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

Abstract

The invention discloses a predefined time tracking control method of an electro-hydraulic proportional multi-way valve position control system, which is based on constructed predefined time adaptive control and a disturbance observer and fuses an instruction filtering backstepping control thought. And designing a nonlinear predefined time tracking controller considering the uncertainty of unknown system parameters and unmodeled disturbance compensation. For the electro-hydraulic proportional multi-way valve position control problem, it can be guaranteed that system uncertainty is accurately compensated within the predefined time, the system anti-interference performance is improved, the differential explosion phenomenon in the high-order electro-hydraulic proportional multi-way valve system backstepping control process can be avoided, the influence of measurement noise on control precision is reduced, and the control precision is improved. Meanwhile, the problem that a traditional nonlinear control method is poor in convergence performance is effectively solved, convergence time does not depend on the initial state of the system, and good transient state and steady state tracking performance is achieved.

Description

Technical Field

[0001] The invention relates to an 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 Art

[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 multi-way valves has significantly improved the performance of multi-way valves and its automation level, making multi-way valves applicable in many major equipment fields such as aerospace. However, due to the influence of machining accuracy, parameter uncertainty caused by pressure and temperature, and external disturbances, multi-way valves show complex nonlinear characteristics in practical applications, which is a bottleneck factor restricting the improvement of their control performance. This makes the application of traditional control strategies very limited, and control in practical engineering applications is more difficult. Therefore, studying the nonlinear characteristics of multi-way valves and designing advanced controllers based on electro-hydraulic proportional control technology for multi-way valve systems are of great significance to improving the control accuracy and overall control performance of electro-hydraulic proportional multi-way valve systems, and promoting multi-way valves to meet the control needs of more different application scenarios.

[0003] Many methods have been studied and applied to the nonlinear control problem of electro-hydraulic proportional multi-way valve position control system. Such as sliding mode control, adaptive robust control (ARC), etc. However, sliding mode control usually leads to discontinuous control input and jitter problems in physical systems; adaptive robust control can only guarantee that the tracking error is bounded when parameter uncertainty and unmodeled disturbance exist at the same time. It is worth noting that most of the existing electro-hydraulic proportional control technologies can only guarantee that the system tracking error is close to zero or tends to be arbitrarily small as time is infinite. For practical 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 designs have obvious shortcomings. The system convergence time under the finite time controller often depends on the initial conditions of the system. When the initial state value is large or difficult to obtain accurately, the performance of the control method will be significantly reduced. Moreover, whether it is finite time control or fixed time control, its stabilization time is inevitably affected by multiple design parameters, which makes the description of system performance inaccurate. To this end, the concept of predefined time control provides substantial theoretical value and practical significance, because this control method helps to arbitrarily pre-specify the stabilization time and is independent of the initial conditions and design parameters of the system. It has good application prospects in electro-hydraulic proportional multi-way valve position control systems. Summary of the invention

[0004] The purpose of the present invention is to provide a predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system with low computational complexity and high control performance, which can not only ensure the practical stability of the predefined time of the system as a whole, but also avoid the differential explosion problem existing in the traditional backstepping control method.

[0005] The technical solution to achieve the purpose of the present invention is: a predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system, comprising the following steps:

[0006] Step 1, establish the mathematical model of the electro-hydraulic proportional multi-way valve position control system, and then proceed to step 2.

[0007] Step 2, design a predefined time tracking controller according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, and then proceed 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 a predefined time tracking controller, and obtain the result that the tracking error converges to a neighborhood near zero within the system's predefined time.

[0009] Compared with the prior art, the present invention has the following significant advantages: it can accurately estimate the uncertainty of system parameters and unmodeled disturbances, effectively solve the problem of poor transient tracking error convergence performance of traditional nonlinear methods, and the system stabilization time does not depend on the initial state and controller parameters, thus achieving better tracking performance. The simulation results verify its effectiveness. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0011] Figure 2 It is a schematic diagram of the principle of the predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system.

