Reduced-order self-adaptive backstepping anti-interference control method for valve-controlled asymmetric cylinder system

Abstract

The invention discloses a reduced-order self-adaptive backstepping anti-interference control method for a valve-controlled asymmetric cylinder system, and belongs to the field of valve-controlled asymmetric cylinder system control. For the valve control asymmetric cylinder system, firstly, a full-state model of the system is established, secondly, order reduction processing is carried out based on the singular perturbation theory, and an order reduction model is obtained; secondly, designing a low-gain state observer, a non-linear interference observer and a backstepping controller based on the reduced-order model, and combining the low-gain state observer, the non-linear interference observer and the backstepping controller to obtain a backstepping anti-interference controller; finally, unknown parameters of the backstepping anti-interference controller are approached through two adaptive strategies, a reduced-order adaptive backstepping anti-interference controller is obtained, high-precision control over position output of the joint driving system is achieved, the speed and disturbance of the output state of the system are effectively observed, and higher robustness is achieved for parameter changes.

Description

Technical Field

[0001] The present invention relates to the technical field of valve-controlled asymmetric cylinder system control, and particularly to a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system. Background Art

[0002] A typical valve-controlled asymmetric cylinder system has strong non-linear characteristics such as dead zone, time-varying parameters, internal and external disturbances, etc. These non-linearities pose challenges to the high-performance tracking control of the system. To overcome the above problems, scholars have developed various effective control methods for valve-controlled asymmetric cylinder systems, aiming to improve the control performance. Among the existing methods, the observer-based backstepping control has shown strong competitiveness and is widely applied to valve-controlled asymmetric cylinder systems. However, it has deficiencies such as complex structure, weak global robustness, poor disturbance estimation performance, and inability to eliminate disturbance estimation errors. Therefore, it cannot meet the high-performance control requirements of valve-controlled asymmetric cylinder systems for fast response speed, high precision, and no overshoot. Summary of the Invention

[0003] Aiming at the above existing technical deficiencies, the purpose of the present invention is to provide a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system.

[0004] To solve the above technical problems, the present invention adopts the following technical solutions:

[0005] The present invention provides a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system, including the following steps:

[0006] S1. Establish a full-state model of the valve-controlled asymmetric cylinder system;

[0007] S2. Based on the singular perturbation theory, perform reduced-order processing on the full-state model in step S1 to obtain a reduced-order model of the system;

[0008] S3. Based on the reduced-order model of the system obtained in step S2, design a low-gain observer and a non-linear disturbance observer, and combine them with a backstepping controller to form a backstepping disturbance rejection observer;

[0009] S4. Based on the backstepping disturbance rejection controller in step S3, approximate the unknown parameters of the sliding mode disturbance rejection controller through two adaptive strategies of fuzzy adaptation method and neural network adaptation to obtain a backstepping adaptive disturbance rejection reduced-order controller.

[0010] Preferably, in step S1, the full-state model of the valve-controlled asymmetric cylinder system is as follows:

[0011]

[0012] where x1, x2, x3, x4 are state variables, A1 is the area of the rodless chamber; A2 is the area of the rod chamber; 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 is the volume of the inlet and return oil chambers; V1, V2 include the valve, connecting pipelines and the volume of the inlet and return oil chambers; C d is the flow coefficient of the valve; k u is the valve gain; w is the spool area gradient; ρ is the density of the hydraulic oil; s(u) is the sign function; p s is the supply pressure.

[0013] Preferably, in the step S2, the reduced-order system model obtained after the reduced-order processing is as follows:

[0014]

[0015] where where x1, x2 are state variables; A1 is the area of the rodless chamber; A2 is the area of the rod chamber; 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 is the volume of the inlet and return oil chambers; p1 is the pressure of the inlet oil chamber; p2 is the pressure of the return oil chamber;

[0016]

[0017] u is the control input voltage; y is the output of the system, i.e., the displacement x1.

