Gain self-learning position axis control method for electro-hydraulic proportional servo valve

Abstract

Disclosed in the present invention is a gain self-learning position axis control method for an electro-hydraulic proportional servo valve. In the axis control method, a nonlinear robust position axis controller with a gain self-learning mechanism is designed on the basis of a constructed gain self-learning mechanism and by incorporating the concept of dynamic surface control. For the position axis control problem of an electro-hydraulic proportional servo valve, the present invention can not only realize autonomous learning of a system gain, thereby simplifying the complexity of actual gain adjustment, but can also prevent the problem in respect of differential explosions in the traditional backstepping control of an axis control system of the electro-hydraulic proportional servo valve, thereby reducing the impact of measurement noise on control accuracy and achieving a high-precision tracking performance.

Description

A self-learning gain position axis control method for electro-hydraulic proportional servo valve Technical Field

[0001] The present invention relates to the technical field of electromechanical servo control, and in particular to a self-learning gain position axis control method (ALGRC) for an electro-hydraulic proportional servo valve. Background Art

[0002] Electro-hydraulic proportional servo valve axis control systems, with their high power density, high force / torque output, and fast dynamic response, play a pivotal role in robotics, heavy machinery, high-performance load testing equipment, and other fields. These systems are typical nonlinear systems, characterized by numerous nonlinear characteristics and modeling uncertainties. These nonlinear characteristics include input nonlinearities such as hysteresis and saturation, proportional servo valve flow and pressure nonlinearities, and friction nonlinearities. Modeling uncertainties include parameter uncertainty and uncertainty nonlinearities. Parameter uncertainty primarily relates to load mass, actuator viscous friction coefficient, leakage coefficient, servo valve flow gain, and hydraulic fluid elastic modulus. Uncertain nonlinearities primarily include unmodeled friction dynamics, high-order system dynamics, external disturbances, and unmodeled leakage. As electro-hydraulic proportional servo valve axis control systems develop towards higher precision and higher frequency response, the impact of these nonlinear characteristics on system performance becomes increasingly significant. Furthermore, modeling uncertainty can lead to instability or downgraded order of controllers designed based on the nominal system model. Therefore, the nonlinear characteristics and modeling uncertainty of electro-hydraulic proportional servo valve axis control systems are significant factors limiting system performance. With the continuous advancement of technology in the industrial and defense fields, the controllers designed based on traditional linear theory have gradually failed to meet the high performance requirements of the system. Therefore, it is necessary to study more advanced nonlinear control strategies based on the nonlinear characteristics of the electro-hydraulic proportional servo valve axis control system.

[0003] Many methods have been proposed to solve the nonlinear control problem of electro-hydraulic proportional servo valve axis control system. Adaptive control methods are very effective in dealing with parameter uncertainty and can achieve asymptotic tracking steady-state performance. However, they are unable to cope with uncertainty nonlinearities such as external load disturbances. When the uncertainty nonlinearity is too large, the system may become unstable. Actual electro-hydraulic proportional servo valve axis control systems all have uncertainty nonlinearities. Therefore, adaptive control methods cannot achieve high-precision control performance in practical applications. As a robust control method, classical sliding mode control can effectively handle any bounded modeling uncertainty and achieve asymptotic tracking steady-state performance. However, the discontinuous controller designed for classical sliding mode control is prone to chattering of the sliding mode surface, thereby deteriorating the tracking performance of the system. To simultaneously address the problems of parameter uncertainty and uncertainty nonlinearity, adaptive robust control methods have been proposed. This control method can enable the system to achieve deterministic transient and steady-state performance when both modeling uncertainties exist. To achieve high-precision tracking performance, the feedback gain must be increased to reduce the tracking error. Due to the presence of measurement noise, an excessively large gain often leads to high-gain feedback, which causes chattering of the control input, further deteriorating the control performance and even causing system instability.

[0004] Summary of the Invention

[0005] The purpose of the present invention is to provide an electro-hydraulic proportional servo valve position axis control method with self-learning gain, strong anti-interference ability and high tracking performance, which can not only realize the autonomous learning of system gain and simplify the complexity of actual gain adjustment, but also avoid the differential explosion problem in the traditional backstepping control of the electro-hydraulic proportional servo valve axis control system, reduce the influence of measurement noise on control accuracy, and achieve high-precision tracking performance.

