Electro-hydraulic servo system filtering backstepping sliding mode control method and system based on RCFO

Abstract

The invention belongs to the technical field of electro-hydraulic servo control, and discloses an electro-hydraulic servo system filtering backstepping sliding mode control method and system based on RCFO, and the method comprises the steps: building a nonlinear dynamic model of an electro-hydraulic servo system based on the working principle and structural composition of the electro-hydraulic servo system; based on the nonlinear dynamic model, obtaining matching uncertainty; an RCFO observer is constructed based on an RBF neural network, and then a filtering backstepping sliding mode controller is constructed; and the matching uncertainty existing in the system is compensated by using an RCFO observer, and tracking control is performed on the electro-hydraulic servo system based on a filtering backstepping sliding mode controller. According to the method, the RBF adaptive weight adjustment law is combined with the compensation function observer, so that the robustness of the system is improved; a second-order instruction filter and a backstepping sliding mode control method are combined, the problem of calculation explosion occurring in the backstepping technology is effectively eliminated, meanwhile, due to introduction of filtering, the influence of high-frequency noise is reduced, and the control precision of the system can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electro-hydraulic servo control, and in particular relates to a filtering backstepping sliding mode control method and system for an electro-hydraulic servo system based on RCFO. Background Art

[0002] The electro-hydraulic servo system, a key branch of the hydraulic servo system, uses electrical signals for control input, enabling rapid information transmission and combining the advantages of both electrical and hydraulic transmission. As a complex, nonlinear mechatronic system, the electro-hydraulic servo system offers numerous advantages, such as rapid response, high load capacity, and a high power-to-weight ratio. These advantages have led to its widespread application in modern industry, including applications such as ship steering gears, robotic excavators, robotic arms, and hydraulic presses.

[0003] Against this backdrop, electro-hydraulic servo systems, after decades of development, have gradually become an indispensable core component of modern industrial equipment, thanks to their high-precision control and rapid response. While electro-hydraulic servo systems possess many excellent electro-hydraulic properties, they are often subject to various uncertainties in practical applications. For example, model parameters such as load mass, effective oil bulk modulus, and leakage coefficient can vary significantly with operating conditions, temperature, and equipment wear. Furthermore, hydraulic systems exhibit strong nonlinearities in terms of control valve flow and pressure dynamics, oil compressibility, and leakage. Furthermore, due to the complexity of their operating environment, electro-hydraulic servo systems are inevitably affected by unknown external load forces and disturbances. All of these uncertainties can severely degrade system control performance or even destroy the system. Therefore, achieving high-precision tracking control of electro-hydraulic servo systems using advanced control methods in the presence of these uncertainties remains a challenge for engineers.

[0004] In summary, research on control schemes for electro-hydraulic servo systems is a key technological challenge in my country's intelligent manufacturing sector. Currently, scholars both domestically and internationally have conducted in-depth research in this area and achieved remarkable results. However, existing research often relies on idealized assumptions and fails to meet the demands of practical engineering applications. Therefore, the problem of high-precision trajectory tracking control for electro-hydraulic servo systems under complex operating conditions has become a key technical bottleneck that urgently needs to be overcome. Summary of the Invention

[0005] The present invention aims to solve the deficiencies of the prior art and provides the following solutions: The filter backstepping sliding mode control method of the electro-hydraulic servo system based on RCFO includes the following steps: Based on the working principle and structural composition of the electro-hydraulic servo system, a nonlinear dynamic model of the electro-hydraulic servo system is constructed; Based on the nonlinear dynamic model, a matching uncertainty is obtained; Based on the RBF neural network, an RCFO observer is constructed, and then a filtered backstepping sliding mode controller is constructed; The matching uncertainty in the system is compensated by using the RCFO observer, and tracking control is performed on the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

[0006] Preferably, the method for constructing the nonlinear dynamic model includes: Construct the pressure-flow characteristic equation of the servo valve: , , in, Indicates the load flow of the asymmetric hydraulic cylinder, represents the flow gain of the hydraulic cylinder, Indicates the servo valve input voltage, Indicates the oil supply pressure, Indicates the load pressure of the asymmetric hydraulic cylinder, represents the symbolic function, represents a positive constant, represents the flow coefficient, represents the area gradient of the servo valve, Indicates the density of the oil; Construct the flow continuity equation for the valve-controlled hydraulic cylinder: , in, represents the total leakage coefficient, It represents the average effective area of ​​the left and right chambers of the oil cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder, represents the effective oil bulk modulus, Expresses the derivative of the load pressure difference; Construct the equilibrium equation of the asymmetric hydraulic cylinder load force: , in, represents the total mass of the load and the piston, represents the displacement acceleration, B represents the viscous friction coefficient, represents the elastic stiffness coefficient, represents the output displacement, Indicates external load force.

