectively. and , representing the steering speeds of the left and right tires respectively, and T, U, and D representing the kinetic energy, potential energy, and dissipated energy of the steering mechanism respectively. and The generalized forces for the left and right tires are expressed as follows:

[0101]

[0102] ,

[0103]

[0104]

[0105] In the formula, J L and J R The equivalent moments of inertia of the left and right tires, J, are respectively. HL and J HR The equivalent moments of inertia of the left and right tie rods are ω and ω, respectively. H v is the rotational speed of the tie rod. HL and v HR The horizontal velocity of the left and right tie rods is m. HL and m HR The equivalent masses of the left and right tie rods are C and C, respectively. L and C R The equivalent damping of the left and right tires are respectively; C LC and C RC The equivalent damping of the left and right booster cylinders are respectively; C HC For the equivalent damping of the tie rod cylinder, v L and v R v represents the piston speed of the left and right booster cylinders. H For the piston speed of the tie rod cylinder, F L and F R These represent the output force of the left and right power assist cylinders, respectively; F HL and F HR These represent the output forces of the left and right chambers of the tie rod, respectively; n is the distance from the hinge point between the steering knuckle arm and the power steering cylinder to the line connecting the steering knuckle arm and the axle; m is the length of the steering knuckle arm; M L and M R These are the steering damping moments for the left and right tires, respectively; θ L θ R θ represents the angle between the piston speeds of the left and right power steering cylinders and the tangential speeds of the left and right steering knuckle arms, respectively. HL θ HR These are the angles between the piston speed of the tie rod cylinder and the tangential speeds of the left and right arms, respectively.

[0106] Combining the above equations, and considering that the dynamics of the tie rod cylinder have a relatively small impact on the overall dynamics, the dynamic model of the steering mechanism is derived:

[0107]

[0108] In the formula, F dL and F dRThis represents the unmodeled dynamics and sets of perturbations.

[0109] Considering only the kinetic friction generated during the piston movement of the left and right booster cylinders, the output force of the left and right booster cylinders is:

[0110]

[0111] In the formula, p1 and p2 represent the inlet and outlet pressures of the directional valve, respectively; B L and B R These are the viscous damping coefficients of the left and right assist cylinders, respectively.

[0112] Taking into account the effects of internal oil leakage and the compressibility of the fluid within the two steering cylinders, the pressure dynamics formula of the main system is as follows, based on the flow continuity equation:

[0113]

[0114] In the formula, A and a are the areas of the large and small chambers of the power-assisted cylinder, respectively, and C... ip and C ep The main system has internal and external leakage. V1 and V2 are the left and right main cavities of the dual booster cylinders. , V t The main system consists of the left and right auxiliary cylinders and the main pipeline cavity.

[0115] The main system consists of a servo motor, a fixed displacement pump, solenoid valves, and left and right power steering cylinders. Considering that the frequency response of the servo motor is much higher than the operating frequency of the steering system, its dynamic response is considered a first-order element.

[0116]

[0117] In the formula, u m k m n m and represent the control voltage, dynamic gain, speed, and time constant of the servo motor, respectively; k T T is the gain due to the change in speed caused by the motor load torque; L The load torque of the servo motor is mainly determined by the output pressure of the fixed displacement pump, and its expression is: D P For pump displacement, This refers to the pump output pressure.

[0118] The servo pump control unit needs to supply flow to both the main system and the auxiliary system simultaneously. Considering leakage in the metering pump outlet chamber and oil compression, a dynamic equation for the pump output pressure is established:

[0119]

[0120] In the formula, V pβ represents the volume of the pump outlet oil chamber and the pipeline cavity; e q represents the elastic modulus of the oil. LP Main system load traffic; q LA To assist the system load traffic.

