An adaptive anti-disturbance reduced-order control method for electro-hydraulic system
Through the adaptive anti-interference step reduction control method, the problem of complex structure and insufficient robustness in electro-hydraulic system control is solved, and high-precision and robust electro-hydraulic system control is achieved.
Patent Information
- Application Number
- CN202410775703.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-06-17
- Publication Date
- 2025-02-28
- Estimated Expiration
- 2044-06-17
AI Technical Summary
The existing electro-hydraulic system control methods have shortcomings such as complex structure, weak global robustness, poor disturbance estimation performance, inability to eliminate disturbance estimation errors and slip mode vibration, and cannot meet the high-performance control requirements of electro-hydraulic servo systems for fast response speed, high accuracy and no overshoot.
Adaptive anti-interference step reduction control method is adopted, and the full state model of the electro-hydraulic system is established, and the order reduction process is performed based on the singular perturbation theory is designed. A linear expansion state observer and sliding mode controller are designed, and a sliding mode controller are combined with an adaptive strategy to approximate the sliding mode immunity controller to achieve high-precision control and robustness improvement.
It realizes high-precision control of the position output of the joint drive system, effectively observes the system output status speed and disturbance, has stronger robustness, and can maintain high-performance control when parameters change.
Smart Images
Figure CN118795771B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of electro-hydraulic system control, and in particular to an electro-hydraulic system adaptive anti-disturbance reduced-order control method. Background Art
[0002] Typical electro-hydraulic systems have strong nonlinear characteristics such as dead zones, time-varying parameters, internal and external disturbances, etc. These nonlinearities pose challenges to the high-performance tracking control of the system. In order to overcome the above problems, scholars have developed various effective electro-hydraulic system control methods to improve control performance. Among the existing methods, sliding mode control based on extended state observer has shown strong competitiveness and is widely used in electro-hydraulic systems. However, it has shortcomings such as complex structure, weak global robustness, poor disturbance estimation performance, inability to eliminate disturbance estimation errors and sliding mode jitter, etc., and thus cannot meet the high-performance control requirements of electro-hydraulic servo systems for fast response speed, high accuracy, and no overshoot. Summary of the invention
[0003] In view of the above technical deficiencies, the purpose of the present invention is to provide an electro-hydraulic system adaptive anti-disturbance reduced-order control method, which does not rely on the joint drive system parameters, only needs to know the system displacement output, and effectively reduces the number of control parameters. It realizes high-precision control of the position output of the joint drive system, effectively observes the system output state speed and disturbance, and has stronger robustness to parameter changes.
[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:
[0005] The present invention provides an electro-hydraulic system adaptive anti-disturbance reduced-order control method, comprising the following steps:
[0006] S1. Establish a full-state model of the electro-hydraulic system;
[0007] S2. Based on the singular perturbation theory, the full-state model is reduced to obtain a system reduced-order model;
[0008] S3, design a linear extended state observer and a sliding mode controller based on the reduced-order model, and combine them to obtain a sliding mode anti-disturbance controller;
[0009] S4. The unknown parameters of the sliding mode anti-disturbance controller are approximated by three adaptive strategies, and an adaptive anti-disturbance reduced-order controller is obtained, which are the adaptive method without physical parameters, the neural network adaptive method and the fuzzy adaptive method.
[0010] Preferably, the full state model of the electro-hydraulic system is as follows:
[0011]
[0012] In the formula, x1, x2, x3, x4 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load disturbance force; C ip Oil inlet and return chamber volume;
[0013] Preferably, the specific process of step S2 is as follows: define the mechanical state and pressure state as x h =[x1,x2] T and z h =[x3,x4] T ;set up The boundary layer model of the electro-hydraulic system is constructed as:
[0014]
[0015] Let p L =p1-p2, ε=0, then the quasi-static state equation of the system is:
[0016]
[0017] In the formula, therefore,
[0018]
[0019] The reduced-order electro-hydraulic system model is:
[0020]
[0021] In the formula,
[0022] Where x1, x2 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load disturbance force; C ip Oil inlet and return chamber volume; V1 and V2 include valves, connecting pipes and the volume of the oil inlet and return chambers.
[0023] Preferably, the process of step S3 is as follows: Based on the reduced-order model (5), assume is the total disturbance, and assumes Differentiable, so the system model is re-described as:
[0024]
[0025] Where h(t) is the rate of change of the total disturbance of the system;
[0026] definition Then the linear extended state observer of the system is
[0027]
[0028] In the formula, z i (i=1,2,3) is The estimated value of; ω0 is the bandwidth of the observer; b0 is the compensation factor, b0>0; According to model (5) and the tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then The sliding mode control law is obtained as:
[0029]
[0030] The disturbance observed by observation formula (7) is compensated in control law (8) to obtain the sliding mode disturbance rejection reduced order controller:
[0031]
[0032] Where z3 is the disturbance observed by the linear extended state observer.