[0007] Preferably, the method for obtaining the matching uncertainty includes: Based on the nonlinear dynamic model, the state space equation of the uncertain electro-hydraulic servo system is obtained: , , in, express The derivative of express The derivative of express The derivative of 、 、 represents the state variables of the system, represents the known part of the model, 、 and Represents constants related to electro-hydraulic servo system parameters, i =1, 2, 3, Indicates matching uncertainty; Based on the state space equation, the matching uncertainty is obtained: , in, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters b perturbation term.

[0008] Preferably, the RCFO observer is: , in, express The derivative of express The derivative of express The derivative of represents the adaptive weight adjustment law, express The estimated value of 、 、 represents the state variable of the observer, represents the gain of the observer, represents the observation error vector, represents the compensation function, represents the adjustment factor, represents the sliding surface function, express The observation error, represents the Gaussian function.

[0009] Preferably, the filtered backstepping sliding mode controller is: , in, represents the first virtual control law, 、 、 represents a positive design parameter, 、 represents the tracking error, express The derivative of represents the second virtual control law, represents the second-order filter output, Indicates the servo valve input voltage, 、 represents a positive constant, represents the second-order filter output, represents the sliding mode function.

[0010] The present invention also provides a filtered backstepping sliding mode control system for an electro-hydraulic servo system based on RCFO, wherein the control system applies the above-mentioned control method and comprises: a model construction module, a matching uncertainty acquisition module, an observer and controller construction module, and a compensation control module; The model building module builds a nonlinear dynamic model of the electro-hydraulic servo system based on the working principle and structural composition of the electro-hydraulic servo system; The matching uncertainty acquisition module obtains the matching uncertainty based on the nonlinear dynamic model; The observer and controller construction module constructs an RCFO observer based on the RBF neural network, and then constructs a filtered backstepping sliding mode controller; The compensation control module utilizes the matching uncertainty of the RCFO observer compensation system and performs tracking control on the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

[0011] Preferably, the workflow of the model building module includes: Construct the pressure-flow characteristic equation of the servo valve: , , in, Indicates the load flow of the asymmetric hydraulic cylinder, represents the flow gain of the hydraulic cylinder, Indicates the servo valve input voltage, Indicates the oil supply pressure, Indicates the load pressure of the asymmetric hydraulic cylinder, represents the symbolic function, represents a positive constant, represents the flow coefficient, represents the area gradient of the servo valve, Indicates the density of the oil; Construct the flow continuity equation for the valve-controlled hydraulic cylinder: , in, represents the total leakage coefficient, It represents the average effective area of ​​the left and right chambers of the oil cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder, represents the effective oil bulk modulus, Expresses the derivative of the load pressure difference; Construct the equilibrium equation of the asymmetric hydraulic cylinder load force: , in, represents the total mass of the load and the piston, represents the displacement acceleration, B represents the viscous friction coefficient, represents the elastic stiffness coefficient, represents the output displacement, Indicates external load force.

[0012] Preferably, the workflow of the matching uncertainty acquisition module includes: Based on the nonlinear dynamic model, the state space equation of the uncertain electro-hydraulic servo system is obtained: , , in, express The derivative of express The derivative of express The derivative of 、 、 represents the state variables of the system, represents the known part of the model, 、 and Represents constants related to electro-hydraulic servo system parameters, i =1, 2, 3, Indicates matching uncertainty; Based on the state space equation, the matching uncertainty is obtained: , wherein, denotes a perturbation term of the parameter , denotes a perturbation term of the parameter , denotes a perturbation term of the parameter , denotes a perturbation term of the parameter b .