[0121] The servo pump control unit outputs hydraulic fluid, which is directly delivered to the left and right power steering cylinders via an electromagnetic directional valve. This electromagnetic directional valve is typically a four-sided spool valve used to change the steering direction of the tires. Even when the valve core is fully open, a small amount of throttling loss still occurs in the hydraulic fluid passing through the valve. Therefore, a nonlinear equation for valve flow-pressure is established:

[0122]

[0123] In the formula, q1 and q2 are the inlet and outlet flow rates of the electromagnetic directional valve, and C d w, x v1max These are the flow gain, valve core gradient, and valve core displacement of the electromagnetic directional valve, respectively. u v1 The control voltage for the solenoid valve is +10V when the tire turns left and -10V when turning right. v1 ρ is the control gain of the solenoid valve core, p1 is the oil density, and p2 is the inlet and outlet pressure of the solenoid directional valve, respectively.

[0124] Define the flow rate entering the dual-boost cylinder as the main system load flow rate:

[0125]

[0126] Considering the kinetic friction generated during the movement of the tie rod cylinder, the output force of the tie rod cylinder is:

[0127]

[0128] In the formula, B H is the coefficient of dynamic friction of the tie rod cylinder.

[0129] The tie rod cylinder is a symmetrical cylinder. Considering oil leakage and compression, the dynamic pressure balance equation for the tie rod cylinder is established as follows:

[0130]

[0131] In the formula, A H C is the piston area of ​​the tie rod cylinder; Hip and C Hep These are the internal and external leaks of the tie rod cylinder, respectively; V Ht Due to the symmetrical design of the tie rod cylinder, A is for horizontal tension. H This represents the cross-sectional area of ​​the left and right chambers. Additionally, V... H1 and V H2 This indicates the total volume of the chambers on both sides of the pull rod. H1 and qH1 and p H2 and q H2 These correspond to the inlet and outlet pressures and flow rates of the servo valve, respectively.

[0132] Furthermore, the inlet and outlet flow rates of the tie rod system are controlled by the orifice flow equation, as follows:

[0133]

[0134] In the formula, C dH w H These represent the flow gain and spool gradient of the servo proportional valve, respectively; k v2 For the servo proportional valve spool control gain; u v2 The control voltage for the servo proportional valve; p H1 and p H2 These are the inlet and outlet oil pressures of the servo proportional valve, respectively; q H1 and q H2 These represent the flow rates of oil entering and exiting the servo proportional valve, respectively.

[0135] Define the flow rate entering the tie rod cylinder as the auxiliary system load flow rate:

[0136]

[0137] By simultaneously solving the above equations, the comprehensive dynamic model of the pump-valve coordinated electric steering system can be obtained as follows:

[0138]

[0139] like Figure 2 As shown, the adaptive robust synchronization control method of the pump-valve coordinated electro-hydraulic steering system of the present invention is as follows:

[0140] Virtual control torque design: The state-space equations of the mechanical system are restated as follows:

[0141]

[0142] in, ;

[0143] The virtual control law is:

[0144] Define tire angle tracking error The target values ​​of x2 and x4 are designed as follows: Therefore, the sliding mode class variable can be obtained as

[0145]

[0146]

[0147] Based on the principle of adaptive robust control, the target value of the virtual control torque is determined by the model compensation term F. dm and robust feedback item F ds composition:

[0148]

[0149] Considering the impact of uncertain nonlinearity and modeling errors on model compensation, the overall fast model compensation components are further subdivided into static compensation components d1 and d2 and high-frequency dynamic compensation component d1. ∗ d2 ∗ .

[0150]

[0151] Static compensation components d1 and d2 can be conveniently obtained through model estimation. However, high-frequency dynamic compensation components are difficult to handle analytically. Therefore, an RBF neural network is used to provide online approximation and compensation for this part. The corresponding RBFNN compensation terms are designed for the right wheel of the mechanical system control layer, and the design for the left wheel is similar.