[0012] Figure 3 The system expects the instruction to be x 1d =0.2·sin(π·t)-0.05m, a comparison curve of the tracking error of the system under the predefined time tracking control method (ADOPTC) of the electro-hydraulic proportional multi-way valve position control system designed by the present invention and the velocity feedforward PI controller (VFPI).

[0013] Figure 4 The system expects the instruction to be x 1d =0.2·sin(π·t)-0.05m, a curve diagram of the tracking process of the system output to the expected instruction under the action of ADOPTC designed by the present invention.

[0014] Figure 5 The system expects the instruction to be x 1d =0.2·sin(π·t)-0.05m, a graph showing the change of system control input over time under the action of ADOPTC designed by the present invention.

[0015] Figure 6 The system expects the instruction to be x 1d =0.2·sin(π·t)-0.05m is the estimation curve of the ADOPTC designed by the present invention for the unknown parameters of the system.

[0016] Figure 7 The system expects the instruction to be x 1d =0.2·sin(π·t)-0.05m is the estimation curve of the ADOPTC designed by the present invention for the system lumped uncertainty. DETAILED DESCRIPTION

[0017] The present invention proposes a predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system, introduces a predefined time adaptive law to handle parameter uncertainty, and designs a new disturbance observer to dynamically compensate for unmodeled disturbances; subsequently, 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 invention is that the present invention proposes for the first time 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 stabilization time does not depend on the initial state conditions and controller parameters, thereby achieving better tracking performance.

[0018] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] Combination Figure 1-2 The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system of the present invention comprises the following steps:

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

[0021] Step 1-1, assuming that the electro-hydraulic proportional multi-way valve position control system directly drives the inertial load through a valve-controlled double-rod hydraulic cylinder. The control goal is to enable the inertial load to track any smooth motion trajectory. The electro-hydraulic proportional multi-way valve position control system is ideally simplified, mainly considering the influence of the characteristics of the main valve and the hydraulic cylinder:

[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, and P L is the pressure difference between the two chambers 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 system mismatch, is the speed of the inertial load, is the acceleration of the inertial load, 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, Indicates P L The derivative of e is the effective bulk modulus of hydraulic oil, C t is the leakage coefficient, Q L is the flow rate, q(t) represents the model uncertainty due to complex internal leakage, parameter uncertainty and unmodeled dynamic effects;

[0028] Ignoring the dynamics of the valve core, 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 displacement of the main valve core, which serves as the system control input; C d is the flow coefficient, w is the area gradient, ρ is the oil density, and the sign function sign(u) is defined as:

[0031]

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

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

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

[0035] Step 1-2: When ignoring the viscous damping of the main valve, define the state variable x: Then the state equation of the electro-hydraulic proportional multi-way valve position control system is:

[0036]

[0037] Among them, x 1 represents the displacement of the inertial load, x 2 represents the speed of the inertial load, x 3 Indicates the pressure difference between the two chambers of the hydraulic cylinder. Represents x 1 The derivative of Represents x 2 The derivative of Represents x 3 The derivative of

[0038] Define the unknown parameter variable θ 1 =B v / m, unknown parameter variable θ 2 =4β e (C t +k d2 ) / V t , then formula (5) can be written as

[0039]

[0040] Among them, the coefficient g 1 , g 2 , g 3 All are known constants: g 1 =A / m, g 2 =4β e k d1 / V t , g 3 =4β e A / V t ; Model term Model Item System non-matching interference term d 1 =f(t) / m, interference term d of system matching 2 =4β e q(t) / V t ;

[0041] To facilitate controller design, the following assumptions are made:

[0042] Assumption 1: The position instruction x that the system expects to track d The second order is continuously differentiable and bounded;

[0043] Assumption 2: The electro-hydraulic position servo system works under normal working conditions, and the pressure P of the hydraulic cylinder oil inlet and outlet chambers is 1 and P 2The following conditions must be met: 0 <P r <P 1 <P s , 0 <P r <P 2 <P s ;P r Indicates the system return oil pressure;

[0044] Assumption 3: The uncertainty of system matching and mismatching satisfies: in Indicates d 1 The first derivative of Indicates d 2 The first derivative of K 1 , K 2 All are known normal numbers.