[0033] Preferably, in step S4, the process without physical parameter adaptation method is as follows: rewrite the reduced-order model formula (5) as follows:
[0034] In the formula,
[0035]
[0036] According to model (10) and tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then
[0037] Assuming that the disturbance term D(t) is bounded, the total disturbance observed by the observer is also bounded The above formula can be rewritten as:
[0038]
[0039] Where, η>D, k>0;
[0040] Next, an adaptive control law is designed to approximate the unknown parameters φ i (i=1,2,3,4);
[0041] Define the Lyapunov function as
[0042]
[0043] In the formula, γ i >0, for The estimated value of
[0044]
[0045] According to formula (17), the adaptive law is designed as
[0046]
[0047] Substituting equation (15) and equation (18) into equation (17), we can obtain
[0048]
[0049] Therefore, according to the Lyapunov stability criterion, the designed adaptive disturbance rejection reduced-order controller is stable.
[0050] Preferably, in step S4, the neural network adaptive method process is as follows:
[0051] The RBF network input and output algorithm is:
[0052]
[0053] g(x)=V *T h g (x)+ε g (17);
[0054] Where x is the network input; i represents the input of the i-th network input layer; j is the j-th network input of the network hidden layer; h = [h j ] T is the output of the Gaussian basis function; W * and V * are the ideal network weights approximating f(x) and g(x) respectively; ε f and ε g is the network approximation error, |ε f |≤ε Mf ,|ε g |≤ε Mg ;
[0055] Take x = [x1, x2] T , then the RBF output is:
[0056]
[0057] In the formula, h f (x) and hg (x) is the Gaussian basis function of the RBF network;
[0058] The control law is designed as
[0059]
[0060] Where η≥D
[0061] Take the adaptive law as
[0062]
[0063] Preferably, in step S4, the fuzzy adaptive method process is as follows: the fuzzy system is composed of fuzzy rules in the form of IF-THEN:
[0064]
[0065] Using the product inference engine, single-valued fuzzifier and central average defuzzifier, the output of the fuzzy system is
[0066]
[0067] In the formula, For x i The membership function of
[0068] Introducing the vector ξ(x), equation (22) becomes:
[0069] y(x)=θ T ξ(x) (23)
[0070] Where θ=(y 1 ,y 2 ,…,y m ) T , ξ(x)=(ξ 1 (x),ξ 2 (x),…ξ m (x)) T ;
[0071]
[0072] If the fuzzy system is used to approximate f(x) and g(x), the control law becomes:
[0073]
[0074] ξ(x) is the fuzzy vector, parameter and Changes according to the adaptive law; the designed adaptive law is:
[0075]
[0076] The beneficial effects of the present invention are:
[0077] 1. In the present invention, based on the reduced-order model, a linear extended state observer is designed to directly use the observation information of the linear extended state observer as feedback information. It does not depend on the parameters of the joint drive system and only needs to know the system displacement output to achieve adaptive anti-disturbance control, which effectively improves the robustness.
[0078] 2. In the present invention, the research shows that the adaptive anti-disturbance reduced-order controller can not only realize high-precision control of the position output of the joint drive system, but also effectively observe the system output state speed and disturbance, and has stronger robustness to parameter changes. BRIEF DESCRIPTION OF THE DRAWINGS
[0079] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0080] Figure 1 A flowchart of an electro-hydraulic system adaptive anti-disturbance reduced-order control method provided by the present invention;
[0081] Figure 2 A tracking response diagram of a system in an adaptive anti-disturbance reduced-order control method for an electro-hydraulic system provided by the present invention;
[0082] Figure 3 A tracking error diagram in an adaptive anti-disturbance reduced-order control method for an electro-hydraulic system provided by the present invention;
[0083] Figure 4 A control input diagram of a system in an adaptive anti-disturbance reduced-order control method for an electro-hydraulic system provided by the present invention. DETAILED DESCRIPTION
[0084] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0085] like Figures 1 to 3 As shown, an adaptive anti-disturbance reduced-order control method for an electro-hydraulic system includes the following steps: S1: The full state model of the electro-hydraulic system is as follows:
[0086]
[0087] In the formula, x1, x2, x3, x4 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load disturbance force; C ip Oil inlet and return chamber volume;
[0088] S2: Based on the singular perturbation theory, the full-state model is reduced to obtain the specific process of the system reduced-order model as follows:
[0089] Define the mechanical state and pressure state as x h =[x1,x2] T and z h =[x3,x4] T ;set up The boundary layer model of the electro-hydraulic system is constructed as:
[0090]
[0091] Let p L =p1-p2, ε=0, then the quasi-static state equation of the system is:
[0092]
[0093] In the formula, therefore,
[0094]
[0095] The reduced-order electro-hydraulic system model is:
[0096]
[0097] In the formula,
[0098] Where x1, x2 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load disturbance force; C ip Oil inlet and return chamber volume; V1 and V2 include valves, connecting pipes and the volume of the oil inlet and return chambers.