[0013] Preferably, the RCFO observer is: , wherein, denotes a derivative of , denotes a derivative of , denotes a derivative of , denotes an adaptive weight adjustment law, denotes an estimate of , , , denotes a state variable of the observer, denotes a gain of the observer, denotes an observation error vector, denotes a compensation function, denotes an adjustment factor, denotes a sliding mode surface function, denotes an observation error of , denotes a Gaussian function.

[0014] Preferably, the filter backstepping sliding mode controller is: , wherein, denotes a first virtual control law, , , denotes a positive design parameter, , denotes a tracking error, denotes a derivative of , denotes a second virtual control law, denotes a second order filter output, denotes a servo valve input voltage, , denotes a positive constant, denotes a second order filter output, denotes a sliding mode function.

[0015] Compared with the prior art, the present invention has the following beneficial effects: The present invention combines the RBF adaptive weight adjustment law with the compensation function observer to achieve online approximation of matching uncertainty with nonlinear terms, and feeds back the processed approximation value to the controller to improve the robustness of the system; combined with the second-order command filter and the backstepping sliding mode control method, it effectively eliminates the "computational explosion" problem that occurs in the backstepping technology. At the same time, the introduction of filtering reduces the influence of high-frequency noise, which can effectively improve the control accuracy of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings required for use in the embodiments. 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 any creative work.

[0017] Figure 1 Schematic diagram of a method flow in an embodiment of the present invention; Figure 2 Schematic diagram of the system structure of an embodiment of the present invention; Figure 3 2 is a system block diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0019] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] Example 1 In this embodiment, if Figure 1 As shown, the filtered backstepping sliding mode control method of the electro-hydraulic servo system based on RCFO includes the following steps: S1. Based on the working principle and structural composition of the electro-hydraulic servo system, a nonlinear dynamic model of the electro-hydraulic servo system is constructed.

[0021] Methods for constructing nonlinear dynamic models include: Constructing the pressure-flow characteristic equation of the servo valve: In this embodiment, the electro-hydraulic servo valve serves as the core control element of the electro-hydraulic servo system. It realizes precise regulation of flow, pressure and direction through the coordinated movement of precision components such as the valve core and valve sleeve. Its dynamic response characteristics are directly affected by the motion state of the components. The ideal zero-opening four-way valve studied in this embodiment uses the flow-pressure equation to describe the working characteristics, where the load flow is the key indicator for measuring system performance. In order to simplify the design and improve the universality of the model, the assumptions include: using an ideal zero-opening four-way sliding valve (no leakage, symmetrical matching), no friction loss in the pipeline and negligible dynamic characteristics, the fluid is incompressible and the parameters are constant; the fluid volume is constant and the density is uniform; the oil supply pressure Set to a fixed value, return oil pressure ; The pressure in the hydraulic cylinder cavity is equal, and the bulk elastic modulus Is a fixed constant. The flow rate of the two chambers of the hydraulic cylinder and Displacement of the servo valve spool relative to the neutral position The equation relationship between them is as follows: , (1) , (2) in, represents the flow coefficient, represents the area gradient of the servo valve, Indicates the displacement of the servo valve core relative to the neutral position, Indicates the density of the oil, Indicates the oil supply pressure, Indicates the return oil pressure, Indicates the pressure in the left chamber of the hydraulic cylinder. Indicates the pressure in the right chamber of the hydraulic cylinder. Defines the load pressure of the asymmetric hydraulic cylinder for: , (3) in, A 1 represents the effective area of ​​the cylinder rodless cavity, A 2 represents the effective area of ​​the cylinder rod cavity. η It represents the ratio of the effective area of ​​the two cavities. From formula (3), we can know that , then the load flow of the asymmetric hydraulic cylinder It can be expressed as: , (4) From formula (1), (2), and (4), we can get that When the flow-pressure characteristic equation of the electro-hydraulic servo valve is Written as a specific equation, it can be expressed as: , (5) when When the load flow It can be expressed as: , (6) Combining equations (5) and (6), we can obtain: , (7) in, represents the asymmetry factor, represents the symbolic function, Indicates the servo valve input voltage; when Sometimes, there are ;when Sometimes, there are Since most electro-hydraulic servo valves have high response characteristics, the dynamic models of servo amplifiers and servo valves are usually ignored in practical engineering applications. Therefore, the relationship between the spool displacement and the control input is approximately ,in is a positive constant; therefore, Equation (7) can be rewritten as: , (8) In order to ensure the convenience of modeling the electro-hydraulic servo system, it is assumed that the effective areas of the pistons on both sides of the hydraulic cylinder are equal, and we can get ,in, It represents the average value of the effective area of ​​the left and right chambers of the cylinder. , Equation (3) and Equation (4) can be rewritten as: , (9) , (10) Therefore, formula (7) can be simplified as: , (11) in, represents the flow gain of the hydraulic cylinder, .