[0045] Go to step 2.

[0046] Step 2: Design a predefined time tracking controller based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system. The steps are as follows:

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

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

[0049]

[0050] In formula (7), x 2f 、x 3f , u f ,d 1f ,d 2f Corresponding to x 2 、x 3 , u、d 1 ,d 2 The corresponding filter output;

[0051] Defining intermediate variables and

[0052]

[0053] Define the intermediate variable M 1 、N 1 、M 2 and N 2 :

[0054]

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

[0056] Then solving equation (9) yields:

[0057]

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

[0059] From formula (10), we can get N i =M i θ i ,

[0060] Then get

[0061] Among them, the adaptive law estimation error represents the unknown parameter θ i estimates;

[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 formula (11), the first adaptive coefficient The second adaptive coefficient The third adaptive coefficient δ、τ i1 , τ i2 , τ i ′ are all adjustable parameters, satisfying 0<δ<1, τ i1 >0,τ i2 >0, The time parameter T is predefined in the uncertainty estimation u >0 can be defined arbitrarily by the user, intermediate variables

[0065] In order to realize the unmodeled disturbance compensation of the electro-hydraulic proportional multi-way valve position control system, a preset time disturbance observer with the following form is constructed:

[0066]

[0067] In formula (12), Indicates d i The estimated value of Represents x i+1 The estimated value of , s represents the independent variable of the integral function, and the first observer coefficient Second observer coefficient The third observer coefficient

[0068] Step 2-2: Based on the active compensation of 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 traditional backstepping control, a predefined time command filter is constructed:

[0069]

[0070] In formula (13), the predefined time parameter T in the predefined time instruction filter design is c >0 can be defined arbitrarily by the user, the adjustable filter coefficient ζ is a positive constant satisfying 0<ζ<1, α i Represents x i+1 Virtual control, Represents α i The filtered signal.

[0071] Step 2-3: According to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, combined with the predefined time adaptive control law, the predefined time disturbance observer, and the predefined time command filter, a predefined time tracking controller u is designed that takes into account uncertainty compensation, as follows:

[0072] Define the tracking error of the system 1 =x 1 -x d , x d is the position command that the system expects to track, and defines the virtual error Defining Virtual Error Define the error compensation signal ξ 1 =e 1 -η 1 , define the error compensation signal ξ 2 =e 2 -η 2 , define the error compensation signal ξ 3 =e 3 -η 3 , where η 1 , η 2 , η 3 represents the designed filter error compensator;

[0073] For 1 Derivation, according to e 2 The definition is:

[0074]

[0075] Select filter error As the input signal, construct a virtual control α 1 The filter error compensator η 1 :

[0076]

[0077] The predefined time parameter T in formula (15) e >0 can be defined arbitrarily by the user, η 1 , η 2 They are α 1 and α 2 The filter error compensator is γ, which is an adjustable controller coefficient and satisfies 0<γ<1. The function sig 1- γ(η 1 ) is defined as: sig 1-γ (η 1 )=|η 1 | 1-γ sign(η 1 );

[0078] Error compensation signal ξ 1 =e 1 -η 1 Taking the derivatives of both sides, we get:

[0079]

[0080] Considering the influence of control singularity, the control system virtual control α is constructed based on command filter backstepping design 1 :

[0081]

[0082] The auxiliary variable M ξ1 Designed for:

[0083]

[0084] The design parameter ν in formula (18) 10 >0, j is the summation independent variable, auxiliary variable b γj The assignment is as follows:

[0085]

[0086] For 2 Derivation, according to e 3 The definition is:

[0087]

[0088] Select filter error As the input signal, construct the virtual control α 2 The filter error compensator η 2 :

[0089]

[0090] Error compensation signal ξ 2 =e 2 -η 2 Taking the derivatives of both sides, we get:

[0091]

[0092] Considering the influence of control singularity, the control system virtual control α is constructed based on command filter backstepping design 2 :

