A shaft control method for electro-hydraulic proportional servo valve considering time-varying parameter uncertainty
By designing an adaptive dynamic surface controller, the time-varying parameter uncertainty problem of the electro-hydraulic proportional servo valve axis control system is solved, high-precision tracking performance and anti-interference ability are achieved, and the instability and noise influence of traditional control methods are avoided.
Patent Information
- Application Number
- CN202210538766.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-05-18
- Publication Date
- 2025-10-03
- Estimated Expiration
- 2042-05-18
AI Technical Summary
The electro-hydraulic proportional servo valve axis control system has time-varying parameter uncertainty and uncertainty nonlinearity, which leads to the instability or order reduction of the existing controller design, making it difficult to achieve high-precision tracking performance.
An adaptive dynamic surface controller considering time-varying parameter uncertainty is designed. Its stability is proved by Lyapunov stability theory. It can actively compensate for the uncertainty of time-varying parameters of the system, avoid the differential explosion problem, reduce the influence of measurement noise, and improve control accuracy.
The system effectively compensates for the uncertainty of time-varying parameters, improves the anti-interference ability, avoids the differential explosion problem, and achieves high-precision tracking performance.
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Figure CN114879501B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of electromechanical servo control, and in particular to an electro-hydraulic proportional servo valve axis control method (ADSC) taking into account uncertainty of time-varying parameters. 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 previously 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. Among them, adaptive control methods are very effective for dealing with parameter uncertainty and can achieve steady-state performance with asymptotic tracking. 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 deal with any bounded modeling uncertainty and achieve steady-state performance with asymptotic tracking. 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. Summary of the Invention
[0004] The present invention proposes an electro-hydraulic proportional servo valve axis control method that takes into account the uncertainty of time-varying parameters. It can not only ensure the active elimination of the uncertainty of the system's time-varying parameters and improve the system's ability to resist parameter uncertainty, but also avoid the differential explosion problem in traditional backstepping control of electro-hydraulic systems, reduce the impact of measurement noise on control accuracy, and achieve high-precision tracking performance.
[0005] The technical solution for achieving the purpose of the present invention is: a method for controlling an axis of an electro-hydraulic proportional servo valve taking into account the uncertainty of time-varying parameters, comprising the following steps:
[0006] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve position axis control system, and then proceed to step 2;
[0007] Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, design an adaptive dynamic surface controller that takes into account the uncertainty of time-varying parameters, and then proceed to step 3;
[0008] Step 3: Use Lyapunov stability theory to prove the stability of the adaptive dynamic surface controller considering time-varying parameter uncertainty, and obtain the result that the system tracking error is asymptotically stable.
[0009] Compared with the existing technology, the present invention has the following significant advantages: (1) it realizes active compensation of system time-varying parameter uncertainty and unknown disturbances, and has strong anti-interference ability; (2) it avoids the differential explosion problem in traditional backstepping control of electro-hydraulic systems, 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
[0010] Figure 1 It is a schematic diagram of the principle of the electro-hydraulic proportional servo valve axis control method considering the uncertainty of time-varying parameters of the present invention.
[0011] Figure 2 This is a schematic diagram of the principle of the electro-hydraulic proportional servo valve axis control system of the present invention.
[0012] Figure 3 It is a curve diagram of the tracking process of the system output to the expected instruction under the action of the ADSC controller designed by the present invention.
[0013] Figure 4 It is a graph showing the tracking error of the system changing with time under the action of the ADSC controller designed by the present invention.
[0014] Figure 5 This is a comparison curve of the tracking errors of the system under the action of the ADSC controller designed by the present invention and the traditional PID controller.
[0015] Figure 6 It is a control input curve diagram of the system under the action of the ADSC controller designed by the present invention. DETAILED DESCRIPTION
[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0017] Combine Figure 1 and Figure 2 The present invention provides an electro-hydraulic proportional servo valve axis control method considering the uncertainty of time-varying parameters, comprising the following steps:
[0018] Step 1: Establish a mathematical model of the electro-hydraulic proportional servo valve position axis control system.
[0019] 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.
[0020] According to Newton's second law, the force balance equation of the electro-hydraulic proportional servo valve position axis control system is:
[0021]
[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, It represents the acceleration of the hydraulic cylinder piston rod, A represents the effective area of the hydraulic cylinder piston, P1 represents the oil pressure of the hydraulic cylinder inlet chamber, P2 represents the oil pressure of the hydraulic cylinder outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder ... effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston, B represents the effective area of the hydraulic cylinder piston, A represents the effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston f represents the Coulomb friction amplitude of the hydraulic cylinder, represents the approximate shape function of the Coulomb friction 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]
[0025] In the electro-hydraulic proportional servo valve position axis control system, ignoring the leakage of oil in the cylinder, the pressure dynamic equation is:
[0026]
[0027] In formula (3), β e Indicates the effective elastic modulus of the 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.
[0028] 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:
[0029]
[0030] 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:
[0031]
[0032] 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:
[0033]
[0034] Formula (6), intermediate variable k u =k q k i , intermediate variables Intermediate variables
[0035] Step 1-2, define state variables: Among them, the intermediate variable x1=y, the intermediate variable Intermediate variable x3 = (AP1-AP2) / m, unknown time-varying parameters of the system Θ1 = [θ1, θ2, θ3] T =[B,A f ,D1] T , where intermediate variable θ1 = B, intermediate variable θ2 = A f , intermediate variable θ3=D1, unknown time-varying parameter Θ2=D2, then transform Equation (2) into the state equation:
[0036]
[0037] Formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, Represents the first-order derivative of x3, an intermediate variable Intermediate variables Intermediate variable D1=d1(t) / m, intermediate variable Intermediate variables Intermediate variables Intermediate variables
[0038] To facilitate the design of the controller and the unknown dynamic observer, the following assumptions are made:
[0039] 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.
[0040] Assumption 2: The unknown time-varying parameters Θ1 and Θ2 of the system satisfy:
[0041] ||Θ1||≤δ1,||Θ2||≤δ2 (8)
[0042] In formula (8), δ1 and δ2 are both unknown positive constants.
[0043] Go to step 2.
[0044] Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, an adaptive dynamic surface controller is designed that takes into account the uncertainty of time-varying parameters. The specific steps are as follows:
[0045] 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 command, and the following nonlinear filter is designed:
[0046]
[0047] Formula (9), filter gain τ1>0, α1 represents the virtual control of x2, α 1f represents the filtered signal of α1, α 1f The error with x2 is z2 = x2-α 1f , α1 filtering error ε1 = α 1f -α1, gain l1>0 means The upper bound of , 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 .
[0048] Taking the derivative of z1, we get:
[0049]
[0050] Design the virtual control α1 as:
[0051]
[0052] in, Represents x d The first-order derivative of , gain k1>0, then
[0053]
[0054] Step 2-2, take the derivative of z2 and get:
[0055]
[0056] Design the following nonlinear filter:
[0057]
[0058] Formula (14), 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 , α2 filtering error ε2 = α 2f -α2, gain l2>0 means The upper bound of , 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 .
[0059] Defining intermediate variables Design the virtual control α2 as:
[0060]
[0061] In formula (15), χ1 represents the intermediate variable, express The estimated value of the gain k2>0, the intermediate variable The update law for
[0062]
[0063] Formula (16), gain μ1>0.
[0064] Substituting formula (15) into formula (13), we get:
[0065]
[0066] Step 2-3, take the derivative of z3 and get:
[0067]
[0068] Defining intermediate variables According to formula (18), the control input of the valve core, that is, the adaptive dynamic surface controller u designed considering the uncertainty of time-varying parameters, is:
[0069]
[0070] Formula (19), gain k3>0, intermediate variable χ2 represents the intermediate variable, express The estimated value of Update Law for
[0071]
[0072] Formula (20), gain μ2>0.