[0006] The technical solution to achieve the purpose of the present invention is: a self-learning gain position axis control method for an electro-hydraulic proportional servo valve, comprising the following steps:

[0007] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve position axis control system, and then proceed to step 2.

[0008] Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, design a nonlinear robust position axis control controller with a gain self-learning mechanism, and then go to step 3.

[0009] Step 3: Use Lyapunov stability theory to prove the stability of the nonlinear robust position axis control controller, and obtain the result that the system tracking error is asymptotically stable.

[0010] Compared with the existing technology, the present invention has the following significant advantages: (1) it realizes autonomous learning of system gain and simplifies the complexity of actual gain adjustment; (2) it avoids the differential explosion problem in the traditional backstepping control of the electro-hydraulic proportional servo valve axis control system, reduces the influence of measurement noise on control accuracy, and achieves high-precision tracking performance. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG1 is a schematic diagram showing the principle of the self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to the present invention.

[0012] FIG2 is a schematic diagram showing the principle of the axis control system of the electro-hydraulic proportional servo valve of the present invention.

[0013] FIG3 is a curve diagram showing the tracking process of the system output to the desired instruction under the action of the ALGRC controller designed by the present invention.

[0014] FIG4 is a graph showing the tracking error of the system changing with time under the action of the ALGRC controller designed by the present invention.

[0015] FIG5 is a comparison curve diagram of the tracking errors of the system under the action of the ALGRC controller designed by the present invention and the traditional PID controller.

[0016] FIG6 is a control input curve diagram of the system under the action of the ALGRC controller designed by the present invention. DETAILED DESCRIPTION

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] 1 and 2 , the present invention provides a method for self-learning gain position axis control of an electro-hydraulic proportional servo valve, comprising the following steps:

[0019] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve position axis control system, as follows:

[0020] Step 1-1, the electro-hydraulic proportional servo valve position axis control system is applied to the linear motion of large industrial heavy-load mechanical equipment, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the electro-hydraulic proportional servo valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move.

[0021] According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve position axis control system is:

[0022] In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, Indicates the speed of the hydraulic cylinder piston rod, represents the acceleration of the hydraulic cylinder piston rod, A represents the effective working area of ​​the hydraulic cylinder piston, P1 represents the oil pressure in the hydraulic cylinder oil inlet chamber, P2 represents the oil pressure in the hydraulic cylinder oil outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder, d1(t) represents the unmodeled mechanical disturbance of the system, and t represents time.

[0023] Then formula (1) can be rewritten as:

[0024] In the electro-hydraulic proportional servo valve position axis control system, ignoring the leakage of oil in the cylinder, the pressure dynamic equation is:

[0025] In formula (3), β e Indicates the effective elastic modulus of oil, C t Indicates the leakage coefficient of the hydraulic cylinder, the oil pressure difference P on both sides of the cylinder in and out of the oil chamber L =P1-P2, the control volume of the oil inlet chamber V1=V 01 +Ay, the control volume of the oil outlet chamber V2=V 02 -Ay, V 01 Indicates the initial volume of the oil inlet chamber, V 02 represents the initial volume of the oil outlet cavity, Q1 represents the flow rate of the oil inlet cavity, Q2 represents the flow rate of the oil outlet cavity, q1 represents the unmodeled interference of P1, q2 represents the unmodeled interference of P2, represents the first-order derivative of P1, represents the first derivative of P2.

