Predefined time tracking control method for electro-hydraulic proportional multi-way valve position control system

Abstract

The application discloses a predefined time tracking control method of an electro-hydraulic proportional multi-way valve position control system, which is based on a constructed predefined time adaptive control and a disturbance observer, fuses an instruction filter backstepping control thought, and designs a nonlinear predefined time tracking controller which considers unknown system parameter uncertainty and unmodeled disturbance compensation. For the electro-hydraulic proportional multi-way valve position control problem, the application can not only ensure accurate compensation of system uncertainty within the predefined time, improve the anti-interference performance of the system, but also avoid the differential explosion phenomenon in the backstepping control process of the high-order electro-hydraulic proportional multi-way valve system, reduce the influence of measurement noise on the control precision, effectively solve the problem of poor convergence performance of the traditional nonlinear control method, and make the convergence time not dependent on the initial state of the system, so that good transient and steady-state tracking performance is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to electro-hydraulic proportional control technology, and in particular to a predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system. BACKGROUND

[0002] The multi-way valve is one of the core control components of engineering machinery equipment. High precision, high frequency response, and strong anti-interference ability have become the urgent needs of the multi-way valve position control system. With the development of technology, the application of electro-hydraulic proportional control technology in the multi-way valve has significantly improved the performance of the multi-way valve and improved its automation level, so that the multi-way valve can be applied in many major equipment fields such as aerospace. However, due to the influence of machining precision, parameter uncertainty caused by pressure and temperature, and external disturbances, the multi-way valve presents complex nonlinear characteristics in actual application, which is a bottleneck factor restricting the improvement of its control performance, which makes the application of traditional control strategies have great limitations, and the control in actual engineering application is more difficult. Therefore, it is of great significance to study the nonlinear characteristics of the multi-way valve and design advanced controllers for the multi-way valve system based on electro-hydraulic proportional control technology to improve the control precision and overall control performance of the electro-hydraulic proportional multi-way valve system, and to promote the multi-way valve to meet the control needs of more different application scenarios.

[0003] Many methods have been studied and applied for the nonlinear control problem of the electro-hydraulic proportional multi-way valve position control system, such as sliding mode control, adaptive robust control (ARC), etc. However, sliding mode control often leads to control input discontinuity and chattering problems in physical systems; adaptive robust control can only guarantee that the tracking error is bounded in theory when both parameter uncertainty and unmodeled disturbances exist. It is worth noting that most existing electro-hydraulic proportional control techniques can only guarantee that the system tracking error approaches zero or tends to be arbitrarily small as time goes to infinity. For actual engineering applications, response speed is a key indicator for evaluating the dynamic tracking characteristics of the controlled system. Therefore, in the past few decades, the response time constraint of nonlinear controllers has received widespread attention from control scholars. In order to deal with such problems, finite / fixed time control has been gradually introduced. However, these two types of controller design have obvious shortcomings. The convergence time of the system under the finite time controller often depends on the initial conditions of the system, and the performance of the control method will decrease significantly in the case of large initial state values or difficult to obtain accurately, and whether it is finite time control or fixed time control, the stabilization time is inevitably affected by multiple design parameters, which makes the description of the system performance inaccurate. Therefore, the concept of predefined time control provides substantial theoretical value and practical significance, because this control method helps to arbitrarily specify the stabilization time, and is independent of the initial conditions of the system and the design parameters, and has good application prospects in the electro-hydraulic proportional multi-way valve position control system. SUMMARY

[0004] The present application aims to provide a pre-defined time tracking control method for electro-hydraulic proportional multi-way valve position control system with low calculation complexity and high control performance, which can ensure the overall pre-defined time practical stability of the system and avoid the problem of differential explosion in traditional backstepping control method.

[0005] The technical solution for achieving the present application is as follows: a pre-defined time tracking control method for electro-hydraulic proportional multi-way valve position control system, comprising the following steps:

[0006] Step 1: establishing the mathematical model of the electro-hydraulic proportional multi-way valve position control system, and going to Step 2.

[0007] Step 2: designing a pre-defined time tracking controller according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, and going to Step 3.