[0018] Preferably, the step S3 specifically includes:

[0019] (1) Design a low-gain observer:

[0020] Based on the reduced-order model, select the vector k = [k1 k2] T such that A0 = A - kc T is Hurwitz, and construct the following observer:

[0021]

[0022] where ω, v are the observer state vectors, e = [0 1] T ; Define the state estimate as The estimation error Obtain:

[0023]

[0024] wherein b = g(x); c =

[01] T ;

[0025] Define the Lyapunov function of the observer as to obtain:

[0026]

[0027] Design the parameters k1, k2 in A0 to ensure that tends to zero exponentially;

[0028] (2) Design a nonlinear disturbance observer

[0029] For the subsystem design a nonlinear disturbance observer to observe the composite disturbance d i-1 (x, t), assuming that the composite disturbance is a slow disturbance, is the observed value of d i-1 (x, t), and the disturbance observer is designed as:

[0030]

[0031] where p i-1 (x) satisfies Design L i-1 (x) to make the composite disturbance observation error converge exponentially; select L i-1 (x) = c i-1 , p i-1 (x) = c i-1 x i , then the dynamic equation of the composite disturbance observation error is:

[0032]

[0033] The solution of the above equation is Adjust the convergence accuracy of the observation by adjusting the value of L i-1 (x); (3) Design a reduced-order backstepping disturbance rejection controller

[0034] For the reduced-order model of the valve-controlled asymmetric cylinder system, use the backstepping method to design the controller. The steps are as follows: Step1. Design the first subsystem without disturbance; define e1 = x1 - x 1d , then Take the Lyapunov function as then

[0035]

[0036] Let e2 = x2 - α1, then Take α1 as the low-pass filter of the output, define the virtual controller and satisfy Therefore the generated filtering error is That is

[0037] Step 2: Design the second subsystem with compound disturbances, use the disturbance observer to estimate the compound disturbances, and compensate in the virtual controller; the disturbance observer is designed as follows:

[0038]

[0039] Design L(x) = c, p(x) = cx2, and satisfy c is a constant greater than 0;

[0040] Define e2 = x2 - α1, then Define the Lyapunov function

[0041]

[0042]

[0043] Then the designed controller is

[0044]

[0045] Preferably, in step S4, the specific steps of approximating the unknown parameters of the sliding mode disturbance rejection controller by the fuzzy adaptive method include:

[0046] Use the fuzzy basis function to approximate f(x) and g(x) in the reduced-order model of the valve-controlled asymmetric cylinder system. The fuzzy system consists of a series of fuzzy rules based on the IF-THEN structure. Each rule describes the fuzzy relationship between the input and the output. The fuzzy basis function of the IF-THEN fuzzy system is:

[0047]

[0048] In the formula, is the membership function of x i The approximation of f(x) and g(x) of the valve-controlled asymmetric cylinder system by the fuzzy system is expressed as:

[0049]

[0050] In the formula, and are the network weights for approximating f(x) and g(x) respectively. Define the ideal approximation of f(x) and g(x) as Then the approximation error is:

[0051]

[0052] Wherein, and are the optimal parameters.

[0053] Preferably, in step S4, the unknown parameters of the neural network adaptive approximation sliding mode disturbance rejection controller specifically include:

[0054] Use the RBF neural network to approximate f(x) and g(x) in the reduced-order model of the valve-controlled asymmetric cylinder system. The output of the Gaussian basis function of the RBF neural network is:

[0055]

[0056] Wherein, x = [x1, x2,..., x i is the network input, i represents the input of the i-th in the network output layer; j is the input of the j-th network in the network hidden layer. Using the RBF neural network to approximate f(x) and g(x) of the valve-controlled asymmetric cylinder system is expressed as:

[0057]

[0058] Wherein, and are the network weights for approximating f(x) and g(x) respectively. Define the ideal approximation of f(x) and g(x) as Then the approximation error is:

[0059]

[0060] Wherein, and are the ideal network weights for approximating f(x) and g(x) respectively.

[0061] Preferably, in step S4, obtaining the backstepping adaptive disturbance rejection reduced-order controller specifically includes:

[0062] Unify the definition of the parameter error of the fuzzy system and the RBF neural network as The adaptive basis function is Υ(x). f(x) and g(x) of the valve-controlled asymmetric cylinder system are expressed as Define the Lyapunov function

[0063]

[0064] Then

[0065]

[0066] Design the controller as Adaptive rate Let Then

[0067]

[0068] Denote M as the upper bound of B, take η1≥r + 1, r>0, η2≥r + 1 / 2, c≥r + 1 / 2, 1 / τ≥r + M / 2 + 1 / 2, then:

[0069]

[0070] The solution of the above formula is:

[0071]

[0072] That is

[0073] V2(t) asymptotically converges, and the convergence accuracy depends on r. When Υ(x) = ξ(x), the reduced - order backstepping adaptive disturbance rejection control becomes the reduced - order fuzzy adaptive backstepping disturbance rejection control; when Υ(x)＝ h(x), the reduced - order backstepping adaptive disturbance rejection control becomes the reduced - order neural network adaptive backstepping disturbance rejection control.