[0152] definition These are used as the network input vectors for the right and left wheels, respectively. A single hidden layer structure is adopted, with the number of hidden nodes set to i = 5, to strike a balance between the network's approximation capability and computational efficiency. These are the hidden layer basis function vectors. W∈R 5 This is the weight vector. The Gaussian radial basis function is chosen as the activation function for the hidden layer, and its expression is:

[0153]

[0154] Where c j ∈R 5 It is the center of node j. j > 0 indicates the width parameter. Due to its local response, this function can well approximate the nonlinear mapping of the input domain. The structural parameters of the RBFNN are initialized to ensure efficient performance of the system dynamics. Center vector c j Optimization is achieved using the K-means clustering algorithm, which divides the input space into i clusters and centers the clusters at the centroids of these regions to minimize intra-cluster variance. This ensures that neurons are assigned to the most active regions within the system's domain. Subsequently, the width parameter b... j The distribution of the optimized centers is determined to ensure sufficient overlap between adjacent receptive fields. Specifically, the width is proportional to the average Euclidean distance between the centers, calculated using the following formula:

[0155]

[0156] in This represents the total number of unique center pairs. This initialization strategy ensures a smooth transition of activation values ​​in the input space, effectively preventing dead zones in the approximation while maintaining effective local sensitivity. To guarantee online approximation with uncertainty, an adaptive weight update law is defined as follows:

[0157]

[0158] Where γ > 0 represents the learning rate, adjusting the parameter update speed; η > 0 serves as a weight decay factor to prevent unbounded divergence. Based on the RBFNN structure, a fast model compensation term F is defined. 1dm2 F 2dm2 for:

[0159]

[0160] in, Given , For positive constants, the composition of the projection mapping is:

[0161]

[0162] in This is a term of RBF. Its main purpose is to compensate for high-frequency dynamics, providing comprehensive compensation for unmodeled dynamics and disturbances in mechanical systems.

[0163]

[0164]

[0165] in , To represent the approximate residual of the neural network, a nonlinear robust feedback term is introduced. It satisfies the following two realizability conditions:

[0166]

[0167] in and All numbers greater than 0 are arbitrarily small positive integers. Therefore, this term is constructed as:

[0168]

[0169] Decoupling control input design:

[0170] Define the error between the virtual control torque and the target value of the backward step. Similarly, based on Lyapunov's stability theory, the left and right wheels Q...1d and Q 2d The virtual control flow design is as follows:

[0171]

[0172]

[0173]

[0174]

[0175] in The damping coefficient of the right-side power cylinder is defined as follows: Left side and tie rod therefore:

[0176]

[0177]

[0178] Based on mechanical methods, the rapid compensation of the hydraulic model is divided into static terms d3 and d4 and high-frequency dynamic component d3. * d4 * .

[0179]

[0180]

[0181] Similarly, the static compensation term can be given as follows:

[0182]

[0183]

[0184] in , It is a positive constant. For nonlinear robust feedback, the following two implementation conditions are applied:

[0185]

[0186] in and >0 are all arbitrarily small positive numbers. Similarly, the nonlinear robust feedback term is also set as:

[0187]

[0188] Considering the dynamic model of the right wheel, the time-varying hydraulic damping coefficient is defined as By separating the known total hydraulic drive torque and M R The system dynamics can be reformulated in a parametric form:

[0189]

[0190] in The net pressure torque of the booster cylinder and the tie rod cylinder, This represents the kinematic transmission of the damping force. To avoid noise in angular acceleration measurements, a first-order filter is introduced. Apply this filter to the drive torque. and regressor The filtered signal is obtained.

[0191]

[0192] At the same time, utilizing properties This allows us to obtain a filter inertia term without direct differentiation. Therefore, the filter dynamics can be derived as:

[0193]

[0194] A computable observation signal is defined as Then, the prediction error The mismatch between observed and estimated values ​​can be written as

[0195]

[0196] To ensure the boundedness and convergence of the parameters, a projective-based fitness theorem is adopted:

[0197]

[0198]

[0199] Where Γ R It is the adaptive gain matrix. It is a variable forgetting factor. Saturation function. Defined as limiting the update rate to a preset limit. Inside:

[0200]

[0201] Meanwhile, discontinuous projection mapping Designed to estimate values Restricted to known convex sets Inside:

[0202]

[0203] in Represents the feasible parameter set The boundary, n represents The external unit normal vector at the location. This projection mechanism ensures that the parameter estimates remain within their physical range without compromising the adaptive directionality. Finally, considering structural symmetry, the parameter estimation of the left wheel controller follows the same process.