[0008] Step 3: using Lyapunov stability theory to prove the stability of the electro-hydraulic proportional multi-way valve position control system using the pre-defined time tracking controller, and obtaining the result that the tracking error of the system within the pre-defined time converges to the neighborhood of zero.

[0009] Compared with the prior art, the present application has the following significant advantages: while accurately estimating the parameter uncertainty and unmodeled disturbance of the system, it effectively solves the problem of poor transient tracking error convergence performance of the traditional nonlinear method, and the system stable time is independent of the initial state and the controller parameters, thus obtaining better tracking performance. The simulation results verify the effectiveness thereof. BRIEF DESCRIPTION OF DRAWINGS

[0010] Figure 1 is the principle diagram of the electro-hydraulic proportional multi-way valve position control system of the present application.

[0011] Figure 2 is the principle diagram of the pre-defined time tracking control method for the electro-hydraulic proportional multi-way valve position control system.

[0012] Figure 3 is the tracking error curve of the electro-hydraulic proportional multi-way valve position control system of the present application under the action of the pre-defined time tracking control method (ADOPTC) and the speed feedforward PI controller (VFPI) when the expected instruction of the system is x 1d = 0.2·sin(π·t)-0.05m.

[0013] Figure 4 is the tracking process curve of the system output under the action of the ADOPTC of the present application when the expected instruction of the system is x 1d = 0.2·sin(π·t)-0.05m.

[0014] Figure 5 is the system desired command for x 1d is the system desired command for x

[0015] Figure 6 is the system desired command for x 1d is the system desired command for x

[0016] Figure 7 is the system desired command for x 1d is the system desired command for x DETAILED DESCRIPTION

[0017] The present application is directed to an electro-hydraulic proportional multi-way valve position control system, and proposes a predefined time tracking control method, introduces a predefined time adaptive law to deal with parameter uncertainty, and designs a new disturbance observer to dynamically compensate for unmodeled disturbances; then, based on the command filter backstepping control framework, a predefined time tracking controller using a predefined time command filter is developed. The innovation of the present application is that the present application first proposes a predefined time tracking control method that can be applied to an electro-hydraulic proportional multi-way valve position control system, which can simultaneously estimate and actively compensate for system parameter uncertainty and unmodeled disturbances, effectively solving the problem of poor transient tracking error convergence performance of traditional nonlinear methods, and the system stable time is independent of the initial state condition and the controller parameter, and better tracking performance is obtained.

[0018] The present application will be further described in detail below in combination with the accompanying drawings and specific embodiments.

[0019] In combination with Figures 1-2 , the predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system according to the present application comprises the following steps:

[0020] Step 1, establish a mathematical model of the electro-hydraulic proportional multi-way valve position control system;

[0021] Step 1-1, assume that the electro-hydraulic proportional multi-way valve position control system is directly driving an inertial load through a valve-controlled double-rod hydraulic cylinder, and the control target is to enable the inertial load to track any smooth motion trajectory, idealize the electro-hydraulic proportional multi-way valve position control system by simplifying the electric proportional pressure reducing valve, and mainly consider the influence of the characteristics of the main valve and the hydraulic cylinder part:

[0022] Therefore, according to Newton's second law, the motion equation of the electro-hydraulic proportional multi-way valve position control system is:

[0023]

[0024] In formula (1), m is the mass of the inertial load, y is the displacement of the inertial load, P L is the differential pressure of the two cavities of the hydraulic cylinder, A is the working area of the hydraulic cylinder, B v represents the effective viscous damping coefficient, f(t) is the uncertainty of the system that is not matched, is the velocity of the inertial load, is the acceleration of the inertial load, and t represents the running time;

[0025] The flow continuity equation of the electro-hydraulic proportional multi-way valve position control system is:

[0026]

[0027] In formula (2), V t is the volume of the hydraulic cylinder, represents the derivative of P L , β e is the effective bulk modulus of the hydraulic oil, C t is the leakage coefficient, Q L is the flow rate, and q(t) represents the model uncertainty caused by complex internal leakage, parameter uncertainty and unmodeled dynamic effect factors;