[0074] The beneficial effects of the present invention are as follows:

[0075] 1. The present invention reduces the order of the model of the valve - controlled asymmetric cylinder system through the singular perturbation theory, effectively simplifies the design process of the controller and the observer, and reduces the design difficulty; at the same time, the order reduction avoids the problem of the decrease in the accuracy of the observer caused by the high - order system, and improves the accuracy and reliability of the observer.

[0076] 2. Based on the reduced - order model, the present invention designs a low - gain state observer and a non - linear disturbance observer respectively. The low - gain state observer is used to observe the state information of the system, and the non - linear disturbance observer is used to observe the unknown disturbance existing in the system in real time. Combining these two kinds of observation information with the backstepping controller forms a backstepping disturbance rejection observer; the backstepping disturbance rejection observer directly uses the observation information as feedback, does not depend on the parameters of the joint drive system, and only uses the system displacement output to achieve adaptive disturbance rejection control, effectively improving the robustness of the system

[0077] 3. The adaptive backstepping disturbance rejection reduced - order controller of the present invention can not only achieve high - precision control of the position output of the joint drive system, but also effectively observe the output state, speed and unknown disturbance of the system in real time, and shows stronger robustness to the change of system parameters. Description of the Drawings

[0078] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.

[0079] Figure 1 It is a flowchart of a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system of the present invention;

[0080] Figure 2 It is a tracking response diagram of the system in a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system of the present invention;

[0081] Figure 3 It is a tracking error diagram in a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system of the present invention;

[0082] Figure 4 It is a control input diagram of the system in a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system of the present invention. Specific embodiments

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0084] Embodiment:

[0085] As Figures 1 to 4 shown, this embodiment provides a reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system, which specifically includes the following steps:

[0086] S1: Establish the full-state model of the valve-controlled asymmetric cylinder system as follows:

[0087]

[0088] In the formula, x1, x2, x3, x4 are state variables; A1 is the area of the rodless chamber; A2 is the area of the rod chamber; 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 is the volume of the inlet and return oil chambers; V1, V2 include the valve, connecting pipelines and the volume of the inlet and return oil chambers; C d is the flow coefficient of the valve; ku is the valve gain; w is the spool area gradient; ρ is the density of the hydraulic oil; s(u) is the sign function; p s is the supply pressure.

[0089] S2: Based on the singular perturbation theory, reduce the order of the full-state model in S1 to obtain the following reduced-order system model:

[0090]

[0091] In the formula, where x1 and x2 are state variables; A1 is the area of the rodless chamber; A2 is the area of the rod chamber; 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 is the volume of the inlet and return oil chambers; p1 is the pressure of the inlet oil chamber; p2 is the pressure of the return oil chamber; is the control input voltage; y is the output of the system, i.e., the displacement x1.

[0092] S3: Based on the reduced-order model in S2, design a low-gain state observer and a nonlinear disturbance observer, and combine them with the backstepping controller to form a backstepping disturbance rejection observer. The process is as follows:

[0093] (1) Design a low-gain state observer

[0094] Based on the reduced-order model, select the vector k = [k1 k2] T such that A0 = A - kc T is Hurwitz, and construct the following observer:

[0095]

[0096] In the formula, ω and v are the observer state vectors,

[0097] Define the state estimate as Then the estimation error Therefore

[0098]

[0099] Thus

[0100]

[0101] In the formula, b = g(x); c = [0 1] T ;

[0102] Define the Lyapunov function of the observer as There is

[0103]

[0104] Therefore, by designing the parameters k1 and k2 in A0, it is possible to ensure that tends to zero exponentially.