[0099] S3: Based on the reduced-order model, the linear extended state observer and sliding mode controller are designed, and the sliding mode anti-disturbance controller is obtained as follows:
[0100] Based on the reduced-order model (5), let is the total disturbance, and assumes Differentiable, so the system model can be re-described as:
[0101]
[0102] Where h(t) is the rate of change of the total disturbance of the system.
[0103] definition Then the linear extended state observer of the system is
[0104]
[0105] In the formula, z i (i=1,2,3) is The estimated value of ω0 is the bandwidth of the observer; b0 is the compensation factor, b0>0. According to model (5) and the tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then The sliding mode control law is obtained as:
[0106]
[0107] The disturbance observed by observation formula (7) is compensated in control law (8) to obtain the sliding mode disturbance rejection reduced order controller:
[0108]
[0109] Where z3 is the disturbance observed by the linear extended state observer.
[0110] Without referring to the model information, the parameters in the controller u1 are unknown and cannot be used directly in the control. Therefore, an adaptive law is designed to approximate the unknown parameters. Three adaptive methods are adopted to approximate the unknown parameters, namely, the adaptive method without physical parameters, the neural network adaptive method, and the fuzzy adaptive method.
[0111] S4: The process of approximating the unknown parameters of the sliding mode disturbance rejection controller by three adaptive strategies to obtain the adaptive disturbance rejection reduced-order controller is as follows:
[0112] Among them, the process of the adaptive method without physical parameters is as follows:
[0113] The reduced-order model (5) is rewritten as:
[0114]
[0115] In the formula, According to model (10) and tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then
[0116] Assuming that the disturbance term D(t) is bounded, the total disturbance observed by the observer is also bounded Then the above formula
[0117] (9) can be rewritten as:
[0118]
[0119] In the formula, η>D, k>0.
[0120] Next, an adaptive control law is designed to approximate the unknown parameters φ i (i=1,2,3,4)
[0121] Define the Lyapunov function as
[0122]
[0123] In the formula, γ i >0, for The estimated value of
[0124]
[0125] According to formula (17), the adaptive law is designed as
[0126]
[0127] Substituting equation (15) and equation (18) into equation (17), we can obtain
[0128]
[0129] Therefore, according to the Lyapunov stability criterion, the designed adaptive disturbance rejection reduced-order controller is stable. (2) The process of the neural network adaptive method is as follows:
[0130] The RBF network input and output algorithm is:
[0131]
[0132] Where x is the network input; i represents the input of the i-th network input layer; j is the j-th network input of the network hidden layer; h = [h j ] T is the output of the Gaussian basis function; W * and V * are the ideal network weights approximating f(x) and g(x) respectively; ε f and ε g is the network approximation error, |ε f |≤εMf ,|ε g |≤ε Mg .
[0133] Take x = [x1, x2] T , then the RBF output is:
[0134]
[0135] In the formula, h f (x) and h g (x) is the Gaussian basis function of the RBF network.
[0136] The control law is designed as
[0137]
[0138] Where η≥D
[0139] Take the adaptive law as
[0140]
[0141] (3) The process of fuzzy adaptive method is as follows:
[0142] Define vector x d ,e and sliding mode function s are as follows:
[0143]
[0144] In the formula, λ>0.
[0145] For the controlled object (5), the ideal sliding mode controller is
[0146]
[0147] In the formula,
[0148] There exists an ideal network weight W * ,have
[0149] u * (z) = W *T h(z)+μ l (twenty three)
[0150] Where h(z) is the Gaussian basis function; μ1 is the approximation error of the network, and satisfies |μ l |≤μ0,
[0151]
[0152] The control law is designed as the output of the RBF neural network, that is,
[0153]
[0154] In the formula, W * The estimated value of .
[0155] The adaptive law is designed as
[0156]
[0157] Where Γ = Γ T >0,σ>0.