[0028] Neglecting the spool dynamics, the flow equation of the electro-hydraulic proportional multi-way valve is:

[0029]

[0030] In formula (3), P s is the constant oil supply pressure of the system; u is the spool displacement of the main valve, which is the system control input; C d is the flow coefficient, w is the area gradient, and ρ is the oil density. The sign function sign(u) is defined as:

[0031]

[0032] After linear processing of formula (3), the following is obtained:

[0033] Q L =k d1 u-k d2 P L (4)

[0034] In formula (4), k d1 is the flow gain, and k d2 is the pressure-flow coefficient;

[0035] Step 1-2, when the viscous damping on the main valve is neglected, the state variable x is defined: The state equation of the electro-hydraulic proportional multi-way valve position control system is:

[0036]

[0037] wherein x1 represents the displacement of the inertial load, x2 represents the speed of the inertial load, x3 represents the pressure difference between the two cavities of the hydraulic cylinder, represents the derivative of x1, represents the derivative of x2, represents the derivative of x3;

[0038] Define unknown parameter variable θ1=B v / m, unknown parameter variable θ2=4β e (C t +k d2 ) / V t , then equation (5) is written as

[0039]

[0040] wherein coefficients g1, g2, g3 are all known constants: g1=A / m, g2=4β e k d1 / V t , g3=4β e A / V t ; model term model term System non-matching interference term d1=f(t) / m, system matching interference term d2=4β e q(t) / V t ;

[0041] For the convenience of controller design, the following is assumed:

[0042] Assumption 1: The position command x d to be tracked by the system is a second-order continuous differentiable and bounded;

[0043] Assumption 2: The electro-hydraulic position servo system works under normal working conditions, and the pressures P1 and P2 of the inlet and outlet cavities of the hydraulic cylinder must satisfy the following conditions: 0<P r <P1<P s , 0<P r <P2<P s ; P r represents the system back pressure;

[0044] Assumption 3: The matching and non-matching uncertainties of the system satisfy: wherein represents the first-order derivative of d1, denotes the first derivative of d2, K1, K2 are known normal numbers.

[0045] Go to Step 2.

[0046] Step 2, according to the mathematical model of electro-hydraulic proportional multi-way valve position control system, design pre-defined time tracking controller, the steps are as follows:

[0047] Step 2-1, in order to realize the active compensation of the uncertainty in the electro-hydraulic proportional multi-way valve position control system, the pre-defined time adaptive control law is constructed to estimate the parameter uncertainty of the system, and the pre-defined time disturbance observer is constructed to estimate the unknown disturbance of the system, the specific steps are as follows:

[0048] In order to design the pre-defined time adaptive control, the first order filter form is as follows for the channel with uncertainty in equation (6): * f | t＝0 = 0, where * represents the filter input, f represents the filter output, represents the first derivative of the variable *, κ is the filter coefficient, and the following equation relationship is obtained:

[0049]

[0050] In equation (7), x 2f , x 3f , u f , d 1f , d 2f correspond to x2, x3, u, d1, d2 corresponding filter output;

[0051] Define intermediate variables and

[0052]

[0053] Define intermediate variables M1, N1, M2 and N2:

[0054]

[0055] In equation (9), the independent variable i = 1, 2, and λ is the filter coefficient;

[0056] Then the solution of equation (9) is:

[0057]

[0058] In equation (10), τ represents the independent variable of the integral function;

[0059] N is obtained from equation (10) i =M i θ i ,

[0060] And thus obtain

[0061] Among them, the adaptive law estimation error Representing the unknown parameter θ i The estimate;

[0062] The predefined time-adaptive control law based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system is designed as follows:

[0063]

[0064] In equation (11), the first adaptive coefficient Second adaptive coefficient Third adaptive coefficient δ、τ i1 τ i2 τ i ' are all adjustable parameters, satisfying 0 < δ < 1, τ i1 >0, τ i2 >0, Predefined time parameter T in uncertainty estimation u >0 can be arbitrarily defined by the user; it is an intermediate variable.

[0065] To achieve unmodeled disturbance compensation in the position control system of an electro-hydraulic proportional multi-way valve, a preset time disturbance observer with the following form is constructed:

[0066]

[0067] In equation (12), d i The estimated value, x represents i+1 The estimated value, s represents the independent variable of the integral function, and the coefficient of the first observer. Second observer coefficients Third observer coefficients

[0068] Step 2-2: Based on the proactive compensation for system uncertainties and unknown disturbances in Step 2-1, to avoid the potential differential explosion problem in traditional backstepping control of the electro-hydraulic proportional multi-way valve position control system, a predefined time command filter is constructed:

[0069]

[0070] In formula (13), the predefined time parameter T c > 0 can be defined by the user at will, the adjustable filter coefficient ζ is a normal number satisfying 0 < ζ < 1, and α i represents the virtual control of x i+1 . represents the filter signal of α i .

[0071] Step 2-3, according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, combining the predefined time adaptive control law, the predefined time disturbance observer, and the predefined time command filter, a predefined time tracking controller u considering the compensation of uncertainty is designed, which is as follows:

[0072] The tracking error e1 = x1-x d of the system is defined, and x d is the position command expected to be tracked by the system. The virtual error e2 = e1-α1 is defined. The error compensation signal ξ1 = e1-η1 is defined, the error compensation signal ξ2 = e2-η2 is defined, and the error compensation signal ξ3 = e3-η3 is defined, wherein η1, η2, and η3 represent the designed filter error compensator.

[0073] The derivative of e1 is obtained, and according to the definition of e2, the following is obtained:

[0074]

[0075] The filter error is selected as the input signal, and the filter error compensator η1 of the virtual control α1 is constructed.

[0076]

[0077] In formula (15), the predefined time parameter T e > 0 can be defined by the user at will, η1 and η2 are filter error compensators of α1 and α2 respectively, γ is an adjustable controller coefficient, and satisfies 0 < γ < 1, and the function sig 1- γ(η1) is defined as: sig 1-γ (η1) = |η1| 1-γ sign(η1);

[0078] The derivative of the error compensation signal ξ1 = e1-η1 is obtained.

[0079]

[0080] Considering the influence of control singularity, the virtual control α1 of the control system is constructed based on the command filter backstepping design.

[0081]

[0082] Where the auxiliary variable M ξ1 Designed as follows:

[0083]

[0084] In equation (18), the design parameter ν 10 >0, j is the independent variable for summation, and b is the auxiliary variable. γj The assignment is as follows:

[0085]

[0086] Taking the derivative of e2, according to the definition of e3, we get:

[0087]

[0088] Selecting filter error As the input signal, construct the filter error compensator η2 for virtual control α2:

[0089]

[0090] Differentiating both sides of the error compensation signal ξ2=e2-η2, we get:

[0091]

[0092] Considering the impact of control singularities, a virtual control α2 is constructed based on instruction filtering and backstepping design for the control system:

[0093]

[0094] Where the auxiliary variable M ξ2 Designed as follows:

[0095]

[0096] Taking the derivative with respect to e3, we get:

[0097]

[0098] Construct the filter error compensator η3:

[0099]

[0100] Differentiating both sides of the error compensation signal ξ3=e3-η3, we get:

[0101]

[0102] Considering the impact of control singularities, a predefined time-tracking control u is constructed based on instruction filtering and backstepping design:

[0103]

[0104] Where the auxiliary variable M ξ3 Designed as follows:

[0105]

[0106] Proceed to step 3.

[0107] Step 3: The stability of the electro-hydraulic proportional multi-way valve position control system under the predefined time tracking control method is proved using Lyapunov stability theory. The results show that the tracking error converges to the neighborhood of zero within the predefined time period, as detailed below:

[0108] Lyapunov's predefined time stability theory: Consider a continuously differentiable function V x Satisfying the inequality: And V x ≥0, where the constant ρ, Satisfying 0 < ρ < 1, Then the corresponding control system at the predefined time T c It is internally convergent and has a steady-state error of zero.

[0109] Lyapunov's Practical Predefined Time Stability Theory: Consider a continuously differentiable function V x Satisfying the inequality: And V x ≥0, where constants ρ and L satisfy 0 < ρ < 1 and 0 < L < ∞ respectively, then the corresponding control system is in the predefined time 2T c Internally stable convergence and the steady-state error will be confined to the residual set.

[0110] Define the Lyapunov function V u as follows:

[0111]

[0112] Differentiating equation (29) yields:

[0113]

[0114] In equation (30), the intermediate variable ω i The first derivative of (t) Satisfy ω i (0) = 0, K i As defined in Assumption 3, the corollary derived from the intermediate variable is ω. i The sign of (t) and The sign is opposite, that is Then equation (30) can be simplified to:

[0115]

[0116] In formula (31), the coefficient τ' m , τ m1 , τ m2 can be expressed as a function form associated with the coefficients κ i1 , κ i2 , κ i3 , Γ i1 , Γ i2 , Γ i3 .

[0117] Using Lyapunov stability theory, it is proved that the estimation error of the unknown parameters of the system and the estimation error of the state of the system converge to zero within a predefined time. The estimation error of the unknown parameters of the system converges to zero within a predefined time.

[0118] The Lyapunov function V α is defined as follows:

[0119]

[0120] where the filter errors λ1 and λ2 are defined as

[0121] Since there are inequalities and where the constant Λ i satisfies the constant and the constant ζ>0, the derivative of formula (32) is

[0122]

[0123] where the constant

[0124] Using Lyapunov stability theory, it is proved that the filter errors λ1 and λ2 of the system under the predefined time command filter converge within a predefined time.

[0125] The Lyapunov function V η is defined as follows:

[0126]

[0127] Since there are inequalities:

[0128]

[0129] where constant χ i satisfies

[0130] Derivation of (34) gives

[0131]

[0132] where coefficient G1=1, coefficient G2=g1.

[0133] Constant

[0134] The stability proof is made by using Lyapunov stability theory, and the results that the designed system filter error compensators η1, η2, η3 are bounded convergence in predefined time are obtained.

[0135] Define Lyapunov function V ξ as follows:

[0136]

[0137] Derivation of (36) gives

[0138]

[0139] where h is the independent variable of the summation function, and constant

[0140]

[0141] The stability proof is made by using Lyapunov stability theory, and the results that the error compensation signals ξ1, ξ2, ξ3 are bounded convergence in predefined time are obtained, and the results that the tracking error e1 of the electro-hydraulic proportional multi-way valve position control system under the predefined time tracking control method of the present application converges to the neighborhood of zero in predefined time are obtained since e1=ξ1+η1.

[0142] Therefore, the conclusion is that the predefined time tracking control method designed for the electro-hydraulic proportional multi-way valve position control system (such as formula (5)) can make the system obtain the result that the tracking error converges to the neighborhood of zero in predefined time, and adjusting the uncertainty estimation parameters δ, τ i1 , τ i2 , T u , filter parameters ζ, T c and controller parameters γ, T e can make the tracking error of the system converge to the neighborhood of zero in predefined time. The principle diagram of the predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system is shown in Figure 2 .

[0143] Embodiment

[0144] To examine the performance of the designed controller, the following parameters are taken in simulation to model the electro-hydraulic proportional servo valve position axis control system:

[0145] Inertial load mass m = 1000 kg, effective viscous damping coefficient B v = 20 N·s / m, hydraulic cylinder working area A = 0.018 m 2 , hydraulic cylinder volume V t = 0.01062 m 3 , effective bulk modulus of liquid elasticity β e = 2.2 × 10 8 Pa, flow gain k d1 = 1.608 m 2 / s, pressure flow coefficient k d2 = 3.717 × 10 -12 m 5 / (N·s), flow coefficient C t = 3 × 10 -11 ;

[0146] The desired instruction of the given system is 0.2·sin(π·t)-0.05 m

[0147] The following controller is taken in simulation for comparison:

[0148] The preset time axis control method (NFPTC) of the electro-hydraulic proportional servo valve based on the disturbance observer designed in the application takes the controller parameters κ = 0.01, λ = 1, T u = 1 s, δ = 0.6, τ 11 = τ 21 = 0.01, τ 21 = τ 22 = 100, K1 = 0.02, K2 = 3.5 × 10 4 , ζ = 0.2, T c = 0.5 s, γ = 0.48, T e = 1 s.

[0149] The speed feedforward PI controller (VFPI) is: Wherein the error z1 = x 1d -x1, t is the integral time independent variable, and the controller parameters are k P = 0.03, k I = 0.08, k F = 0.01, respectively representing the proportional constant, the integral constant and the speed feedforward coefficient.

[0150] The system tracking error comparison curves under the action of ADOPTC and VFPI, and the tracking curve of the electro-hydraulic proportional multi-way valve position control system output under the action of ADOPTC to the expected command are respectively shown in Figs. Figure 3 , Figure 4 It can be seen from Fig. Figure 3 that, compared with VFPI, ADOPTC has good ability to compensate modeling uncertainty, and the obtained tracking error is smaller. By introducing the predefined time tracking control design, ADOPTC realizes the result that the tracking error converges to the neighborhood of zero after the predefined time, and the tracking performance is greatly improved. Therefore, compared with VFPI, ADOPTC realizes better tracking performance.

[0151] When the expected command of the given system is x 1d = 0.2·sin(π·t)-0.05m, Figure 5 is the curve graph of the control input of the electro-hydraulic proportional multi-way valve position control system under the action of ADOPTC changing with time. It can be seen from the graph that the obtained control input is a continuous signal, which is more conducive to the execution in actual application. Figure 6 is the estimation curve graph of ADOPTC to the unknown parameters of the system, Figure 7 is the estimation curve graph of ADOPTC to the lumped uncertainty of the system. It can be seen from the graph that the estimation of ADOPTC to the parameters of the electro-hydraulic proportional multi-way valve position control system and the lumped uncertainty of the system is stable within the predefined time.

Claims

1. A pre-defined time tracking control method of an electro-hydraulic proportional multi-way valve position control system, characterized by, Comprising the following steps: Step 1, a mathematical model of the electro-hydraulic proportional multi-way valve position control system is established, and step 2 is entered; Define unknown parameter variable θ1 = B v / m, unknown parameter variable θ2 = 4β e (C t +k d2 ) / V t Then: wherein denotes the first derivative of the variable, the coefficients g1, g2, g3 are known constants: g1 = A / m, g2 = 4β e k d1 / V t , g3 = 4β e A / V t ; model term model term system non-matched interference term d1 = f(t) / m, system matched interference term d2 = 4β e q(t) / V t ; m is the mass of the inertial load, B v denotes the effective viscous damping coefficient, β e is the effective bulk modulus of the hydraulic oil, C t is the leakage coefficient, V t is the hydraulic cylinder volume, A is the hydraulic cylinder working area, k d1 is the flow gain, k d2 is the pressure flow coefficient, x1 denotes the displacement of the inertial load, x2 denotes the speed of the inertial load, x3 denotes the pressure difference between the two chambers of the hydraulic cylinder, denotes the derivative of x1, denotes the derivative of x2, denotes the derivative of x3; u is the displacement of the main valve spool, as the system control input; Step 2, according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, a pre-defined time tracking controller is designed, Specifically as follows: Step 2-1, in order to realize active compensation of the uncertainty in the electro-hydraulic proportional multi-way valve position control system, a pre-defined time adaptive control law is constructed to estimate the uncertainty of the system parameters, and a pre-defined time disturbance observer is constructed to estimate the unknown disturbance of the system; The specific steps are as follows: To predefine the time-adaptive control design, a first-order filter is applied to both sides of the uncertain channel in equation (6) as follows: * f | t＝0 =0, where * represents the filtered input, * f Let κ represent the filtered output and the filter coefficients, resulting in the following equation: In formula (7), x 2f , x 3f , u f , d 1f , d 2f respectively correspond to x2, x3, u, d1, d2 correspond to the filter output; Defining intermediate variables and Define intermediate variables M1, N1, M2 and N2: In formula (9), the independent variable i=1, 2, and λ is the filter coefficient; Then the solution of formula (9) is: In formula (10), τ represents the independent variable of the integral function; N is obtained from formula (10) i = M i θ i , Further, it is obtained where the adaptive law estimation error denotes the estimate of the unknown parameter i ; Then the pre-defined time adaptive control law based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system is: In formula (11), the first adaptive coefficient The second adaptive coefficient The third adaptive coefficient δ, τ i1 , τ i2 , τ i are adjustable parameters, satisfying 0 < δ < 1, τ i1 > 0, τ i2 > 0, The predefined time parameter T in the uncertainty estimation u > 0 can be arbitrarily defined by a user, and the intermediate variable In order to realize the compensation of the unmodeled disturbance of the electro-hydraulic proportional multi-way valve position control system, a pre-defined time disturbance observer with the following form is constructed: in formula (12), denotes d i the estimate of denotes x i+1 the estimate of s denotes the integral function argument, the first observer coefficient the second observer coefficient the third observer coefficient Step 2-2, based on the active compensation of the system uncertainty and unknown disturbance in step 2-1, in order to avoid the potential differential explosion problem of the electro-hydraulic proportional multi-way valve position control system in the traditional backstepping control, a pre-defined time command filter is constructed; Step 2-3, according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, combined with the pre-defined time adaptive control law, the pre-defined time disturbance observer and the pre-defined time command filter, a pre-defined time tracking controller considering uncertainty compensation is designed; Enter step 3; Step 3, using Lyapunov stability theory, the stability of the electro-hydraulic proportional multi-way valve position control system using the pre-defined time tracking controller is proved, and the result that the tracking error of the system converges to the neighborhood of zero within the pre-defined time is obtained.