[0105] (2) Design a nonlinear disturbance observer

[0106] For the subsystem design a nonlinear disturbance observer to observe the combined disturbance d i-1 (x, t); assuming that the combined disturbance is a slow disturbance, then is the observed value of d i-1 (x, t); then the disturbance observer is designed as follows:

[0107]

[0108] where p i-1 (x) should satisfy Design L i-1 (x) to enable the combined disturbance observation error to converge exponentially; select L i-1 (x) = c i-1 , p i-1 (x) = c i-1 x i , then the dynamic equation of the combined disturbance observation error is:

[0109] The solution of equation (8) is This shows that the disturbance observer approximates exponentially and the convergence accuracy of the observation can be adjusted by adjusting the value of L i-1 (x).

[0110] (3) Design a reduced-order backstepping disturbance rejection controller

[0111] For the reduced-order model of the valve-controlled asymmetric cylinder system, backstepping is used for controller design. The steps are as follows: Step1, design the first subsystem without disturbance. Define e1 = x1 - x 1d , then Take the Lyapunov function as Then

[0112]

[0113] Let e2 = x2 - α1, then Take α1 as the output of the low-pass filter of Define the virtual controller and satisfy Therefore The generated filtering error is That is

[0114]

[0115] Step 2: There are composite disturbances in the design of the second subsystem. Therefore, a disturbance observer is used to estimate the composite disturbances and compensate them in the virtual controller. The design of the disturbance observer is as follows:

[0116]

[0117] Design \(L(x)=c\), \(p(x)=cx^2\), satisfying c is a constant greater than 0.

[0118] Define \(e_2 = x_2 - \alpha_1\), then Define the Lyapunov function

[0119]

[0120] Then the designed controller is

[0121]

[0122] Without referring to the model information, the parameters in the controller \(u\) are unknown and cannot be directly used in control. Therefore, an adaptive law is designed to approximate the unknown parameters. Two adaptive methods are adopted to approximate the unknown parameters, namely the fuzzy adaptive method and the RBF neural network adaptive method;

[0123] S4: The process of approximating the unknown parameters of the sliding mode disturbance rejection controller through two adaptive strategies to obtain the adaptive disturbance rejection reduced-order controller is as follows:

[0124] Among them, the process of the fuzzy adaptive method is as follows:

[0125] Since the fuzzy system has the universal approximation property, the fuzzy basis function can be used to approximate \(f(x)\) and \(g(x)\) in the reduced-order model of the valve-controlled asymmetric cylinder system; The fuzzy system consists of a series of fuzzy rules based on the IF-THEN structure, and each rule describes the fuzzy relationship between the input and the output; The fuzzy basis function of the IF-THEN fuzzy system is:

[0126]

[0127] In the formula, is the membership function of \(x\) i Therefore, the approximation of \(f(x)\) and \(g(x)\) of the valve-controlled asymmetric cylinder system by the fuzzy system is expressed as:

[0128]

[0129] wherein, and are the network weights for approximating f(x) and g(x) respectively. The ideal approximations of f(x) and g(x) are defined as Then the approximation error is:

[0130]

[0131] wherein, and are the optimal parameters.

[0132] (2) The process of the RBF neural network adaptive method is as follows:

[0133] Similarly, the RBF network has the universal approximation property and can use the RBF neural network to approximate f(x) and g(x) in the reduced-order model of the valve-controlled asymmetric cylinder system; the output of the Gaussian basis function of the RBF neural network is:

[0134]

[0135] wherein, x = [x1, x2,..., x i is the network input, i represents the input of the i-th in the network output layer; j is the input of the j-th network in the network hidden layer; therefore, the approximation of f(x) and g(x) of the valve-controlled asymmetric cylinder system by the RBF neural network can be expressed as:

[0136]

[0137] wherein, and are the network weights for approximating f(x) and g(x) respectively; the ideal approximations of f(x) and g(x) are defined as Then the approximation error is:

[0138]

[0139] wherein, and are the ideal network weights for approximating f(x) and g(x) respectively.

[0140] For the convenience of proving the controller, the parameter error of the fuzzy system and the RBF neural network is uniformly defined as The adaptive basis function is Υ(x); therefore, f(x) and g(x) of the valve-controlled asymmetric cylinder system are expressed as: Define the Lyapunov function

[0141]

[0142] Then:

[0143]

[0144] The designed controller is Adaptive rate Let Then:

[0145]

[0146] Denote M as the upper bound of B. Take η1≥r + 1, r>0, η2≥r + 1 / 2, c≥r + 1 / 2, 1 / τ≥r + M / 2 + 1 / 2. Then:

[0147]

[0148] The solution of the above formula is:

[0149]

[0150] That is:

[0151]

[0152] Therefore, V2(t) asymptotically converges, and the convergence accuracy depends on r. According to the above proof, it can be seen that the valve-controlled asymmetric cylinder system using the reduced-order backstepping adaptive disturbance rejection algorithm is stable.