[0073] Substituting formula (19) into formula (18) yields:
[0074]
[0075] Go to step 3.
[0076] Step 3: Lyapunov stability theory is used to prove the stability of the adaptive dynamic surface controller considering time-varying parameter uncertainty, and the result that the system tracking error is asymptotically stable is obtained, as follows:
[0077] The Lyapunov function is defined as follows:
[0078]
[0079] Among them, the intermediate variable Intermediate variables
[0080] Taking the derivative of equation (22) and substituting equations (9), (12), (14), (16), (17), (20) and (21) into it, we can obtain:
[0081]
[0082] Taking into account and The expression can be obtained:
[0083]
[0084] Notice
[0085]
[0086] Available
[0087]
[0088] Substituting equations (25) and (26) into equation (24), we can obtain
[0089]
[0090] Define the intermediate variables z and Λ as:
[0091] z=[z1;z2;z3;ε1;ε2] (28)
[0092]
[0093] Formula (29), the intermediate variables Λ1 and Λ2 are
[0094]
[0095] 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:
[0096]
[0097] Formula (31), intermediate variable Φ = z T Λz.
[0098] Integrating both sides of equation (31) we can get:
[0099]
[0100] From Equation (32), we can see that V is bounded and Φ is integrally bounded. Furthermore, we can conclude that all signals in the system are bounded. Therefore, Φ is uniformly continuous. According to Barbalat's lemma, as time approaches positive infinity, the tracking error z1 approaches 0.
[0101] Therefore, it is concluded that by adjusting the gains k1, k2, k3 and the filter gains τ1, τ2, the adaptive dynamic surface controller designed for the electro-hydraulic proportional servo valve position axis control system considering the uncertainty of time-varying parameters can make the system obtain the result that the tracking error converges to 0 asymptotically. The principle diagram of the adaptive dynamic surface controller for the electro-hydraulic proportional servo valve position axis control system considering the uncertainty of time-varying parameters is shown in the figure. Figure 1 shown.
[0102] Example
[0103] 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:
[0104] Table 1 System physical parameters
[0105] Physical parameters Numerical Physical parameters Numerical <![CDATA[A(m 2 )]]> <![CDATA[2×10 -4 ]]> <![CDATA[β e (Well)]]> <![CDATA[2×10 8 ]]> m(kg) 40 B (N·s / m) 80 <![CDATA[C t (m 5 / (N·s))]]> <![CDATA[7×10 -12 ]]> <![CDATA[k u (m / V)]]> <![CDATA[4×10 -8 ]]> <![CDATA[V 01 (m 3 )]]> <![CDATA[1×10 -3 ]]> <![CDATA[V 02 (m 3 )]]> <![CDATA[1×10 -3 <!-- 7 -->]]> <![CDATA[P s (MPa)]]> 7 <![CDATA[P r (MPa)]]> 0 <![CDATA[A f (N·s / m)]]> 10
[0106] The expected instructions for a given system are The Coulomb friction shape function is S f (x2) = 2arctan(1000x2) / π.
[0107] The following controllers are used for comparison in the simulation:
[0108] Electro-hydraulic proportional servo valve position axis control controller (UDORC) considering unknown dynamic compensation of the system: take gains k1=10, k2=1, k3=1, μ1=20, μ2=20, τ1=100, τ2=1000, l1=l2=1.
[0109] 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 =10,k I =1,k D =1.
[0110] The expected command of the system, the tracking error of the ADSC controller, and the tracking error comparison between the ADSC controller and the PID controller are as follows: Figure 3 、 Figure 4 and Figure 5 As shown. Figure 4 It can be seen that under the action of the ADSC 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 -4 m. From Figure 5 The comparison of the tracking errors of the two controllers shows that the tracking error of the ADSC controller proposed in the present invention is much smaller than that of the PID controller, and the tracking performance is more superior.
[0111] Figure 6 This is a graph showing the change of control input of the electro-hydraulic proportional servo valve axis control system over time under the action of the ADSC controller. It can be seen from the figure that the obtained control input is a continuous signal, which is more conducive to execution in practical applications.