2. The pre-defined time tracking control method of an electro-hydraulic proportional multiple valve position control system according to claim 1, characterized by, In step 1, the mathematical model of the electro-hydraulic proportional multi-way valve position control system is established, specifically as follows: Step 1-1, assuming that the electro-hydraulic proportional multi-way valve position control system is directly driven by a valve-controlled double-rod hydraulic cylinder to drive an inertial load, the control objective is to make the inertial load track any smooth motion trajectory, the ideal simplification is made to the electro-hydraulic proportional multi-way valve position control system, and the influence of the characteristics of the main valve and the hydraulic cylinder is mainly considered: Therefore, according to Newton's second law, the motion equation of the electro-hydraulic proportional multi-way valve position control system is: In formula (1), y is displacement of the inertial load, P L is the differential pressure of the two chambers of the hydraulic cylinder, f(t) is the uncertainty of the system mismatch, is the velocity of the inertial load, is the acceleration of the inertial load, t represents the running time; The flow continuity equation of the electro-hydraulic proportional multi-way valve position control system is: In formula (2), represents P L derivative, Q L is the flow rate, q(t) represents model uncertainty due to complex internal leakage, parameter uncertainty and unmodeled dynamic effects factors; Neglecting the spool dynamics, the flow equation of the electro-hydraulic proportional multi-way valve is: In formula (3), P s is a system constant oil supply pressure; C d is a flow coefficient, w is an area gradient, p is oil density, and a sign function sign(u) is defined as: After linear processing of formula (3), the following formula is obtained: Q L = k d1 u - k d2 P L (4) Step 1-2, Define state variable x when ignoring the viscous damping of the main valve: Then the state equation of the electro-hydraulic proportional multi-way valve position control system is: Then formula (5) is written as In order to facilitate controller design, the following assumptions are made: Assumption 1: The position command x that the system is expected to track d Second order continuous differentiable and bounded; Assumption 2: The electro-hydraulic position servo system works in normal working condition, the pressures P1 and P2 of the inlet and outlet oil chambers of the hydraulic cylinder must satisfy the following conditions: 0 < P r <P1<P s , 0 < P r <P2<P s ; P r represents the system back pressure; Assumption 3: The uncertainty of system matching and mismatching satisfies: wherein denotes the first derivative of d1, denotes the first derivative of d2, K1, K2 are both known normal numbers.

3. The pre-defined time tracking control method of an electro-hydraulic proportional multiple valve position control system according to claim 2, characterized in that, In step 2-2, in order to avoid the potential differential explosion problem of the electro-hydraulic proportional multi-way valve position control system in the traditional backstepping control, a pre-defined time command filter with the following form is constructed: In formula (13), the predefined time parameter T in the predefined time command filter design c > 0 can be arbitrarily defined by a user, and the adjustable filter coefficient ζ is a normal number satisfying 0 < ζ < 1, and α i represents a virtual control of x i+1 represents a filter signal of α i .​ 4. The pre-defined time tracking control method of an electro-hydraulic proportional multiple valve position control system according to claim 3, characterized by, In step 2-3, based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system, a pre-defined time tracking controller u considering uncertainty compensation is designed, specifically as follows: The tracking error of the system is defined as e1 = x1 - x d , x d is the position command that the system is expected to track, and the virtual error is defined as e1 - x The error compensation signals are defined as ξ1 = e1 - η1, ξ2 = e2 - η2, and ξ3 = e3 - η3, where η1, η2, and η3 represent the designed filter error compensators. Differentiate e1, according to the definition of e2, we have: selecting a filtered error For the input signal, a filtered error compensator η1 of the virtual control α1 is constructed: The predefined time parameter T in formula (15) e > 0 can be arbitrarily defined by the user, η1 and η2 are filter error compensators of α1 and α2 respectively, γ is an adjustable controller coefficient, and satisfies 0 < γ < 1, and the function sig 1-γ (η1) is defined as: sig 1-γ (η1) = |η1| 1-γ sign(η1); Differentiate the error compensation signal ξ1=e1-η1 on both sides, we have: Considering the influence of control singularity, the virtual control α1 is designed based on command filtered backstepping: where the auxiliary variable M ξ1 is designed to: The design parameter v in equation (18) 10 > 0, j is the summation argument, and the auxiliary variable b γj is assigned the value Taking the derivative of e2, according to the definition of e3, we have: selecting the filtered error As an input signal, construct a filtered error compensator η2 of the virtual control α2, and derive η2: Taking the derivative of the error compensation signal ξ2 = e2- η2, we have: Considering the influence of control singularity, the virtual control α2 is designed based on command filtered backstepping: where the auxiliary variable M ξ2 is designed to: Taking the derivative of e3, we have: The filter error compensator η3 is constructed, and the derivative of η3 is taken: Taking the derivative of the error compensation signal ξ3 = e3- η3, we have: Considering the influence of control singularity, the predefined time tracking control u is designed based on command filtered backstepping: where the auxiliary variable M ξ3 is designed to:

5. The pre-defined time tracking control method of an electro-hydraulic proportional multiple valve position control system according to claim 4, characterized by, In step 3, the Lyapunov stability theory is used to prove the stability of the electro-hydraulic proportional multi-way valve position control system under the action of the predefined time tracking controller, and the result that the tracking error of the system converges to the neighborhood of zero within the predefined time is obtained, as follows: Defining a Lyapunov function V u As follows: The stability proof is done by using Lyapunov stability theory, and the estimation error of the unknown parameters of the system by the predefined time adaptive control law and the estimation error of the states of the system by the predefined time disturbance observer converges to zero in a predefined time, and the result after the predefined time the estimation error of the unmodeled disturbances of the system by the predefined time disturbance observer converges to zero in a predefined time; Defining a Lyapunov function V α As follows: wherein the filter errors λ1, λ2 are defined as argument i = 1, 2; The Lyapunov stability theory is used to prove the stability, and the result that the filter errors λ1, λ2 of the system under the command filter are bounded and converge within the predefined time is obtained; Defining a Lyapunov function V η As follows: The Lyapunov stability theory is used to prove the stability, and the result that the filter error compensators η1, η2, η3 of the designed system are bounded and converge within the predefined time is obtained; Defining a Lyapunov function V ξ As follows: The Lyapunov stability theory is used to prove the stability, and the result that the error compensation signals ξ1, ξ2, ξ3 are bounded and converge within the predefined time is obtained. Since e1 = ξ1 + η1, the result that the tracking error e1 of the electro-hydraulic proportional multi-way valve position control system under the predefined time tracking control method converges to the neighborhood of zero within the predefined time is obtained.

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