[0022] Constructing a flow continuity equation for a valve-controlled hydraulic cylinder: In this embodiment, the hydraulic cylinder serves as the actuator of an electro-hydraulic servo system, moving the piston to control load displacement. Thanks to advances in precision machining and sealing technology (such as optimized gap seals and improved dust seal structures), external leakage in modern hydraulic cylinders has been significantly reduced. Therefore, external leakage in valve-controlled hydraulic cylinders can be ignored. The flow continuity equations for the two chambers within the cylinder are as follows: , (12) in, Indicates speed, is the sum of the internal leakage and external leakage coefficients, recorded as the total leakage coefficient, represents the initial volume of the left side cavity of the hydraulic cylinder and its pipeline, represents the initial volume of the right side cavity of the hydraulic cylinder and its pipeline, represents the effective oil bulk modulus, represents the piston displacement, Represents the derivative of the left chamber pressure of the hydraulic cylinder, Represents the derivative of the pressure in the right chamber of the hydraulic cylinder. The volume of the valve-controlled hydraulic cylinder is defined as: , (13) in, V l Indicates the left volume of the valve-controlled hydraulic cylinder, V r represents the right volume of the valve-controlled hydraulic cylinder. Therefore, formula (12) can be simplified as: , (14) because 、 , and Can be ignored. Secondly, combined with formula (9), Approximately regarded as , so formula (14) can be simplified as: , (15) Substituting formula (15) into formula (10) yields: , (16) in, According to the existing technology, the relationship between the hydraulic cylinder flow continuity equation and the effective area of ​​the two chambers is: ,because ,at this time The ratio of the two chamber volumes is defined as: , (17) According to formula (17), combined with the total volume of the hydraulic cylinder , we can infer the following relationship: , (18) According to the power matching principle of hydraulic system power components, we can get , combining formula (18) and substituting it into formula (16), we can get: , (19) in, N represents a positive constant, ,because ,at this time Therefore, the flow continuity equation of the valve-controlled hydraulic cylinder is written as: , (20) in, Indicates the derivative of the load pressure difference.

[0023] Constructing a force balance equation for an asymmetric hydraulic cylinder: In this embodiment, the load and piston are subjected to an overall force analysis. The object is subject to spring force, load force, viscous force, and other external forces. According to Newton's law, ignoring the friction force and the influence of the system's own oil quality in the working state, the force balance equation is as follows: , (twenty one) in, represents the total mass of the load and the piston, represents the displacement acceleration, B represents the viscous friction coefficient, represents the elastic stiffness coefficient, represents the output displacement, Represents external load force; due to , combined with formula (9), formula (21) can be simplified as: . (twenty two) Based on the pressure-flow characteristic equation (11) of the servo valve, the flow continuity equation (20) of the valve-controlled hydraulic cylinder, and the load force balance equation (22) of the asymmetric hydraulic cylinder derived from the above discussion, the dynamic model of the electro-hydraulic servo system is as follows: . (twenty three) S2. Based on the nonlinear dynamic model, the matching uncertainty is obtained.