[0153] When Υ(x) = ξ(x), the reduced-order backstepping adaptive disturbance rejection control is the reduced-order fuzzy adaptive backstepping disturbance rejection control; when Υ(x) = h(x), the reduced-order backstepping adaptive disturbance rejection control is the reduced-order neural network adaptive backstepping disturbance rejection control. The specific research process is as follows: Taking the valve-controlled asymmetric cylinder system as the research object to verify the effectiveness of the proposed method;

[0154] The desired trajectory of the system is set to x d = 0.1sin(0.4πt); The parameters of the reduced-order fuzzy adaptive backstepping disturbance rejection control are η1 = 100, η2 = 710, τ1 = 0.01, γ1 = 10, γ2 = 0.1, c = 1, T = 18.5, k1 = 30, k2 = 9995 。 The parameters of the reduced-order fuzzy adaptive backstepping disturbance rejection control are η1 = 100, η2 = 340, τ1 = 0.02, γ1 = 4, γ2 = 0.001, c = 0.1, T = 18.5, k1 = 30, k2 = 9995, b j = 10, c j = [-1, -0.5, 0, 0.5, 1].

[0155] The tracking response of the system is as Figure 2 shown. Correspondingly, Figure 3The response trajectory of the tracking error is shown, Figure 4 and the control input of the system is shown. The above results verify that the proposed control method can achieve accurate tracking performance with a relatively low control input, thus verifying the effectiveness of the proposed method.

[0156] 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 equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system, characterized in that, It includes the following steps: S1. Establish the full-state model of the valve-controlled asymmetric cylinder system; S2. Based on the singular perturbation theory, reduce the order of the full-state model in step S1 to obtain the reduced-order model of the system; S3. Based on the reduced-order model of the system obtained in step S2, design a low-gain observer and a non-linear disturbance observer, and combine them with a backstepping controller to form a backstepping disturbance rejection observer; S4. Based on the backstepping disturbance rejection controller in step S3, approximate the unknown parameters of the sliding mode disturbance rejection controller through two adaptive strategies, namely, fuzzy adaptive method and neural network adaptive method, to obtain a backstepping adaptive disturbance rejection reduced-order controller.

2. The reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, characterized in that, In step S1, the full-state model of the valve-controlled asymmetric cylinder system is as follows: where x 1, x2, x 3, x4 are state variables; A1 is the area of the rodless chamber; A2 is the area of the rod chamber; 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 is the volume of the inlet and return oil chambers; V1, V2 include the valve, connecting pipelines and the volume of the inlet and return oil chambers; C d is the flow coefficient of the valve; k u is the valve gain; w is the spool area gradient; ρ is the density of the hydraulic oil; s(u) is the sign function; p s is the supply oil pressure.

3. The reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, characterized in that In step S2, the reduced-order model of the system obtained after the order reduction process is as follows: In the formula, where x1 and x2 are state variables; A1 is the area of the rodless chamber; A2 is the area of the rod chamber; m is the total equivalent mass on the hydraulic piston rod; B is the viscous friction coefficient; k is the elastic coefficient; Fd is the external load disturbance force; Cip is the volume of the inlet and return oil chambers; p1 is the pressure of the inlet oil chamber; p2 is the pressure of the return oil chamber; u is the control input voltage; y is the output of the system, i.e., the displacement x1.