Claims
1. A method for controlling an electro-hydraulic proportional servo valve axis taking into account the uncertainty of time-varying parameters, 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, 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 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; 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, It represents the acceleration of the hydraulic cylinder piston rod, A represents the effective area of the hydraulic cylinder piston, P1 represents the oil pressure of the hydraulic cylinder inlet chamber, P2 represents the oil pressure of the hydraulic cylinder outlet chamber, B represents the viscous damping coefficient of the hydraulic cylinder ... effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston, B represents the effective area of the hydraulic cylinder piston, A represents the effective area of the hydraulic cylinder piston, P2 represents the effective area of the hydraulic cylinder piston f represents the Coulomb friction amplitude of the hydraulic cylinder, represents the approximate shape function of the Coulomb friction 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 the 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: Formula (6), intermediate variable k u =k q k i , intermediate variables Intermediate variables Step 1-2, define state variables: Among them, the intermediate variable x1=y, the intermediate variable Intermediate variable x3 = (AP1-AP2) / m, unknown time-varying parameters of the system Θ1 = [θ1, θ2, θ3] T =[B,A f ,D1] T , where intermediate variable θ1 = B, intermediate variable θ2 = A f , intermediate variable θ3=D1, unknown time-varying parameter Θ2=D2, then transform Equation (2) into the state equation: Formula (7), represents the first-order derivative of x1, represents the first-order derivative of x2, Represents the first-order derivative of x3, an intermediate variable Intermediate variables Intermediate variable D1=d1(t) / m, intermediate variable Intermediate variables Intermediate variables Intermediate variables To facilitate the design of the controller and the unknown dynamic observer, 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 time-varying parameters Θ1 and Θ2 of the system satisfy: In formula (8), δ1 and δ2 are both unknown positive constants; Go to step 2; Step 2: Based on the mathematical model of the electro-hydraulic proportional servo valve position axis control system, an adaptive dynamic surface controller is designed that takes into account the uncertainty of time-varying parameters. The specific steps are as follows: 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 command, and the following nonlinear filter is designed: Formula (9), filter gain τ1>0, α1 represents the virtual control of x2, α 1f represents the filtered signal of α1, α 1f The error with x2 is z2 = x2-α 1f , α1 filtering error ε1 = α 1f -α1, gain l1>0 means The upper bound of , 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 ; Taking the derivative of z1, we get: Design the virtual control α1 as: in, Represents x d The first-order derivative of , gain k1>0, then Step 2-2, take the derivative of z2 and get: Design the following nonlinear filter: Formula (14), 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 , α2 filtering error ε2 = α 2f -α2, gain l2>0 means The upper bound of , 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 ; Define the intermediate variable θ1 = sup t≥0 ||Θ1||, design the virtual control α2 as: In formula (15), χ1 represents the intermediate variable, represents the estimated value of θ1, gain k2>0, intermediate variable The update law for Formula (16), gain μ1>0; Substituting formula (15) into formula (13), we get: Step 2-3, take the derivative of z3 and get: Define the intermediate variable θ2 = sup t≥0 ||Θ2||, according to formula (18), the control input of the valve core, that is, the adaptive dynamic surface controller u designed considering the uncertainty of time-varying parameters, is: Formula (19), gain k3>0, intermediate variable χ2 represents the intermediate variable, represents the estimated value of θ2, Update Law for Formula (20), gain μ2>0; Substituting formula (19) into formula (18) yields: Go to step 3; Step 3: Use Lyapunov stability theory to prove the stability of the adaptive dynamic surface controller considering time-varying parameter uncertainty, and obtain the result that the system tracking error is asymptotically stable.
2. The electro-hydraulic proportional servo valve axis control method considering time-varying parameter uncertainty according to claim 1, characterized in that: The stability of the adaptive dynamic surface controller considering time-varying parameter uncertainty 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 The stability is proved by using Lyapunov stability theory, and the result is that the system tracking error is asymptotically stable.