[0093]

[0094] The auxiliary variable M ξ2 Designed for:

[0095]

[0096] For 3 Taking the derivative, we get:

[0097]

[0098] Construct filter error compensator η 3 :

[0099]

[0100] Error compensation signal ξ 3 =e 3 -η 3 Taking the derivatives of both sides, we get:

[0101]

[0102] Considering the influence of control singularity, a predefined time tracking control u is constructed based on command filter backstepping design:

[0103]

[0104] The auxiliary variable M ξ3 Designed for:

[0105]

[0106] Go to step 3.

[0107] Step 3, using Lyapunov stability theory to prove the stability of the electro-hydraulic proportional multi-way valve position control system under the predefined time tracking control method, and obtain the result that the tracking error converges to a neighborhood near zero within the predefined time of the system, as follows:

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

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

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

[0111]

[0112] Derivative of (29) yields:

[0113]

[0114] In formula (30), the intermediate variable ω i The first derivative of (t) Satisfy i (0) = 0, K i Defined in Assumption 3, the inference drawn from the intermediate variable is ω i The sign of (t) is The sign of is opposite, that is Then (30) can be simplified as:

[0115]

[0116] In formula (31), the coefficient τ′ m , τ m1 , τ m2 can be expressed as i1 , κi2 , κ i3 , Γ i1 , Γ i2 , Γ i3 The functional form of the association.

[0117] The stability is proved by using Lyapunov stability theory, and the estimation error of the unknown parameters of the system by the predefined time adaptive control law is obtained. and the estimated error of the system state by the predefined time disturbance observer The result converges to zero within a predefined time, because there exists Get the estimated error of the predefined time disturbance observer for the unmodeled disturbance of the system A result that converges to zero within a predefined time;

[0118] Define the Lyapunov function V α as follows:

[0119]

[0120] Among them, the filtering error λ 1 , 2 They are defined as

[0121] Because of the inequality and inequality The constant Λ i satisfy constant If constant ζ>0, then taking the derivative of equation (32) we get

[0122]

[0123] The constant

[0124] The stability is proved by using Lyapunov stability theory, and the system filtering error λ under the predefined time command filter is obtained. 1 , 2 Results with bounded convergence within a predefined time.

[0125] Define the Lyapunov function V η as follows:

[0126]

[0127] Because of the inequality:

[0128]

[0129] where the constant χ isatisfy

[0130] Derivative of (34) yields:

[0131]

[0132] The coefficient G 1 =1, coefficient G 2 =g 1 .

[0133] constant

[0134] The stability is proved by using Lyapunov stability theory, and the designed system filter error compensator η is obtained. 1 , η 2 , η 3 Results that converge within a predefined time;

[0135] Define the Lyapunov function V ξ as follows:

[0136]

[0137] Derivative of (36) yields:

[0138]

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

[0140]

[0141] The stability is proved by using Lyapunov stability theory, and the error compensation signal ξ is obtained. 1 , 2 , 3 The result of bounded convergence within a predefined time is due to e 1 =ξ 1 +η 1 , the tracking error e of the electro-hydraulic proportional multi-way valve position control system under the predefined time tracking control method of the present invention is obtained 1 A result that converges to a neighborhood around zero within a predefined time.

[0142] Therefore, it is concluded that the predefined time tracking control method designed for the electro-hydraulic proportional multi-way valve position control system (such as formula (5)) can enable the system to obtain the result that the tracking error converges to a neighborhood near zero within the predefined time, and adjust the uncertainty estimation parameters δ, τ i1 , τ i2 , T u , filter parameters ζ, T c And the controller parameters γ, T eThe tracking error of the system can be converged to a neighborhood near zero within a predefined time. The schematic diagram of the principle of the predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system is shown in the figure. Figure 2 shown.