[0026] Q1 and Q2 are respectively related to the displacement of the spool of the electro-hydraulic proportional servo valve x v There are the following relationships:

[0027] Among them, the electro-hydraulic proportional servo valve coefficient C d represents the flow coefficient of the electro-hydraulic proportional servo valve, w0 represents the valve core area gradient of the electro-hydraulic proportional servo valve, ρ represents the oil density, P s Indicates the oil supply pressure, P r represents the return oil pressure, s(·) represents the function of the intermediate variable ·, and is defined as:

[0028] Ignoring the dynamics of the electro-hydraulic proportional servo valve spool, assume that the control input u acting on the spool and the spool displacement x v Proportional relationship, that is, satisfying x v =k i u, where k i represents the voltage-spool displacement gain coefficient, so Equation (4) is rewritten as:

[0029] In formula (6), the intermediate variable k u =k q k i , intermediate variables Intermediate variables

[0030] Step 1-2, define state variables: Among them, the intermediate variable x1=y, the intermediate variable The intermediate variable x3 = (AP1-AP2) / m, then transform equation (2) into the state equation:

[0031] In formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first derivative of x3, the unknown dynamics of the system Intermediate variables Intermediate variables Intermediate variables System unknown dynamics

[0032] To facilitate controller design, the following assumptions are made:

[0033] Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects that the position command, velocity command and acceleration command are all bounded.

[0034] Assumption 2: The unknown dynamics D1 and D2 of the system satisfy:

[0035] In formula (8), δ1 and δ2 are both unknown positive constants.

[0036] Go to step 2.

[0037] Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, a nonlinear robust position axis control controller with a gain self-learning mechanism is designed. The specific steps are as follows:

[0038] Step 2-1: To facilitate controller design, define the tracking error of the system as z1 = x1 - x d , x d The system expects to track the position instruction. The present invention proposes the following nonlinear filter with gain self-learning for the first time:

[0039] Formula (9), filter gain τ1>0, α1 represents the virtual control of x2, α 1f represents the filtered signal of α1, α 1fThe error with x2 is z2 = x2-α 1f , the filtering error of α1 ε1 = α 1f -α1,σ1(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a constant that is always positive, represents the first-order derivative of α1, Represents α 1f The first derivative of l1>0 means The upper bound of Represents the estimated value of l1, and its update law for:

[0040] In formula (10), γ1 represents a positive gain;

[0041] Taking the derivative of z1, we get:

[0042] Design the virtual control α1 as:

[0043] In formula (12), gain k1>0, then

[0044] Step 2-2: The present invention innovatively proposes the following nonlinear filter with gain self-learning:

[0045] In formula (14), the filter gain τ2>0, α2 represents the virtual control of x3, α 2f represents the filtered signal of α2, α 2f The error with x3 is z3 = x3 - α 2f , the filtering error of α2 ε2 = α 2f -α2,σ2(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a constant that is always positive, represents the first-order derivative of α2, Represents α 2f The first derivative of l2>0 means The upper bound of Represents the estimated value of l2, and its update law for:

[0046] In formula (15), γ2 represents a positive gain;

[0047] Taking the derivative of z2 we get:

[0048] The following virtual control α2 with gain self-learning is proposed for the first time: α2=α 2a +α 2s α 2s =α 2s1 +α 2s2 α 2s1 =-k2z2

[0049] In formula (17), gain k2>0, α 2a represents the model-based compensation term, α 2s represents the robust term, α 2s1 represents the linear robust term, α 2s2 represents the nonlinear robust term, σ3(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a positive constant, l3>0 represents the upper bound of D1, Represents the estimated value of l3, and its update law for:

[0050] In formula (18), γ3 represents a positive gain;

[0051] Substituting formula (17) into formula (16), we get:

[0052] Step 2-3, take the derivative of z3 and get:

[0053] According to formula (20), the control input of the valve core, that is, the nonlinear robust position axis control controller u with the first gain self-learning mechanism, is: u s =u s1 +u s2 u s1 =-k3z3

[0054] In formula (21), gain k3>0, u a represents the model-based compensation term, u s represents the robust term, u s1 represents the linear robust term, u s2 represents the nonlinear robust term, σ4(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a positive constant, l4>0 represents the upper bound of D2, Represents the estimated value of l4, and its update law for:

[0055] In formula (22), γ4 represents a positive gain;

[0056] Substituting formula (21) into formula (20) yields:

[0057] Go to step 3.

[0058] Step 3: Use Lyapunov stability theory to prove the stability of the nonlinear robust position axis control controller, and obtain the result that the system tracking error is asymptotically stable, as follows:

[0059] The Lyapunov function is defined as follows:

[0060] Among them, the intermediate variable Intermediate variables Intermediate variables Intermediate variables

[0061] Derivative (24) and substitute (9), (10), (13), (15), (16), (18), (19), (22) and (23) into it to obtain:

[0062] Taking into account |D1|≤l3 and |D2|≤l4, we can get the expression:

[0063] Notice

[0064] Available

[0065] Substituting equations (27) and (28) into equation (26), we can obtain

[0066] Define the intermediate variables z and Λ as: z=[z1;z2;z3;ε1;ε2] (30),

[0067] Formula (31), the intermediate variables Λ1 and Λ2 are

[0068] By adjusting the gains k1, k2, k3 and the filter gains τ1, τ2, the symmetric matrix Λ can be made a positive definite matrix, and then we can get:

[0069] Formula (33), intermediate variable Φ = z T Λz.

[0070] Integrating both sides of equation (33) we can get:

[0071] From Equation (34), we can see that V is bounded and Φ is integrally bounded. It can be concluded that all signals in the system are bounded. Therefore, Φ is uniformly continuous. According to Barbalat’s lemma, when time tends to positive infinity, the tracking error z1 tends to 0.

[0072] Therefore, it is concluded that by adjusting the gains k1, k2, k3 and the filter gains τ1, τ2, the nonlinear robust position axis control controller with a gain self-learning mechanism designed for the electro-hydraulic proportional servo valve position axis control system can enable the system to innovatively obtain the result that the tracking error converges asymptotically to 0. The principle diagram of the nonlinear robust position axis control controller of the electro-hydraulic proportional servo valve position axis control system is shown in Figure 1.

[0073] Example

[0074] In order to evaluate the performance of the designed controller, the physical parameters of the electro-hydraulic proportional servo valve position axis control system in the simulation are shown in Table 1:

[0075] Table 1 System physical parameters

[0076] Given a system with the expected instruction x d =0.02sin(πt)×(1-e -t )m.

[0077] The following controllers are used for comparison in the simulation:

[0078] Electro-hydraulic proportional servo valve self-learning gain position axis control controller (ALGRC): take gains k1=100, k2=50, k3=20, γ1=0.01, γ2=1, γ3=1, γ4=1, τ1=2000, τ2=2000.

[0079] PID controller: The steps for selecting PID controller parameters are: first, ignoring the nonlinear dynamics of the electro-hydraulic proportional servo valve axis control system, obtain a set of controller parameters through the PID parameter self-tuning function in Matlab, and then fine-tune the obtained self-tuning parameters after adding the nonlinear dynamics of the system to achieve the best tracking performance. The selected controller parameters are k P =1000,k I =500,k D =1.

[0080] The expected command of the system, the tracking error of the ALGRC controller, and the comparison of the tracking errors of the ALGRC controller and the PID controller are shown in Figure 3, Figure 4, and Figure 5, respectively. As shown in Figure 4, under the action of the ALGRC controller, the position output of the proportional servo valve axis control system has a high tracking accuracy for the command, and the amplitude of the steady-state tracking error is about 5×10 -5 From the comparison of the tracking errors of the two controllers in FIG5 , it can be seen that the tracking error of the ALGRC controller proposed in the present invention is much smaller than that of the PID controller, and the tracking performance is more superior.

[0081] Figure 6 is a graph showing the change in control input over time for the electro-hydraulic proportional servo valve axis control system under the action of the ALGRC controller. It can be seen from the figure that the obtained control input is a low-frequency continuous signal, which is more conducive to execution in practical applications.

Claims

1. A self-learning gain position axis control method for an electro-hydraulic proportional servo valve, characterized in that: The following steps are involved: Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve position axis control system, and then proceed to step 2; Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, a nonlinear robust position axis control controller with a gain self-learning mechanism is designed, and then the process goes to step 3. Step 3: Use Lyapunov stability theory to prove the stability of the nonlinear robust position axis control controller, and obtain the result that the system tracking error is asymptotically stable.

2. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 1, characterized in that: In step 1, a mathematical model of the electro-hydraulic proportional servo valve position axis control system is established as follows: Step 1-1: The electro-hydraulic proportional servo valve position axis control system is applied to the linear motion of large industrial heavy-load mechanical equipment, wherein the load is fixedly connected to the piston rod of the hydraulic cylinder, and the electro-hydraulic proportional servo valve controls the movement of the piston rod of the hydraulic cylinder, thereby driving the load to move. Based on the dynamic characteristics of the load, hydraulic cylinder, and electro-hydraulic proportional servo valve, a mathematical model of the electro-hydraulic proportional servo valve position axis control system is derived; Step 1-2: To facilitate controller design, define state variables and convert the derived mathematical model of the electro-hydraulic proportional servo valve position axis control system into a state space equation.

3. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 2, characterized in that: Step 1-1: The electro-hydraulic proportional servo valve position axis control system is applied to the linear motion of large industrial heavy-load mechanical equipment, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder. The electro-hydraulic proportional servo valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. Based on the dynamic characteristics of the load, hydraulic cylinder, and electro-hydraulic proportional servo valve, a mathematical model of the electro-hydraulic proportional servo valve position axis control system is obtained, as follows: According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve position axis control system is: In formula (1), m represents the mass of the load, y represents the displacement of the hydraulic cylinder piston rod, Indicates the speed of the hydraulic cylinder piston rod, represents the acceleration of the hydraulic cylinder piston rod, A represents the effective area of ​​the hydraulic cylinder piston, P1 represents the oil pressure in the hydraulic cylinder oil inlet chamber, P2 represents the oil pressure in the hydraulic cylinder oil outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder, d1(t) represents the unmodeled mechanical disturbance of the system, and t represents time; Then formula (1) can be rewritten as: In the electro-hydraulic proportional servo valve position axis control system, ignoring the leakage of oil in the cylinder, the pressure dynamic equation is: In formula (3), β e Indicates the effective elastic modulus of oil, C t Indicates the leakage coefficient of the hydraulic cylinder, the oil pressure difference P on both sides of the cylinder in and out of the oil chamber L =P1-P2, the control volume of the oil inlet chamber V1=V 01 +Ay, the control volume of the oil outlet chamber V2=V 02 -Ay, V 01 Indicates the initial volume of the oil inlet chamber, V 02 represents the initial volume of the oil outlet cavity, Q1 represents the flow rate of the oil inlet cavity, Q2 represents the flow rate of the oil outlet cavity, q1 represents the unmodeled interference of P1, q2 represents the unmodeled interference of P2, represents the first-order derivative of P1, represents the first derivative of P2; Q1 and Q2 are respectively related to the displacement of the spool of the electro-hydraulic proportional servo valve x v There are the following relationships: Among them, the electro-hydraulic proportional servo valve coefficient C d represents the flow coefficient of the electro-hydraulic proportional servo valve, w0 represents the valve core area gradient of the electro-hydraulic proportional servo valve, ρ represents the oil density, P s Indicates the oil supply pressure, P r represents the return oil pressure, s(·) represents the function of the intermediate variable ·, and is defined as: Ignoring the dynamics of the electro-hydraulic proportional servo valve spool, assume that the control input u acting on the spool and the spool displacement x v Proportional relationship, that is, x v =k i u, where k i represents the voltage-spool displacement gain coefficient, so Equation (4) is rewritten as: In formula (6), the intermediate variable k u =k q k i , intermediate variables Intermediate variables 4. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 3, characterized in that: Step 1-2: To facilitate controller design, define state variables and convert the derived mathematical model of the electro-hydraulic proportional servo valve position axis control system into a state space equation, as follows: Define state variables: Among them, the intermediate variable x1=y, the intermediate variable The intermediate variable x3 = (AP1-AP2) / m, then Equation (2) is converted into a state space equation: In formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, represents the first derivative of x3, the unknown dynamics of the system Intermediate variables Intermediate variables Intermediate variables System unknown dynamics 5. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 4, characterized in that: In step 1, to facilitate controller design, the following assumptions are made: Assumption 1: The system is expected to track the position command x d It is second-order continuous, and the system expects position command, velocity command and acceleration command to be bounded; Assumption 2: The unknown dynamics D1 and D2 of the system satisfy: In formula (8), δ1 and δ2 are both unknown positive constants; Go to step 2.

6. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 5, characterized in that: In step 2, based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, a nonlinear robust position axis control controller with a gain self-learning mechanism is designed as follows: Step 2-1: Define the tracking error of the system z1 = x1 - x d , where x d The system expects to track the position command. In order to facilitate the system state x1 to track the expected position command x as accurately as possible under the designed controller drive. d , it is necessary to ensure that the tracking error z1 tends to 0; Step 2-2: Define error z2 = x2 - α 1f , where α 1f Represents the filtered signal of α1, α1 represents the virtual control of x2. To ensure that the tracking error z1 tends to 0, it is necessary to ensure that the error z2 tends to 0; Step 2-3: Define the error z3 = x3 - α 2f , where α 2f Represents the filtered signal of α2, α2 represents the virtual control of x3. To ensure that the error z2 tends to 0, it is necessary to ensure that the error z3 tends to 0.

7. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 6, characterized in that: Step 2-1: Define the tracking error of the system z1 = x1 - x d , where x d The system expects to track the position command. In order to facilitate the system state x1 to track the expected position command x as accurately as possible under the designed controller drive. d , it is necessary to ensure that the tracking error z1 tends to 0, as follows: To facilitate controller design, the following nonlinear filter is designed: Formula (9), filter gain τ1>0, filter error ε1=α 1f -α1,σ1(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a constant that is always positive, represents the first-order derivative of α1, Represents α 1f The first derivative of l1>0 means The upper bound of represents the estimated value of l1; Its update law for: In formula (10), γ1 represents a positive gain; Taking the derivative of z1, we get: Design the virtual control α1 as: In formula (12), gain k1>0, then 8. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 7, characterized in that: Step 2-2: Define error z2 = x2 - α 1f , where α 1f Represents the filtered signal of α1, α1 represents the virtual control of x2. To ensure that the tracking error z1 tends to 0, it is necessary to ensure that the error z2 tends to 0, as follows: Design the following nonlinear filter: In formula (14), the filter gain τ2>0, the filter error ε2 of α2=α 2f -α2,σ2(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a constant that is always positive, represents the first-order derivative of α2, Represents α 2f The first derivative of l2>0 means The upper bound of Represents the estimated value of l2, and its update law for: In formula (15), γ2 represents a positive gain; Taking the derivative of z2 we get: Design the virtual control α2 as: In formula (17), gain k2>0, α 2a represents the model-based compensation term, α 2s represents the robust term, α 2s1 represents the linear robust term, α 2s2 represents the nonlinear robust term, σ3(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a positive constant, l3>0 represents the upper bound of D1, Represents the estimated value of l3, and its update law for: In formula (18), γ3 represents a positive gain; Substituting formula (17) into formula (16), we get:

9. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 8, characterized in that: Step 2-3: Define the error z3 = x3 - α 2f , where α 2f Represents the filtered signal of α2, α2 represents the virtual control of x3. To ensure that the error z2 tends to 0, it is necessary to ensure that the error z3 tends to 0, as follows: Taking the derivative of z3 we get: According to formula (20), the control input of the valve core, that is, the nonlinear robust position axis control controller u with gain self-learning mechanism is: In formula (21), gain k3>0, u a represents the model-based compensation term, u s represents the robust term, u s1 represents the linear robust term, u s2 represents the nonlinear robust term, σ4(t) represents a function that is always positive and satisfies Where ν represents the integration variable, represents a positive constant, l4>0 represents the upper bound of D2, Represents the estimated value of l4, and its update law for: In formula (22), γ4 represents a positive gain; Substituting formula (21) into formula (20) yields: Go to step 3.

10. The self-learning gain position axis control method of the electro-hydraulic proportional servo valve according to claim 9, characterized in that: The stability of the nonlinear robust position axis control controller is proved by using Lyapunov stability theory as described in step 3, and the result that the system tracking error is asymptotically stable is obtained, as follows: The Lyapunov function is defined as follows: Among them, the intermediate variable Intermediate variables Intermediate variables Intermediate variables The stability is proved by using Lyapunov stability theory, and the result is that the system tracking error is asymptotically stable.

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