[0024] The method for obtaining the matching uncertainty includes: obtaining the state space equation of the uncertain electro-hydraulic servo system based on the nonlinear dynamic model. In this embodiment, the state space equation selects the system state as the output displacement ,speed , acceleration , then define the system state variables as , the third-order state space equation of the electro-hydraulic servo system with matching uncertainty is as follows: , (twenty four) in, , (25) The electro-hydraulic servo system will encounter various problems in actual operation. These unfavorable factors are integrated into the matching disturbance in formula (24): d Matching perturbations dIt mainly includes two parts. The first part is the uncertainty of the system's internal parameters, modeling errors and external unknown interference, which are known functions or predictable complex nonlinear terms. The second part is the complex nonlinear terms of parameter perturbations that the system cannot predict and unpredictable external interferences. Among them, the unpredictable complex nonlinear terms can be processed by approximating the RBF neural network proposed in this embodiment. In addition, considering that key parameters such as the effective oil bulk modulus and the viscous friction coefficient in the actual system have parameter perturbation characteristics, the parameters 、 、 and The perturbation term can be expressed as 、 、 and Therefore, the original system equation (24) is reconstructed to obtain the state space model containing the parameter perturbation compensation term in the form of: , (26) in, express The derivative of express The derivative of express The derivative of 、 、 represents the state variables of the system, represents the known part of the model, , 、 and As shown in formula (25), it represents the constant related to the parameters of the electro-hydraulic servo system, i =1, 2, 3, represents the matching uncertainty; based on the state space equation, the matching uncertainty is obtained: , (27) in, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters b perturbation term.

[0025] S3. Construct an RCFO observer based on the RBF neural network, and then construct a filtered backstepping sliding mode controller.

[0026] The RCFO observer is: , (28) in, express The derivative of express The derivative of express The derivative of represents the adaptive weight adjustment law, express The estimated value of express The estimated value of 、 、 represents the state variable of the observer, represents the gain of the observer, represents the compensation function, represents the adjustment factor, represents the sliding surface function, , represents the coefficient of the sliding surface function, represents the observation error vector, l 3 and l 2 indicates a positive observer gain, e c1 express x 1 observation error, e c2 express x 2 observation error, e c3 express The observation error, Represents a Gaussian function. The RBF neural network compensation observer designed in this embodiment can infinitely approach the true unknown function ,Right now: . (29) The proof process is as follows: First, let’s explain the RBF neural network: the RBF neural network is a feedforward neural network that includes an output layer, a hidden layer, and an input layer. The RBF neural network can use its powerful approximation nonlinearity to replace unknown nonlinear uncertainties. If the function set : exist If the range is continuous, then there is a neural network Can infinitely approximate unknown functions , at this time the RBF neural network is designed as: , (30) in, represents the set of real numbers, n express ndimensional space, h j Indicates the j The number of nodes, exp represents the natural exponential function, c j Indicates the j The center point vector value of hidden layer neurons, λ j Indicates the j The width parameter of each node, h represents the input of the Gaussian function, represents the weight of the neural network, δ Represents the approximation error. The output of the RBF neural network, that is, the actual output of the compensation function is: , (31) in, represents the ideal weight The estimated value of is, and the estimation error is defined as .

[0027] The following proves: Subtracting Equation (28) from Equation (26), and combining Equation (30) and Equation (31), we get: , (32) The designed sliding surface function is: , (33) right The derivative is: , (34) in, express The derivative of express e c1 The derivative of express e c2 The derivative of express e c3 The derivative of l 1 indicates a positive observer gain. Define the first Lyapunov function as: , (35) right V Taking the derivative we get: , (36) in, express V Substituting the fourth equation of (28) into (36) yields: , (37) Since the RBF neural network can infinitely approximate the unknown function, the error δ Small enough to get . The proof is complete.

[0028] The filtered backstepping sliding mode controller is: In this embodiment, based on RCFO, a filtered backstepping sliding mode controller is designed to achieve the trajectory tracking control target. First, the tracking error is defined as follows: , (38) in, 、 、 represents the tracking error, 、 is the virtual state variable after the second-order instruction filter, represents the desired tracking trajectory. The control law is then derived using command filtering, recursive backstepping, and sliding mode control. The entire design process of filtered backstepping sliding mode control is divided into the following three steps.