[0204] The virtual control flow rate is restored to the input control voltage of the proportional directional valve as follows:

[0205] Before the decoupling linear transformation, the virtual control law Q 1d and Q 2d satisfy:

[0206]

[0207] Wherein, the coupling matrix coefficients are

[0208] Finally, since matrix L is invertible, the decoupled pump control voltage and valve control voltage can be derived as follows:

[0209] The present invention uses the Lyapunov method to prove the bounded stability of the controller and the convergence of parameter estimation. The process is as follows:

[0210]

[0211] Take V θ Time derivative and application of identity We can obtain:

[0212]

[0213] Projection mapping properties Applying this, we get:

[0214] This differential inequality contains Assuming that the unmodeled dynamics are negligible (i.e., ∆Rf≈0) and satisfy the PE condition, the parameter estimation error converges exponentially to zero.

[0215] Based on the above conditions, the proposed control law guarantees a unified final boundary for the state, and the system's Lyapunov function... The following boundaries are clearly satisfied:

[0216]

[0217] Where λ > 0 determines the convergence rate, and C > 0 denotes the lumped residual limit, this inequality guarantees that the error exponent of the two rounds converges to the set. .

[0218] like Figure 3 and Figure 4 As shown, the proposed radial basis function neural network-assisted DIARC controller has high synchronous control accuracy, with the maximum angular error of both the left and right wheels remaining within 0.2°. This ensures high-precision angular control of the pump-valve coordinated system and enables rapid and accurate estimation of load deviation disturbances, demonstrating superior control performance.

[0219] 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. An adaptive robust control method for a pump-valve parallel steering system based on neural network compensation, characterized in that, include: Step 1: Establish a comprehensive dynamic model of the pump-valve coordinated electro-hydraulic steering system. The upper trapezoidal steering mechanical model is described by the Lagrange dynamic equation, and the hydraulic model is described by the hydraulic cylinder dynamic balance equation, the flow continuity equation, and the servo valve flow equation. Step 2: Design virtual control torque, and provide online approximation and compensation for its high-frequency dynamic compensation components by designing an RBF neural network; design decoupled control input, take the hydraulic damping coefficient as an uncertain parameter, construct a parameter adaptive law, and obtain virtual control flow by combining time-varying model feedforward and robust feedback; Step 3: Linearly transform the virtual control flow into the control voltage of the servo motor pump and servo proportional valve to control the pump-valve coordinated electro-hydraulic steering system; repeat steps 1 to 3 to achieve adaptive robust real-time control of the pump-valve coordinated electro-hydraulic system; use the Lyapunov method to prove the bounded stability of the controller and the convergence of parameter estimation.

2. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 1, characterized in that: In step one, the comprehensive dynamic model of the pump-valve coordinated electro-hydraulic steering system is as follows: in, and These represent the angular accelerations of the right and left wheels, respectively. and F represents the angular velocity of the right wheel and the left wheel, respectively. dR and F dL These represent the unmodeled dynamic and disturbance terms for the left and right wheels, respectively; J L and J R C represents the equivalent moments of inertia of the left and right tires, respectively; L and C R These are the equivalent damping values ​​for the left and right tires, respectively. The elastic modulus of the oil; and These represent the inlet flow rate and outlet flow rate of the electromagnetic directional valve, respectively. and These represent the displacements of the pistons in the left and right booster cylinders, respectively. and These represent the inlet and outlet oil pressures of the solenoid directional valve, respectively. and F represents the first derivative of the inlet and outlet oil pressures of the solenoid directional valve, respectively; L and F R These represent the output force of the left and right power assist cylinders, respectively; F HL and F HR These represent the output forces of the left and right chambers of the tie rod, respectively; n is the distance from the hinge point between the steering knuckle arm and the power steering cylinder to the line connecting the steering knuckle arm and the axle; m is the length of the steering knuckle arm; M L and M R These are the steering damping moments for the left and right tires, respectively; θ L and θ R These are the angles between the piston speed of the left power steering cylinder and the tangential speed of the left steering knuckle arm, and the angles between the piston speed of the right power steering cylinder and the tangential speed of the right steering knuckle arm, respectively; θ HL and θ HR These are the angles between the piston speed of the tie rod cylinder and the tangential speed of the left and right joints, respectively; A and a are the areas of the large and small chambers of the power steering cylinder, respectively; C... ip and C ep The main system has internal and external leakage, and V1 and V2 are the left and right main chambers of the dual booster cylinder; and These represent the displacements of the pistons in the left and right booster cylinders, respectively. p represents the speed of the piston in the tie rod cylinder. H1 and p H2 These are the inlet and outlet oil pressures of the servo proportional valve, respectively. and Take the first derivatives of the inlet and outlet oil pressures of the servo proportional valve, respectively; q H1 and q H2 These are the inlet and outlet oil flow rates through the servo proportional valve, respectively; A H C is the piston area of ​​the tie rod cylinder; Hip and C Hep These are internal and external leaks in the tie rod cylinder, respectively. The pump output flow rate; u m k m n m , These are the control voltage, dynamic gain, speed, and time constant of the servo motor, respectively; k T T is the gain due to the change in speed caused by the motor load torque; L The load torque of the servo motor is expressed as follows: D P For pump displacement, Take the first derivative of the pump output pressure; V p q represents the volume of the pump outlet oil chamber and the pipeline cavity; LP Main system load traffic; q LA To assist the system load flow; The first derivative of the servo motor's rotational speed.

3. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 2, characterized in that, In step two, the virtual control torque is designed as follows: Among them, F 1d and F 2d F represents the virtual control torque of the left and right wheels, respectively. 1dm1 and F 2dm1 F represents the feedforward model compensation term for the left and right wheels; 1dm2 and F 2dm2 These represent the rapid dynamic compensation terms for the left and right wheels, respectively; F 1ds1 and F 2ds1 These represent the linear feedback terms for the left and right wheels, respectively; F 1ds2 and F 2ds2 These represent the nonlinear feedback terms of the left and right wheels, respectively. The feedforward compensation term and linear feedback term of the virtual control torque model are as follows: Where e1 and e3 represent the tracking errors of the right and left wheels of the pump-valve coordinated electro-hydraulic steering system, respectively; ; and These represent the turning angles of the right and left wheels, respectively. They represent and The target value; They represent and The first derivative of the target value; x2 and x4 represent the angular velocities of the right and left wheels, respectively; x 2eq and x 4eq Let x2 and x4 represent the target values ​​respectively, P1 and P2 represent the synovial membrane amounts on both sides respectively, and k1 and k4 both represent the positive definite coefficients of the synovial membrane amounts; This represents the feedforward model compensation term for the left wheel. This represents the equivalent moment of inertia of the right tire. This represents the first derivative of the target value of x2. This indicates the steering damping torque of the right tire. This represents the equivalent damping of the right tire. This represents the estimated values ​​of the unmodeled dynamics and disturbance terms of the right wheel; This represents the feedforward model compensation term for the right wheel. This represents the equivalent moment of inertia of the left tire. This represents the first derivative of the target value of x4. This indicates the steering damping torque of the left tire. This represents the equivalent damping of the left tire. This represents the estimated values ​​of the unmodeled dynamics and disturbance terms of the revolver. , Both represent the proportional gain of linear robust feedback.

4. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 3, characterized in that, In step two, the high-frequency dynamic compensation component is specifically designed using the RBF neural network as follows: Where d1 and d2 represent static compensation components, , Represented as high-frequency dynamic compensation components; O1 and O2 serve as the network input vectors for the left and right wheels, respectively; and F dR and F dL The error value; P1 and P2 represent the amount of synovial membrane on both sides, respectively; Represents a 5-dimensional real vector space; Let represent the radial basis function of the j-th hidden layer neuron; Represented as a vector of hidden layer basis functions; This represents the input vector of the neural network; represents the center vector of the j-th Gaussian kernel function; j represents the index of the hidden layer neuron; i represents the number of hidden layer neuron nodes in the RBF neural network, where i=5; denoted as the width parameter of the RBF neural network; p and q represent the index of the hidden layer neurons; Let represent the center vectors of the Gaussian radial basis functions corresponding to the p-th neuron and the q-th neuron; M represents the total number of unique center pairs. Indicates the discontinuous projection operator; This represents the weight estimate of the j-th neuron; This is expressed as the adaptive weight update law; where >0 indicates the learning rate; > 0 is used as the weight decay factor; T represents transpose; e2 and e4 represent the errors between the virtual control torque of the left and right wheels and the backstep target value, respectively; e1 and e3 represent the tracking errors of the right and left wheels of the pump-valve coordinated electro-hydraulic steering system, respectively; P1 and P2 represent the quasi-slippery amount on both sides, respectively; P1 and P2 represent the quasi-slippery amount on both sides, respectively. and These represent the inlet and outlet oil pressures of the solenoid directional valve, respectively. The fast dynamics compensation term and the nonlinear feedback term are as follows: Among them, F 1dm2 and F 2dm2 These represent the rapid dynamic compensation terms for the left and right wheels, respectively; , Represented as the predicted value of the static compensation component; and express and The first derivative; This represents a pre-set estimated value; and They represent The upper and lower boundaries; and It is represented as a positive constant; The functional relationship representing the projection mapping; , Represented as high-frequency dynamic compensation components; and They represent RBF for and Online estimation; and These represent the error values ​​of the left and right wheels approximated by the neural network, respectively. and This represents the system state variable, which is the network input vector mentioned earlier. / ; and All positive numbers >0 are arbitrarily small positive numbers; and y1 and y2 represent the parameter estimation errors of the static disturbance components of the right and left wheels, respectively; y1 and y2 both represent bounded upper bound functions of the system uncertainty. and These represent the transposes of the weight estimates for the first neuron and the transposes of the weight estimates for the second neuron, respectively. , F represents the hidden layer output vector of a neural network. 1ds2 and F 2ds2 These represent the nonlinear feedback terms of the left and right wheels, respectively.

5. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 4, characterized in that, In step two, the virtual control flow is specifically as follows: Among them, Q 1d and Q 2d These represent the virtual control flow of the left and right wheels, respectively; Q 1dm1 and Q 2dm1 This represents the feedforward model compensation term; Q 1dm2 and Q 2dm2 These represent its fast dynamic compensation term; Q 1ds1 and Q 2ds1 These represent its linear feedback term; Q 1ds2 and Q 2ds2 These represent their nonlinear feedback terms; The feedforward compensation term and linear feedback term of the virtual control flow model are as follows: in, and Both represent adaptive regression vectors; Indicates parameters and The estimated vector; Don't represent parameters and The estimated vector; This represents the online estimate of the viscous damping coefficient of the right main steering cylinder; This represents the online estimate of the viscous damping coefficient of the right main steering cylinder; V1 and V2 represent the online estimated value of the viscous damping coefficient of the tie rod cylinder; V1 and V2 are the left and right total volumes of the dual-boost cylinder. and These represent the displacements of the pistons in the left and right booster cylinders, respectively; A H Here, e1 represents the piston area of ​​the tie rod cylinder; e2 and e4 represent the errors between the virtual control torques of the left and right wheels and the target values ​​of the backstepping, respectively. and These represent the equivalent driving torques of the right-wheel and left-wheel steering mechanisms, respectively. and They represent and The estimated value; B represents the acceleration of the piston in the tie rod cylinder. R B L B H These represent the damping coefficients of the right, left, and tie rod hydraulic cylinders, respectively; f1~f4 and g1~g4 are Q... 1dm1 and Q 2dm1 The linearization coefficients simplify the model structure; The fast dynamic compensation term and nonlinear feedback term of the virtual control flow are as follows: and Both represent positive linear feedback gain coefficients; d3 and d4 represent the static terms of rapid compensation in the hydraulic model, respectively. , These are respectively represented as the high-frequency dynamic components of rapid compensation; and These represent the tracking deviations of the dynamic changes in the equivalent driving torque target of the right-wheel and left-wheel steering mechanisms, respectively. and These represent the online estimates of low-frequency static disturbances d3 and d4, respectively. and These represent the update rates of parameters d3 and d4, respectively. and It is represented as a positive constant; The functional relationship representing the projection mapping; and y3 and y4 represent the estimation errors of d3 and d4, respectively; y3 and y4 both represent bounded upper bound functions of the system uncertainty. and All numbers greater than 0 are arbitrarily small positive numbers.

6. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 5, characterized in that, In step two, the parameter adaptive law is constructed as follows: in, This refers to the total torque of the power assist cylinder and the tie rod cylinder; The kinematic transfer matrix represents the damping force; This represents the model's uncertainty and external disturbances; Represents the vector of unknown parameters to be estimated; express Online matrix estimation; Q(s) is represented as a first-order filter; Y R Defined as a computable observation signal. This is expressed as the error between the observed value and the estimated value; Represents a saturation function; Represents the slowly varying parameter matrix of the system The derivative of the parameter estimation matrix; Indicates that the input is Projective mapping functions; Indicates the forgetting factor; This represents the linear regression matrix used in online squared estimation of a nonlinear dynamic model. This indicates the maximum preset parameter update rate; Represents an input vector; Represents the feasible parameter set The boundary, s represents The external unit normal vector at that location.

7. The adaptive robust control method for a pump-valve parallel steering system based on neural network compensation according to claim 1, characterized in that, In step three, the virtual control flow of the left and right wheels is linearly transformed into the control voltage of the servo motor pump and the servo proportional valve, as follows: Wherein, the coupling matrix coefficients are in, This indicates the actual input control voltage of the servo motor pump. This indicates the control voltage of the directional valve in the pump control circuit; This represents the actual input control voltage of the servo proportional valve. and The target flow rates of the right and left wheel master steering cylinders are represented respectively; Q represents the virtual control flow rate; and L represents the mapping relationship between the virtual control flow rate Q and the actual input control voltage u of the proportional valve of the pump-valve coordinated steering system. Indicates pump control input Right wheel flow The influence coefficient; Indicates valve-controlled input Right wheel flow The influence coefficient; Indicates pump control input For left wheel flow The influence coefficient; Indicates valve-controlled input For left wheel flow The influence coefficient; This indicates the flow coefficient of the solenoid valve. Indicates the valve opening gain; Represents a symbolic function; This represents the pump control dynamic coefficient of the right wheel master cylinder; This indicates the valve-controlled dynamic system of the right wheel tie rod cylinder; This represents the pump control dynamic coefficient of the left wheel master cylinder; This represents the valve control dynamic coefficient of the left wheel tie rod cylinder.

8. An electronic device, characterized in that, include: A mutually coupled memory and processor, wherein the memory stores program data, and the processor invokes the program data to execute an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation as described in any one of claims 1 to 7.

9. A computer-readable storage medium storing program data thereon, characterized in that, When the program data is executed by the processor, it implements an adaptive robust control method for a pump-valve parallel steering system based on neural network compensation as described in any one of claims 1 to 7.

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