4. The reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, wherein, Step S3 specifically includes: (1) Design a low-gain observer: Based on the reduced-order model, select the vector k = [k1 k2] T such that A0 = A - kc T is Hurwitz, and construct the following observer: where ω, v are the observer state vectors, and e = [0 1] T ; Define the state estimate as The estimation error Obtain: In the formula, b = g(x); c = [01] T ; Define the Lyapunov function of the observer as Obtain: The parameters k1 and k2 in Design A0 can ensure that tend to zero exponentially; (2) Design a non-linear disturbance observer For the subsystem Design a nonlinear disturbance observer to observe the composite disturbance d i-1 (x, t), assuming that the composite disturbance is a slow disturbance, Let d i-1 (x, t) be the observed value, and the disturbance observer is designed as follows: where p i-1 (x) satisfies Design L i-1 (x) can make the composite disturbance observation error converge exponentially; Select L i-1 (x) = c i-1 , p i-1 (x) = c i-1 x i , then the dynamic equation of the composite disturbance observation error is:[[]] The solution of the above equation is By adjusting L i-1 (x) to adjust the convergence accuracy of the observation; (3) Design a reduced-order backstepping active disturbance rejection controller For the reduced-order model of the valve-controlled asymmetric cylinder system, the controller is designed using the backstepping method. The steps are as follows: Step1. Design the first subsystem without disturbance; define e1 = x1 - x 1d , then Take the Lyapunov function as then Let e2 = x2 - α1, then Take α1 as the output of the low-pass filter Define the virtual controller and satisfy Therefore The resulting filtering error is That is Step2. Design the second subsystem with compound disturbances, estimate the compound disturbances using a disturbance observer, and compensate for them in the virtual controller; the disturbance observer is designed as follows: Design \(L(x)=c\), \(p(x)=cx^2\), satisfying where \(c\) is a constant greater than 0; Define \(e_2 = x_2-\alpha_1\), then Define the Lyapunov function Then the designed controller is 5. The reduced-order adaptive backstepping active disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, wherein In step S4, the specific process of approximating the unknown parameters of the sliding mode disturbance rejection controller through the fuzzy adaptive method includes: Use fuzzy basis functions to approximate f(x) and g(x) in the reduced-order model of the valve-controlled asymmetric cylinder system. The fuzzy system consists of a series of fuzzy rules based on the IF-THEN structure. Each rule describes the fuzzy relationship between the input and the output. The fuzzy basis function of the IF-THEN fuzzy system is: wherein, is x i The membership function, approximated by the fuzzy system for the valve-controlled asymmetric cylinder system, is expressed as f(x) and g(x): In the formula, and are the network weights for approximating f(x) and g(x) respectively. Define the ideal approximation of f(x) and g(x) as Then the approximation error is: In the formula, and are the optimal parameters.

6. The reduced-order adaptive backstepping active disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, characterized in that, In step S4, the specific process of approximating the unknown parameters of the sliding mode disturbance rejection controller through neural network adaptive method includes: Use a RBF neural network to approximate f(x) and g(x) in the reduced-order model of the valve-controlled asymmetric cylinder system. The output of the Gaussian basis function of the RBF neural network is: where \(x = [x_1, x_2, \ldots, x i \) is the network input, \(i\) represents the input of the \(i\)-th output layer of the network; \(j\) is the \(j\)-th network input of the network hidden layer. The approximation of \(f(x)\) and \(g(x)\) of the valve-controlled asymmetric cylinder system using the RBF neural network is expressed as: In the formula, and are the network weights approximating f(x) and g(x) respectively. Define the ideal approximation of f(x) and g(x) as Then the approximation error is: In the formula, and are the ideal network weights for approximating f(x) and g(x), respectively.

7. A reduced-order adaptive backstepping disturbance rejection control method for a valve-controlled asymmetric cylinder system according to claim 1, characterized in that In step S4, the specific process of obtaining the backstepping adaptive disturbance rejection reduced-order controller includes: The parameter errors of the unified fuzzy system and the RBF neural network are defined as The adaptive basis function is Υ(x), and f(x) and g(x) of the valve-controlled asymmetric cylinder system are expressed as Define the Lyapunov function Then The design controller is Adaptive rate Let Then Denote M as the upper bound of B, take η1≥r + 1, r>0, η2≥r + 1 / 2, c≥r + 1 / 2, 1 / τ≥r + M / 2 + 1 / 2, then: The solution of the above formula is: That is V2(t) asymptotically converges, and the convergence accuracy depends on r. When Υ(x) = ξ(x), the reduced-order backstepping adaptive disturbance rejection control is the reduced-order fuzzy adaptive backstepping disturbance rejection control; when Υ(x) = h(x), the reduced-order backstepping adaptive disturbance rejection control is the reduced-order neural network adaptive backstepping disturbance rejection control.

Images