[0029] Step 1: Define the second Lyapunov function: , (39) in, V 1 represents the second Lyapunov function. According to equations (26) and (38), we can get The derivative of is: , (40) in, express The derivative of express The derivative of . Then V 1 Taking the derivative we can get: , (41) in, express V 1. In order to make is negative, virtual control law Designed to: , (42) in, is a positive design parameter. In order to avoid the virtual control law in the subsequent steps Repeat the derivation and pass it through the second-order instruction filter to obtain Estimated value of (virtual state variable after the second-order command filter) and its derivative estimate , define the filtering error as , by substituting formula (42) into formula (41), we can obtain: . (43) Step 2: Define the third Lyapunov function: , (44) in, V 2 represents the second Lyapunov function. According to equations (26) and (38), we can get The derivative of is: , (45) in, express The derivative of Indicates estimated value The derivative of (the virtual state variable after the second-order instruction filter). V 2 Taking the derivative we can get: , (46) in, express V 2. In order to make is negative, virtual control law Designed to: , (47) in, is a positive design parameter. It is obtained by processing it with a second-order instruction filter. Estimated value of (virtual state variable after the second-order command filter) and its derivative estimate , defining the filtering error , substituting formula (47) into formula (46) yields the following: . (48) Step 3: Define the sliding mode function: , (49) in, represents the sliding mode function, 、 represents a positive constant. According to equations (26) and (38), we can get The derivative of is: , (50) in, express The derivative of Indicates estimated value The derivative of (the virtual state variable after the second-order instruction filter). Taking the derivative of Equation (49) we can get , (51) in, express The derivative of . Define the third Lyapunov function: , (52) in, V 3 represents the third Lyapunov function. Then V 3 Taking the derivative we can get: , (53) in, express V 3. In order to make is negative, the actual servo valve control input voltage Designed to: , (54) in, is a positive design parameter. Substituting equation (54) into equation (54) yields: , (55) in, .

[0030] Based on the above design steps, the structure of the filtered backstepping sliding mode controller based on RCFO designed in this embodiment is: . (56) S4. The matching uncertainty of the system is compensated by using the RCFO observer, and the electro-hydraulic servo system is tracked and controlled based on the filtered backstepping sliding mode controller.

[0031] Example 2 In this embodiment, a stability analysis of the present invention will be provided: using Lyapunov stability proof, a stability proof of the closed-loop control design of the electro-hydraulic servo system is given below.

[0032] Based on the design of the first embodiment, the final Lyapunov function of the backstepping control is designed as: , (57) in, represents the final Lyapunov function. According to (56), The derivative of can be expressed as: , (58) According to Young's inequality, the latter term of formula (58) can be transformed as follows: , (59) Substituting (59) into (58) we obtain: , (60) Equation (60) can be rearranged into a compact inequality as follows: , (61) , (62) , (63) in, represents a positive constant, D express The upper bound of . Select the design parameters 、 、 To ensure Then, according to the mathematical equation of the second-order command filter, the solution of inequality (61) is as follows: , (64) when hour, will converge to the upper bound Therefore, the error after compensation is Bounded. According to formula (29), we know Bounded, so all error signals of the control system are bounded. In order to make the convergence region arbitrarily small, the control parameters can be adjusted Implementation. Proof completed.

[0033] Example 3 In this embodiment, if Figure 2 、 Figure 3 As shown, the filtered backstepping sliding mode control system of the electro-hydraulic servo system based on RCFO includes: a model construction module, a matching uncertainty acquisition module, an observer and controller construction module and a compensation control module.

[0034] The model building module constructs a nonlinear dynamic model of the electro-hydraulic servo system based on the working principle and structural composition of the electro-hydraulic servo system.

[0035] The workflow of the model building module includes: building the pressure-flow characteristic equation of the servo valve: , (65) , (66) in, Indicates the load flow of the asymmetric hydraulic cylinder, Qc represents the flow gain of the hydraulic cylinder, Vc represents the input voltage of the servo valve, Pc represents the supply oil pressure, Pc represents the load pressure of the asymmetric hydraulic cylinder, sign represents the sign function, C represents a constant, C represents the flow coefficient, A represents the area gradient of the servo valve, ρ represents the density of the oil. The flow continuity equation of the valve-controlled hydraulic cylinder is constructed as follows: , (67) wherein, C represents the total leakage coefficient, A represents the average value of the left and right cavity action areas of the oil cylinder, v represents the velocity, V represents the total volume of the hydraulic cylinder, V represents the effective oil volume modulus, dP represents the derivative of the load pressure difference. The balance equation of the load force of the asymmetric hydraulic cylinder is constructed as follows: , (68) wherein, M represents the total mass of the load and the piston, a represents the displacement acceleration, B C represents the viscous friction force coefficient, K represents the elastic stiffness coefficient, x represents the output displacement, F represents the external load force.

[0036] The matching uncertainty acquisition module obtains the matching uncertainty based on the nonlinear dynamics model.

[0037] The working process of the matching uncertainty acquisition module includes: obtaining the state space equation of the uncertain electro-hydraulic servo system based on the nonlinear dynamics model: , (69) , (70) wherein, d represents the derivative of d represents the derivative of d represents the derivative of d represents the derivative of , , , , x represents the state variable of the system, x represents the known part of the model, , and Represents constants related to electro-hydraulic servo system parameters, i =1, 2, 3, represents the matching uncertainty; based on the state space equation, the matching uncertainty is obtained: , (71) in, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters b perturbation term.

[0038] The observer and controller construction module constructs the RCFO observer based on the RBF neural network and the filtered backstepping sliding mode controller.

[0039] The RCFO observer is: , (72) in, express The derivative of express The derivative of express The derivative of represents the adaptive weight adjustment law, express The estimated value of express The estimated value of 、 、 represents the state variable of the observer, represents the gain of the observer, represents the observation error vector, represents the compensation function, represents the adjustment factor, represents the sliding surface function, express The observation error, represents the Gaussian function.

[0040] The filtered backstepping sliding mode controller is: , (73) in, represents the first virtual control law, 、 、 represents a positive design parameter, 、 represents the tracking error, express The derivative of represents the second virtual control law, represents the second-order filter output, Indicates the servo valve input voltage, 、 represents a positive constant, represents the second-order filter output, represents the sliding mode function.

[0041] The compensation control module uses the RCFO observer to compensate for the matching uncertainty of the system, and performs tracking control on the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

[0042] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. The filter backstepping sliding mode control method of the electro-hydraulic servo system based on RCFO is characterized by: The following steps are involved: Based on the working principle and structural composition of the electro-hydraulic servo system, a nonlinear dynamic model of the electro-hydraulic servo system is constructed; Based on the nonlinear dynamic model, a matching uncertainty is obtained; Based on the RBF neural network, an RCFO observer is constructed, and then a filtered backstepping sliding mode controller is constructed; The matching uncertainty in the system is compensated by using the RCFO observer, and tracking control is performed on the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

2. The RCFO-based filtered backstepping sliding mode control method for an electro-hydraulic servo system according to claim 1, characterized in that: The method for constructing the nonlinear dynamic model includes: Construct the pressure-flow characteristic equation of the servo valve: ， ， in, Indicates the load flow of the asymmetric hydraulic cylinder, represents the flow gain of the hydraulic cylinder, Indicates the servo valve input voltage, Indicates the oil supply pressure, Indicates the load pressure of the asymmetric hydraulic cylinder, represents the symbolic function, represents a positive constant, represents the flow coefficient, represents the area gradient of the servo valve, Indicates the density of the oil; Construct the flow continuity equation for the valve-controlled hydraulic cylinder: ， in, represents the total leakage coefficient, It represents the average effective area of ​​the left and right chambers of the oil cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder, represents the effective oil bulk modulus, Expresses the derivative of the load pressure difference; Construct the equilibrium equation of the asymmetric hydraulic cylinder load force: ， in, represents the total mass of the load and the piston, represents the displacement acceleration, B represents the viscous friction coefficient, represents the elastic stiffness coefficient, represents the output displacement, Indicates external load force.

3. The RCFO-based filtered backstepping sliding mode control method for an electro-hydraulic servo system according to claim 2, characterized in that: The method for obtaining the matching uncertainty includes: Based on the nonlinear dynamic model, the state space equation of the uncertain electro-hydraulic servo system is obtained: ， ， in, express The derivative of express The derivative of express The derivative of 、 、 represents the state variables of the system, represents the known part of the model, 、 and Represents constants related to electro-hydraulic servo system parameters, i =1, 2, 3, Indicates matching uncertainty; Based on the state space equation, the matching uncertainty is obtained: ， in, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters b perturbation term.

4. The RCFO-based filtered backstepping sliding mode control method for an electro-hydraulic servo system according to claim 3, characterized in that: The RCFO observer is: ， in, express The derivative of express The derivative of express The derivative of represents the adaptive weight adjustment law, express The estimated value of 、 、 represents the state variable of the observer, represents the gain of the observer, represents the observation error vector, represents the compensation function, represents the adjustment factor, represents the sliding surface function, express The observation error, represents the Gaussian function.

5. The RCFO-based filtered backstepping sliding mode control method for an electro-hydraulic servo system according to claim 4, characterized in that: The filtered backstepping sliding mode controller is: ， in, represents the first virtual control law, 、 、 represents a positive design parameter, 、 represents the tracking error, express The derivative of represents the second virtual control law, represents the second-order filter output, Indicates the servo valve input voltage, 、 represents a positive constant, represents the second-order filter output, represents the sliding mode function.

6. A filtered backstepping sliding mode control system for an electro-hydraulic servo system based on RCFO, wherein the control system applies the control method according to any one of claims 1 to 5, characterized in that: include: Model building module, matching uncertainty acquisition module, observer and controller building module and compensation control module; The model building module builds a nonlinear dynamic model of the electro-hydraulic servo system based on the working principle and structural composition of the electro-hydraulic servo system; The matching uncertainty acquisition module obtains the matching uncertainty based on the nonlinear dynamic model; The observer and controller construction module constructs an RCFO observer based on the RBF neural network, and then constructs a filtered backstepping sliding mode controller; The compensation control module utilizes the matching uncertainty of the RCFO observer compensation system and performs tracking control on the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

7. The RCFO-based electro-hydraulic servo system filtered backstepping sliding mode control system according to claim 6, characterized in that: The workflow of the model building module includes: Construct the pressure-flow characteristic equation of the servo valve: ， ， in, Indicates the load flow of the asymmetric hydraulic cylinder, represents the flow gain of the hydraulic cylinder, Indicates the servo valve input voltage, Indicates the oil supply pressure, Indicates the load pressure of the asymmetric hydraulic cylinder, represents the symbolic function, represents a positive constant, represents the flow coefficient, represents the area gradient of the servo valve, Indicates the density of the oil; Construct the flow continuity equation for the valve-controlled hydraulic cylinder: ， in, represents the total leakage coefficient, It represents the average effective area of ​​the left and right chambers of the oil cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder, represents the effective oil bulk modulus, Expresses the derivative of the load pressure difference; Construct the equilibrium equation of the asymmetric hydraulic cylinder load force: ， in, represents the total mass of the load and the piston, represents the displacement acceleration, B represents the viscous friction coefficient, represents the elastic stiffness coefficient, represents the output displacement, Indicates external load force.

8. The RCFO-based electro-hydraulic servo system filtered backstepping sliding mode control system according to claim 7, characterized in that: The workflow of the matching uncertainty acquisition module includes: Based on the nonlinear dynamic model, the state space equation of the uncertain electro-hydraulic servo system is obtained: ， ， in, express The derivative of express The derivative of express The derivative of 、 、 represents the state variables of the system, represents the known part of the model, 、 and Represents constants related to electro-hydraulic servo system parameters, i =1, 2, 3, Indicates matching uncertainty; Based on the state space equation, the matching uncertainty is obtained: ， in, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters The perturbation term, Representation parameters b perturbation term.

9. The RCFO-based electro-hydraulic servo system filtered backstepping sliding mode control system according to claim 8, characterized in that: The RCFO observer is: ， in, express The derivative of express The derivative of express The derivative of represents the adaptive weight adjustment law, express The estimated value of 、 、 represents the state variable of the observer, represents the gain of the observer, represents the observation error vector, represents the compensation function, represents the adjustment factor, represents the sliding surface function, express The observation error, represents the Gaussian function.

10. The RCFO-based electro-hydraulic servo system filtered backstepping sliding mode control system according to claim 9, characterized in that: The filtered backstepping sliding mode controller is: ， in, represents the first virtual control law, 、 、 represents a positive design parameter, 、 represents the tracking error, express The derivative of represents the second virtual control law, represents the second-order filter output, Indicates the servo valve input voltage, 、 represents a positive constant, represents the second-order filter output, represents the sliding mode function.

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