[0143] Example

[0144] In order to evaluate the performance of the designed controller, the following parameters are taken in the 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 =20N·s / m, hydraulic cylinder working area A = 0.018m 2 , hydraulic cylinder volume V t =0.01062m 3 , effective volume liquid elastic modulus β e =2.2×10 8 Pa, flow gain k d1 =1.608m 2 / s, pressure flow coefficient k d2 =3.717×10 -12 m 5 / (N·s), flow coefficient C t =3×10 -11 ;

[0146] Given the expected command of the system is 0.2·sin(π·t)-0.05m

[0147] The following controllers are used for comparison in the simulation:

[0148] The proposed method for presetting time axis control (NFPTC) of the electro-hydraulic proportional servo valve based on disturbance observer is designed with controller parameters κ=0.01, λ=1, T u =1s,δ=0.6,τ 11 =τ 21 =0.01, τ 21 =τ 22 =100, K 1 =0.02, K 2 =3.5×10 4 ,ζ=0.2,T c =0.5s,γ=0.48,T e =1s,.

[0149] Velocity Feedforward PI Controller (VFPI): The error z 1 =x 1d -x 1 , t is the integral time independent variable, and the controller parameter is kP =0.03, k I =0.08, k F =0.01, representing the proportional constant, integral constant and speed feedforward coefficient respectively.

[0150] The comparison curve of system tracking error under the action of ADOPTC and VFPI, and the tracking curve of the output of the electro-hydraulic proportional multi-way valve position control system to the expected command under the action of ADOPTC are shown in Figure 2. Figure 3 , Figure 4 As shown. Figure 3 It can be seen that compared with VFPI, ADOPTC has a good ability to compensate for modeling uncertainty and obtains a smaller tracking error. By introducing the predefined time tracking control design, ADOPTC achieves the result that the tracking error converges to a neighborhood near zero after the predefined time, and the tracking performance is greatly improved. Therefore, compared with VFPI, ADOPTC achieves better tracking performance.

[0151] Given a system with the expected instruction x 1d =0.2·sin(π·t)-0.05m, Figure 5 It is a curve diagram of the control input of the electro-hydraulic proportional multi-way valve position control system under the action of ADOPTC designed by the present invention changing with time. 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. Figure 6 is the estimated curve of ADOPTC for the unknown parameters of the system, Figure 7 It is the estimated curve of ADOPTC for the system lumped uncertainty. It can be seen from the figure that the estimation of the parameters and the system lumped uncertainty of the electro-hydraulic proportional multi-way valve position control system by ADOPTC is stable within the predefined time.

Claims

1. A predefined time tracking control method for an electro-hydraulic proportional multi-way valve position control system, characterized in that: The following steps are involved: Step 1, establish a mathematical model of the electro-hydraulic proportional multi-way valve position control system, and then proceed to step 2; Step 2, design a predefined time tracking controller according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, and proceed to step 3; Step 3, using Lyapunov stability theory to prove the stability of the electro-hydraulic proportional multi-way valve position control system using a predefined time tracking controller, and obtain the result that the tracking error converges to a neighborhood near zero within the system's predefined time.

2. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 1 is characterized in that: In step 1, a mathematical model of the electro-hydraulic proportional multi-way valve position control system is established, as follows: Step 1-1, assuming that the electro-hydraulic proportional multi-way valve position control system directly drives the inertial load through a valve-controlled double-rod hydraulic cylinder. The control goal is to enable the inertial load to track any smooth motion trajectory. The electro-hydraulic proportional multi-way valve position control system is ideally simplified, mainly considering the influence of the characteristics of the main valve and the hydraulic cylinder: 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), m is the mass of the inertial load, y is the displacement of the inertial load, and P L is the pressure difference between the two chambers 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 system mismatch, is the speed 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), V t is the volume of the hydraulic cylinder, Indicates P L The derivative of e is the effective bulk modulus of hydraulic oil, C t is the leakage coefficient, Q L is the flow rate, q(t) represents the model uncertainty due to complex internal leakage, parameter uncertainty and unmodeled dynamic effects; Ignoring the dynamics of the valve core, the flow equation of the electro-hydraulic proportional multi-way valve is: In formula (3), P s is the constant oil supply pressure of the system; u is the displacement of the main valve core, which serves as the system control input; C d is the flow coefficient, w is the area gradient, ρ is the oil density, and the sign function sign(u) is defined as: After linear processing, formula (3) is obtained: Q L =k d1 u-k d2 P L (4) In formula (4), k d1 is the flow gain, k d2 is the pressure flow coefficient; Step 1-2: When ignoring the viscous damping of the main valve, define the state variable x: Then the state equation of the electro-hydraulic proportional multi-way valve position control system is: Among them, x1 represents the displacement of the inertial load, x2 represents the speed of the inertial load, and x3 represents the pressure difference between the two chambers of the hydraulic cylinder. represents the derivative of x1, represents the derivative of x2, represents the derivative of x3; Define unknown parameter variable θ1 = B v / m, unknown parameter variable θ2=4β e (C t +k d2 ) / V t , then formula (5) can be written as Among them, the coefficients g1, g2, and g3 are all known constants: g1 = A / m, g2 = 4β e k d1 / V t , g3=4β e A / V t ; Model term Model Item System non-matching interference term d1 = f(t) / m, system matching interference term d2 = 4β e q(t) / V t ; To facilitate controller design, the following assumptions are made: Assumption 1: The position instruction x that the system expects to track d The second order is continuously differentiable and bounded; Assumption 2: When the electro-hydraulic position servo system works under normal working conditions, the pressures P1 and P2 of the hydraulic cylinder oil inlet and outlet chambers must meet the following conditions: <P r <P1<P s , 0 <P r <P2<P s ;P r Indicates the system return oil pressure; Assumption 3: The uncertainty of system matching and mismatching satisfies: in represents the first-order derivative of d1, represents the first-order derivative of d2, where K1 and K2 are both known normal constants.

3. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 2 is characterized in that: In step 2, according to the mathematical model of the electro-hydraulic proportional multi-way valve position control system, a predefined time tracking controller taking into account uncertainty compensation is designed, as follows: Step 2-1, in order to realize active compensation of uncertainty in the electro-hydraulic proportional multi-way valve position control system, a predefined time adaptive control law is constructed to estimate the parameter uncertainty of the system, and a predefined time disturbance observer is constructed to estimate the unknown disturbance of the system; Step 2-2, based on the active compensation of 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 traditional backstepping control, a predefined time command filter is constructed; Step 2-3: Based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system, combined with the predefined time adaptive control law, the predefined time disturbance observer, and the predefined time command filter, a predefined time tracking controller that takes into account uncertainty compensation is designed.

4. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 3 is characterized in that: In step 2-1, in order to realize the active compensation of uncertainty in the electro-hydraulic proportional multi-way valve position control system, a predefined time adaptive control law is constructed to estimate the system parameter uncertainty, and a predefined time disturbance observer is constructed to estimate the unknown disturbance of the system. The specific steps are as follows: In order to predefine the time adaptive control design, the first-order filtering form of the uncertain channel in equation (6) is as follows: * f | t＝0 =0, where * represents filter input, * f represents the filter output, represents the first-order derivative of the variable *, κ is the filter coefficient, and the following equation is obtained: In formula (7), x 2f 、x 3f , u f d 1f d 2f They correspond to x2, x3, The filter output corresponding to u, d1, and d2; Defining intermediate variables and Define intermediate variables M1, N1, M2 and N2: In formula (9), the independent variable i = 1, 2, λ is the filter coefficient; Then solving equation (9) yields: In formula (10), τ represents the independent variable of the integral function; From formula (10), we can get N i =M i θ i , Then get Among them, the adaptive law estimation error represents the unknown parameter θ i estimates; 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: In formula (11), the first adaptive coefficient The second adaptive coefficient The third adaptive coefficient δ、τ i1 , τ i2 , τ i ′ are all adjustable parameters, satisfying 0<δ<1, τ i1 >0,τ i2 >0, The time parameter T is predefined in the uncertainty estimation u >0 can be defined arbitrarily by the user, intermediate variables In order to realize the unmodeled disturbance compensation of the electro-hydraulic proportional multi-way valve position control system, a preset time disturbance observer with the following form is constructed: In formula (12), Indicates d i The estimated value of Represents x i+1 The estimated value of , s represents the independent variable of the integral function, and the first observer coefficient Second observer coefficient The third observer coefficient 5. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 4, 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 traditional backstepping control, a predefined time command filter with the following form is constructed: In formula (13), the predefined time parameter T in the predefined time instruction filter design is c >0 can be defined arbitrarily by the user, the adjustable filter coefficient ζ is a positive constant satisfying 0<ζ<1, α i Represents x i+1 Virtual control, Represents α i The filtered signal.

6. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 5, characterized in that: In step 2-3, based on the mathematical model of the electro-hydraulic proportional multi-way valve position control system, a predefined time tracking controller u is designed with uncertainty compensation in mind, as follows: Define the tracking error of the system as e1 = x1-x d , x d is the position command that the system expects to track, and defines the virtual error Defining Virtual Error Define an error compensation signal ξ1 = e1-η1, define an error compensation signal ξ2 = e2-η2, define an error compensation signal ξ3 = e3-η3, where η1, η2, η3 represent the designed filter error compensator; Taking the derivative of e1, according to the definition of e2, we get: Select filter error As the input signal, construct the filter error compensator η1 of the virtual control α1: The predefined time parameter T in formula (15) e >0 can be defined arbitrarily 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, function sig 1-γ (η1) is defined as: sig 1-γ (η1)=|η1| 1-γ sign(η1); Taking the derivative of both sides of the error compensation signal ξ1=e1-η1, we get: Considering the influence of control singularity, the control system virtual control α1 is constructed based on command filtering backstepping design: The auxiliary variable M ξ1 Designed for: The design parameter ν in formula (18) 10 >0, j is the independent variable for summation, auxiliary variable b γj The assignment is as follows: Taking the derivative of e2, according to the definition of e3, we get: Select filter error As the input signal, construct the filter error compensator η2 of the virtual control α2, and take the derivative of η2: Taking the derivative of both sides of the error compensation signal ξ2=e2-η2, we get: Considering the influence of control singularity, the control system virtual control α2 is constructed based on command filtering backstepping design: The auxiliary variable M ξ2 Designed for: Taking the derivative of e3, we get: Construct the filter error compensator η3 and take the derivative of η3: Taking the derivative of both sides of the error compensation signal ξ3=e3-η3, we get: Considering the influence of control singularity, a predefined time tracking control u is constructed based on command filtering backstepping design: The auxiliary variable M ξ3 Designed for:

7. The predefined time tracking control method of the electro-hydraulic proportional multi-way valve position control system according to claim 1, characterized in that: 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 predefined time tracking controller, and the result that the tracking error converges to a neighborhood near zero within the predefined time of the system is obtained, as follows: Define the Lyapunov function V u as follows: The stability is proved by using Lyapunov stability theory, and the estimation error of the unknown parameters of the system by the predefined time adaptive control law is obtained. and the estimated error of the system state by the predefined time disturbance observer The result converges to zero within a predefined time, because there exists Get the estimated error of the predefined time disturbance observer for the unmodeled disturbance of the system A result that converges to zero within a predefined time; Define the Lyapunov function V α as follows: Among them, the filtering errors λ1 and λ2 are defined as Independent variable i = 1, 2; The stability is proved by using Lyapunov stability theory, and the result is that the system filter errors λ1 and λ2 converge within the predefined time under the predefined time command filter; Define the Lyapunov function V η as follows: The stability is proved by using Lyapunov stability theory, and the results show that the designed system filter error compensators η1, η2, and η3 converge within a predefined time. Define the Lyapunov function V ξ as follows: The stability is proved by using Lyapunov stability theory, and the result is that the error compensation signals ξ1, ξ2, and ξ3 converge within a predefined time. Since e1=ξ1+η1, the result is 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 invention converges to a neighborhood near zero within the predefined time.

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