[0158] The specific research process is as follows: Taking the valve-controlled asymmetric cylinder electro-hydraulic system as the research object, the effectiveness of the proposed method is verified;
[0159] The desired trajectory of the system is set to x d =0.1sint; m=1000, c=100, eta=0.1, k=200, ω0=400, b=10, γ1=γ2=γ3=γ4=400.
[0160] The system's tracking response is as follows Figure 2 As shown. Accordingly, Figure 3 shows the tracking error response trajectory, Figure 4 The control input of the system is shown. The above results verify that the proposed control method can achieve accurate tracking performance with lower control input, thus verifying the effectiveness of the proposed method.
[0161] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.
Claims
1. An adaptive anti-disturbance reduced-order control method for an electro-hydraulic system, characterized in that: The following steps are involved: S1. Establish a full-state model of the electro-hydraulic system; The full state model of the electro-hydraulic system is as follows: In the formula, x1, x2, x3, x4 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load interference force; Among them, V1 and V2 include the valve, connecting pipeline and the volume of the oil inlet and return chambers; S2. Based on the singular perturbation theory, the full-state model is reduced to obtain a system reduced-order model; Define the mechanical state and pressure state as x h =[x1,x2] T and z h =[x3,x4] T ;set up The boundary layer model of the electro-hydraulic system is constructed as: Let p L =p1-p2, μ=0, then the quasi-static state equation of the system is: In the formula, therefore, The reduced-order electro-hydraulic system model is: In the formula, Where x1, x2 are state variables, A1 is the area of the rodless cavity; A2 is the area of the rod cavity; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; F d is the external load interference force; V1 and V2 include valves, connecting pipes and the volume of the oil inlet and return chambers; S3, design a linear extended state observer and a sliding mode controller based on the reduced-order model, and combine them to obtain a sliding mode anti-disturbance controller; Based on the reduced-order model (5), let is the total disturbance, and assumes Differentiable, so the system model is re-described as: Where h(t) is the rate of change of the total disturbance of the system; definition Then the linear extended state observer of the system is In the formula, z i (i=1,2,3) is The estimated value of; ω0 is the bandwidth of the observer; b0 is the compensation factor, b0>0; According to model (5) and the tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then The sliding mode control law is obtained as: The disturbance observed by observation formula (7) is compensated in control law (8) to obtain the sliding mode disturbance rejection reduced order controller: Where z3 is the disturbance observed by the linear extended state observer; S4. Approximating the unknown parameters of the sliding mode disturbance rejection controller through three adaptive strategies, the adaptive disturbance rejection reduced-order controller is obtained, which are the adaptive method without physical parameters, the neural network adaptive method and the fuzzy adaptive method; The process of the adaptive method without physical parameters is as follows: rewrite the reduced-order model (5) as follows: In the formula, According to model (10) and tracking error e = x1-x 1d , the sliding mode function is defined as c>0, then Assuming that the disturbance term D(t) is bounded, the total disturbance observed by the observer is also bounded The above formula can be rewritten as: Where, η>D, k>0; Next, an adaptive control law is designed to approximate the unknown parameters φ i (i=1,2,3,4); Define the Lyapunov function as In the formula, γ i >0, is φ i The estimated value of According to formula (17), the adaptive law is designed as Substituting equation (15) and equation (18) into equation (17), we can obtain Therefore, according to the Lyapunov stability criterion, the designed adaptive disturbance rejection reduced-order controller is stable; The process of neural network adaptive method is as follows: The RBF network input and output algorithm is: Where x is the network input; i represents the input of the i-th network input layer; j is the j-th network input of the network hidden layer; h = [h j ] T is the output of the Gaussian basis function; W * and V * are the ideal network weights that approximate f(x) and g(x) respectively; ε f and ε g is the network approximation error, |ε f |≤ε Mf ,|ε g |≤ε Mg ; Take x=[x1,x2] T , then the RBF output is: In the formula, h f (x) and h g (x) is the Gaussian basis function of the RBF network; The control law is designed as Where η≥D Take the adaptive law as The process of fuzzy adaptive method is as follows: the fuzzy system is composed of fuzzy rules in the form of IF-THEN: Using the product inference engine, single-valued fuzzifier and central average defuzzifier, the output of the fuzzy system is In the formula, For x i The membership function of Introducing the vector ξ(x), equation (22) becomes: y(x)=θ T ξ(x)(23) where θ = (y 1 , y 2 , …, y m ), T and ξ(x) = (ξ 1 (x), ξ 2 (x), …, ξ m (x)). T ; If the fuzzy system is used to approximate f(x) and g(x), the control law becomes: ξ(x) is the fuzzy vector, parameter and Changes according to the adaptive law; the designed adaptive law is: