Filtering backstepping sliding mode control method and system for electro-hydraulic servo system based on RCFO

Abstract

The application belongs to the technical field of electro-hydraulic servo control, and discloses a filtering backstepping sliding mode control method and system of an electro-hydraulic servo system based on RCFO, which comprises the following steps: based on the working principle and structural composition of the electro-hydraulic servo system, a nonlinear dynamics model of the electro-hydraulic servo system is constructed; based on the nonlinear dynamics model, matching uncertainty is obtained; an RCFO observer is constructed based on an RBF neural network, and then a filtering backstepping sliding mode controller is constructed; the RCFO observer is used to compensate the matching uncertainty existing in the system, and the filtering backstepping sliding mode controller is used to perform tracking control on the electro-hydraulic servo system. The RBF adaptive weight adjustment law is combined with the compensation function observer, so that the robustness of the system is improved; the second-order command filter and the backstepping sliding mode control method are combined, so that the "calculation explosion" problem caused by the backstepping technology is effectively eliminated, meanwhile, the introduction of the filter reduces the influence of high-frequency noise, and the control precision of the system is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of electro-hydraulic servo control technology, specifically relating to a filtering backstepping sliding mode control method and system for an electro-hydraulic servo system based on RCFO. Background Technology

[0002] Electro-hydraulic servo systems are an important branch of hydraulic servo systems. They use electrical signals for control input, offering fast information transmission and combining the characteristics of electrical signals and hydraulic transmission. As a complex nonlinear mechatronic system, electro-hydraulic servo systems have many outstanding advantages, such as fast response speed, high load capacity, and high power-to-weight ratio. Due to these advantages, electro-hydraulic servo systems have been widely used in modern industry, such as in ship steering gear, excavating robots, robotic arms, and hydraulic presses.

[0003] Against this research backdrop, electro-hydraulic servo systems, after decades of development, have gradually become an indispensable core component of modern industrial equipment due to their high-precision control and rapid response characteristics. Although electro-hydraulic servo systems possess many excellent electro-hydraulic properties, they are always subject to various uncertainties in practical applications. For example, model parameters such as load mass, effective oil bulk modulus, and leakage coefficient may change significantly with operating conditions, temperature, and equipment wear. On the other hand, hydraulic systems exhibit strong nonlinearity in the flow and pressure dynamics of control valves, oil compressibility, and leakage. Furthermore, due to the complexity of the working environment, electro-hydraulic servo systems are inevitably affected by unknown external load forces and disturbances. All 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 uncertainties remains a challenge for engineers.

[0004] In summary, research on control schemes for electro-hydraulic servo systems is one of the key technological challenges in my country's intelligent manufacturing field. Currently, scholars both domestically and internationally have conducted in-depth research in this area and achieved significant results. However, existing research is largely based on idealized assumptions and cannot meet the needs of practical engineering applications. Therefore, the problem of high-precision trajectory tracking control of electro-hydraulic servo systems under complex working conditions has become a critical technological bottleneck that urgently needs to be overcome. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies and provides the following solutions:

[0006] The method for filtering backstepping sliding mode control of an electro-hydraulic servo system based on RCFO includes the following steps:

[0007] 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.

[0008] Based on the aforementioned nonlinear dynamic model, the matching uncertainty is obtained;

[0009] An RCFO observer is constructed based on an RBF neural network, and then a filter backstepping sliding mode controller is constructed.

[0010] The matching uncertainty in the system is compensated by the RCFO observer, and the electro-hydraulic servo system is tracked and controlled based on the filtered backstepping sliding mode controller.

[0011] Preferably, the method for constructing the nonlinear dynamic model includes:

[0012] Construct the pressure-flow characteristic equation for the servo valve:

[0013] ,

[0014] ,

[0015] in, This indicates the load flow rate of an asymmetric hydraulic cylinder. This indicates the flow gain of the hydraulic cylinder. Indicates the input voltage of the servo valve. Indicates the oil supply pressure. This indicates the load pressure of the asymmetric hydraulic cylinder. Represents a symbolic function. To represent a positive integer, Represents the flow coefficient. This represents the area gradient of the servo valve. Indicates the density of the oil;

[0016] Construct the flow continuity equation for valve-controlled hydraulic cylinders:

[0017] ,

[0018] in, Indicates the total leakage coefficient. This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder. Indicates the effective oil bulk modulus. The derivative representing the load pressure difference;

[0019] Construct the equilibrium equation for the load force of an asymmetric hydraulic cylinder:

[0020] ,

[0021] in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. This indicates the external load force.

[0022] Preferably, the method for obtaining the matching uncertainty includes:

[0023] Based on the aforementioned nonlinear dynamic model, the state-space equations of the uncertain electro-hydraulic servo system are obtained as follows:

[0024] ,

[0025] ,

[0026] in, express The derivative of express The derivative of express The derivative of , , Represents the system's state variables. This represents the known part of the model. , and This represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, This indicates uncertainty in the matching process;

[0027] Based on the state-space equation, the matching uncertainty is obtained:

[0028] ,

[0029] in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

[0030] Preferably, the RCFO observer is:

[0031] ,

[0032] in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the observation error vector. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. express The observation error, This represents the Gaussian function.

[0033] Preferably, the filter backstepping sliding mode controller is:

[0034] ,

[0035] in, This represents the first virtual control law. , , Indicates a positive design parameter. , Indicates tracking error. express The derivative of This represents the second virtual control law. This represents the output of a second-order filter. Indicates the input voltage of the servo valve. , Represents a positive constant. This represents the output of a second-order filter. This represents the sliding mode function.

[0036] The present invention also provides a filter backstepping sliding mode control system for an electro-hydraulic servo system based on RCFO. The control system applies the above-mentioned control method and includes: a model building module, a matching uncertainty acquisition module, an observer and controller building module, and a compensation control module.

[0037] The model building module constructs a nonlinear dynamic model of the electro-hydraulic servo system based on its working principle and structural composition.

[0038] The matching uncertainty acquisition module obtains the matching uncertainty based on the nonlinear dynamic model;

[0039] The observer and controller construction module constructs an RCFO observer based on an RBF neural network, and then constructs a filtered backstepping sliding mode controller.

[0040] The compensation control module uses the RCFO observer to compensate for the matching uncertainty in the system, and performs tracking control of the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

[0041] Preferably, the workflow of the model building module includes:

[0042] Construct the pressure-flow characteristic equation for the servo valve:

[0043] ,

[0044] ,

[0045] in, This indicates the load flow rate of an asymmetric hydraulic cylinder. This indicates the flow gain of the hydraulic cylinder. Indicates the input voltage of the servo valve. Indicates the oil supply pressure. This indicates the load pressure of the asymmetric hydraulic cylinder. Represents a symbolic function. To represent a positive integer, Represents the flow coefficient. This represents the area gradient of the servo valve. Indicates the density of the oil;

[0046] Construct the flow continuity equation for valve-controlled hydraulic cylinders:

[0047] ,

[0048] in, Indicates the total leakage coefficient. This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder. Indicates the effective oil bulk modulus. The derivative representing the load pressure difference;

[0049] Construct the equilibrium equation for the load force of an asymmetric hydraulic cylinder:

[0050] ,

[0051] in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. This indicates the external load force.

[0052] Preferably, the workflow of the matching uncertainty acquisition module includes:

[0053] Based on the aforementioned nonlinear dynamic model, the state-space equations of the uncertain electro-hydraulic servo system are obtained as follows:

[0054] ,

[0055] ,

[0056] in, express The derivative of express The derivative of express The derivative of , , Represents the system's state variables. This represents the known part of the model. , and This represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, This indicates uncertainty in the matching process;

[0057] Based on the state-space equation, the matching uncertainty is obtained:

[0058] ,

[0059] in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

[0060] Preferably, the RCFO observer is:

[0061] ,

[0062] in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the observation error vector. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. express The observation error, This represents the Gaussian function.

[0063] Preferably, the filter backstepping sliding mode controller is:

[0064] ,

[0065] in, This represents the first virtual control law. , , Indicates a positive design parameter. , Indicates tracking error. express The derivative of This represents the second virtual control law. This represents the output of a second-order filter. Indicates the input voltage of the servo valve. , Represents a positive constant. This represents the output of a second-order filter. This represents the sliding mode function.

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] This invention combines the RBF adaptive weight adjustment law with the compensation function observer to achieve online approximation of matching uncertainties that take into account nonlinear terms, and feeds back the processed approximation value to the controller to improve the robustness of the system. By combining the second-order command filter and the backstepping sliding mode control method, the "computation explosion" problem of backstepping technology is effectively eliminated. At the same time, the introduction of filtering reduces the influence of high-frequency noise and can effectively improve the control accuracy of the system. Attached Figure Description

[0068] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0070] Figure 2 This is a schematic diagram of the system structure according to an embodiment of the present invention;

[0071] Figure 3 This is a system block diagram according to an embodiment of the present invention. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] Example 1

[0075] In this embodiment, as Figure 1 As shown, the filtered backstepping sliding mode control method for an electro-hydraulic servo system based on RCFO includes the following steps:

[0076] 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.

[0077] Methods for constructing nonlinear dynamic models include:

[0078] Constructing the pressure-flow characteristic equation of the servo valve: In this embodiment, the electro-hydraulic servo valve, as the core control element of the electro-hydraulic servo system, achieves 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 a flow-pressure equation to describe its working characteristics, where the load flow rate is a key indicator for measuring system performance. To simplify the design and improve the model's universality, the following assumptions are made: an ideal zero-opening four-way slide valve (leak-free, symmetrically matched), no frictional loss in the pipeline and negligible dynamic characteristics, incompressible fluid with constant parameters; constant fluid volume and uniform density; and supply pressure... Set to a fixed value, return oil pressure The pressure inside the hydraulic cylinder cavity is equal, and the bulk elastic modulus is... This is a constant, remaining unchanged. The flow rate of the two chambers of the hydraulic cylinder. and Displacement relative to the neutral position of the servo valve spool The equations between them are as follows:

[0079] , (1)

[0080] , (2)

[0081] in, Represents the flow coefficient. This represents the area gradient of the servo valve. This indicates the displacement of the servo valve spool relative to the neutral position. This indicates the density of the oil. Indicates the oil supply pressure. Indicates the return oil pressure. This indicates the pressure in the left chamber of the hydraulic cylinder. This indicates the pressure in the right chamber of the hydraulic cylinder. It defines the load pressure of an asymmetric hydraulic cylinder. for:

[0082] , (3)

[0083] in, A 1 represents the working area of ​​the rodless chamber of the hydraulic cylinder. A 2 indicates the working area of ​​the rod chamber in the hydraulic cylinder. η This represents the ratio of the effective working areas of the two cavities. From equation (3), we can see... The load flow of the asymmetric hydraulic cylinder It can be represented as:

[0084] , (4)

[0085] From equations (1), (2), and (4), we can obtain that when The flow-pressure characteristic equation of the electro-hydraulic servo valve at that time. This can be expressed as a specific equation:

[0086] , (5)

[0087] when At that time, load flow It can be represented as:

[0088] , (6)

[0089] Combining equations (5) and (6), we can obtain:

[0090] , (7)

[0091] in, Indicates the asymmetric factor. Represents a symbolic function. Indicates the input voltage of the servo valve; when Sometimes, ;when Sometimes, Since electro-hydraulic servo valves mostly have high response characteristics, the dynamic model of the servo amplifier and servo valve is usually ignored in practical engineering applications. Therefore, the relationship between the valve displacement and the control input is approximated as follows: ,in Since it is a positive constant, equation (7) can be rewritten as:

[0092] , (8)

[0093] To ensure ease of modeling the electro-hydraulic servo system, it is assumed that the working areas of the pistons on both sides of the hydraulic cylinder are equal, which allows us to obtain... ,in, This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Equations (3) and (4) can be rewritten as:

[0094] , (9)

[0095] , (10)

[0096] Therefore, equation (7) can be simplified to:

[0097] , (11)

[0098] in, This indicates the flow gain of the hydraulic cylinder. .

[0099] Constructing the flow continuity equation for the valve-controlled hydraulic cylinder: In this embodiment, the hydraulic cylinder serves as the actuator of an electro-hydraulic servo system, and its moving piston controls the load displacement. Thanks to advancements 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 the valve-controlled hydraulic cylinder can be ignored. The flow continuity equation for the two chambers within the cylinder is as follows:

[0100] , (12)

[0101] in, Indicates speed, The sum of the internal and external leakage coefficients is denoted as the total leakage coefficient. This indicates the initial volume of the left-side cavity and its pipes in the hydraulic cylinder. This indicates the initial volume of the right-side cavity and its pipes in the hydraulic cylinder. Indicates the effective oil bulk modulus. Indicates piston displacement. The derivative representing the pressure in the left chamber of the hydraulic cylinder. This represents the derivative of the pressure in the right chamber of the hydraulic cylinder. The volume of a valve-controlled hydraulic cylinder is defined as:

[0102] , (13)

[0103] in, V l Indicates the volume of the left side of the valve-controlled hydraulic cylinder. V r Let represent the volume of the right side of the valve-controlled hydraulic cylinder. Therefore, equation (12) can be simplified to:

[0104] , (14)

[0105] because , , and It can be ignored. Secondly, by combining formula (9), it can be... Approximately Therefore, equation (14) can be simplified to:

[0106] , (15)

[0107] Substituting equation (15) into equation (10), we get:

[0108] , (16)

[0109] in, According to existing technology, the relationship between the hydraulic cylinder flow continuity equation and the effective working area of ​​the two chambers is as follows: ,because ,at this time The ratio of the volumes of the two cavities is defined as:

[0110] , (17)

[0111] According to equation (17), combined with the total volume of the hydraulic cylinder From this, we can deduce the following relationship:

[0112] , (18)

[0113] Based on the power matching principle of hydraulic system power components, it can be obtained that... Substituting equation (18) into equation (16), we get:

[0114] , (19)

[0115] in, N Represents positive numbers. ,because ,at this time Therefore, the flow continuity equation for a valve-controlled hydraulic cylinder is written as:

[0116] , (20)

[0117] in, It represents the derivative of the load pressure difference.

[0118] Constructing the load force balance equation for an asymmetric hydraulic cylinder: In this embodiment, a comprehensive force analysis is performed on the load and piston. The object is subjected to spring force, load force, viscous force, and other external forces. According to Newton's laws, the frictional force and the influence of the system's own oil mass under working conditions are ignored. The force balance equation is as follows:

[0119] , (twenty one)

[0120] in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. Indicates external load force; due to Combining equation (9), equation (21) can be simplified to:

[0121] . (twenty two)

[0122] Based on the above discussion and derivation of the servo valve's pressure-flow characteristic equation (11), the valve-controlled hydraulic cylinder's flow continuity equation (20), and the asymmetric hydraulic cylinder's load force balance equation (22), the dynamic model of the electro-hydraulic servo system is as follows:

[0123] . (twenty three)

[0124] S2. Based on the nonlinear dynamics model, the matching uncertainty is obtained.

[0125] Methods for obtaining the matching uncertainty include: deriving the state-space equations of the uncertain electro-hydraulic servo system based on a nonlinear dynamic model. In this embodiment, the output displacement is selected as the system state in the state-space equations. ,speed acceleration At this point, the system state variable is defined as The third-order state-space equation of the electro-hydraulic servo system with matching uncertainty is as follows:

[0126] , (twenty four)

[0127] in,

[0128] , (25)

[0129] In actual operation, electro-hydraulic servo systems will encounter various problems, and these adverse factors are integrated into the matching disturbance in equation (24). d In the middle. Matching perturbation d This mainly comprises two parts. The first part consists of known or predictable complex nonlinear terms, such as uncertainties in the system's internal parameters, modeling errors, and unknown external disturbances. The second part consists of complex nonlinear terms arising from unpredictable parameter perturbations and unpredictable external disturbances. The unpredictable complex nonlinear terms can be approximated using the RBF neural network proposed in this embodiment. Furthermore, considering the parameter perturbation characteristics of key parameters such as the effective oil bulk modulus and viscous friction coefficient in actual systems, the parameters... , , and The perturbation term can be denoted as , , and Therefore, the original system equation (24) is reconstructed to obtain the state-space model containing parameter perturbation compensation terms as follows:

[0130] , (26)

[0131] in, express The derivative of express The derivative of express The derivative of , , Represents the system's state variables. This represents the known part of the model. , , and As shown in equation (25), represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, The matching uncertainty is represented; based on the state-space equations, the matching uncertainty is obtained as follows:

[0132] , (27)

[0133] in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

[0134] S3. Construct an RCFO observer based on the RBF neural network, and then construct a filtered backstepping sliding mode controller.

[0135] The RCFO observer is:

[0136] , (28)

[0137] in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. , The coefficients represent the sliding surface function. Represents the observation error vector. l 3 and l 2 represents a positive observer gain. e c1 express x 1 observation error, e c2 express x 2 observation error, e c3 express The observation error, This represents a Gaussian function. The RBF neural network compensation observer designed in this embodiment can approximate the true unknown function infinitely. ,Right now:

[0138] (29)

[0139] The proof is as follows:

[0140] First, let's explain RBF neural networks: RBF neural networks are feedforward neural networks, consisting of an output layer, hidden layers, and an input layer. RBF neural networks can utilize their powerful ability to approximate nonlinearities to replace unknown nonlinear uncertainties. Suppose a function set... : exist If the data is continuous within a certain range, then a neural network exists. It can approximate an unknown function infinitely. At this point, the RBF neural network is designed as follows:

[0141] , (30)

[0142] in, Represents the set of real numbers. n express n 3D space h j Indicates the first j The number of nodes, where exp represents the natural exponential function. c j Indicates the first j The center point vector value of each hidden layer neuron λ j Indicates the first j The width parameter of each node, h This represents the input to the Gaussian function. Represents the weights of the neural network. δThis represents the approximation error. The output of the RBF neural network, i.e., the actual output of the compensation function, is:

[0143] , (31)

[0144] in, Represents ideal weight The estimated value, the estimation error is defined as .

[0145] The proof is as follows: Subtracting equation (28) from equation (26), and combining equations (30) and (31), we get:

[0146] , (32)

[0147] The sliding surface function is designed as follows:

[0148] , (33)

[0149] right Differentiating, we get:

[0150] , (34)

[0151] 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 represents a positive observer gain. The first Lyapunov function is defined as:

[0152] , (35)

[0153] right V Taking the derivative, we get:

[0154] , (36)

[0155] in, express V The derivative of . Substituting the fourth equation of equation (28) into equation (36), we get:

[0156] , (37)

[0157] Because RBF neural networks can approximate unknown functions infinitely, the error... δSmall enough to obtain Q.E.D.

[0158] The filtered backstepping sliding mode controller is designed in this embodiment based on RCFO to achieve the trajectory tracking control objective. First, the tracking error is defined as follows:

[0159] , (38)

[0160] in, , , Indicates tracking error. , These are the virtual state variables after passing through a second-order instruction filter. The desired tracking trajectory is represented. Then, the control law is derived using instruction filtering, recursive backstepping, and sliding mode control. The entire design process of the filtered backstepping sliding mode control consists of the following three steps.

[0161] Step 1: Define the second Lyapunov function:

[0162] , (39)

[0163] in, V 1 represents the second Lyapunov function. Based on equations (26) and (38), we can obtain... The derivative is:

[0164] , (40)

[0165] in, express The derivative of express The derivative of . Then for V Taking the derivative, we get:

[0166] , (41)

[0167] in, express V The derivative of 1. To make Negative, virtual control law Designed as:

[0168] , (42)

[0169] in, These are positive design parameters. This is to avoid affecting the virtual control law in subsequent steps. Repeatedly differentiate and pass it through a second-order instruction filter to obtain The estimated value Estimates of the virtual state variables (after passing through a second-order instruction filter) and their derivatives. The filtering error is defined as Substituting equation (42) into equation (41) yields:

[0170] (43)

[0171] Step 2: Define the third Lyapunov function:

[0172] , (44)

[0173] in, V 2 represents the second Lyapunov function. Based on equations (26) and (38), we can obtain... The derivative is:

[0174] , (45)

[0175] in, express The derivative of Indicates the estimated value The derivative of the virtual state variable (after passing through the second-order instruction filter). Then, for... V Taking the derivative of 2, we get:

[0176] , (46)

[0177] in, express V The derivative of 2. To make Negative, virtual control law Designed as:

[0178] , (47)

[0179] in, The design parameters are positive. These are obtained by processing them through a second-order instruction filter. The estimated value Estimates of the virtual state variables (after passing through a second-order instruction filter) and their derivatives. Define the filtering error Substituting equation (47) into equation (46) yields the following:

[0180] (48)

[0181] Step 3: Define the sliding mode function:

[0182] , (49)

[0183] in, Represents the sliding mode function. , This represents a positive constant. Based on equations (26) and (38), we can obtain... The derivative is:

[0184] , (50)

[0185] in, express The derivative of Indicates the estimated value The derivative of (the virtual state variable after the second-order instruction filter). Taking the derivative of equation (49) yields...

[0186] , (51)

[0187] in, express The derivative of . Define the third Lyapunov function:

[0188] , (52)

[0189] in, V 3 represents the third Lyapunov function. Then for... V 3. Taking the derivative, we get:

[0190] , (53)

[0191] in, express V The derivative of 3. To make The actual servo valve control input voltage is negative. Designed as:

[0192] , (54)

[0193] in, The design parameters are positive. Substituting equation (54) into equation (54) yields:

[0194] , (55)

[0195] in, .

[0196] Based on the above design steps, the structure of the RCFO-based filter backstepping sliding mode controller designed in this embodiment is as follows:

[0197] (56)

[0198] S4. The matching uncertainty of the system is compensated by the RCFO observer, and the electro-hydraulic servo system is tracked and controlled based on the filtered backstepping sliding mode controller.

[0199] Example 2

[0200] In this embodiment, a stability analysis of the present invention will be provided: using Lyapunov stability proof, the stability proof of the closed-loop control design of the electro-hydraulic servo system is given below.

[0201] Based on the design of Example 1, the final Lyapunov function for backstepping control is designed as follows:

[0202] , (57)

[0203] in, This represents the final Lyapunov function. According to (56)... derivative It can be expressed as:

[0204] , (58)

[0205] According to Young's inequality, the latter terms of equation (58) can be transformed as follows:

[0206] , (59)

[0207] Substituting (59) into (58) yields:

[0208] , (60)

[0209] Equation (60) can be rearranged into a compact inequality as follows:

[0210] , (61)

[0211] , (62)

[0212] , (63)

[0213] in, Represents positive numbers. D express The upper bound. Select design parameters. , , To ensure Then, based on the mathematical equation of the second-order instruction filter, the solution to inequality (61) is as follows:

[0214] , (64)

[0215] when hour, It will converge to the upper boundary. Therefore, the compensated error Bounded. According to formula (29), we know... Since the region of convergence is bounded, all error signals of the control system are bounded. To make the region of convergence arbitrarily small, the control parameters can be adjusted. Achieved. Q.E.D.

[0216] Example 3

[0217] In this embodiment, as Figure 2 , Figure 3 As shown, the electro-hydraulic servo system filtering backstepping sliding mode control system based on RCFO includes: a model building module, a matching uncertainty acquisition module, an observer and controller building module, and a compensation control module.

[0218] The model building module constructs a nonlinear dynamic model of the electro-hydraulic servo system based on its working principle and structural composition.

[0219] The model building module's workflow includes: constructing the pressure-flow characteristic equations for the servo valve.

[0220] , (65)

[0221] , (66)

[0222] in, This indicates the load flow rate of an asymmetric hydraulic cylinder. This indicates the flow gain of the hydraulic cylinder. Indicates the input voltage of the servo valve. Indicates the oil supply pressure. This indicates the load pressure of the asymmetric hydraulic cylinder. Represents a symbolic function. To represent a positive integer, Represents the flow coefficient. This represents the area gradient of the servo valve. This represents the density of the oil. The flow continuity equation for a valve-controlled hydraulic cylinder is constructed as follows:

[0223] , (67)

[0224] in, Indicates the total leakage coefficient. This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder. Indicates the effective oil bulk modulus. The derivative represents the load pressure difference. Construct the equilibrium equation for the load force of the asymmetric hydraulic cylinder:

[0225] , (68)

[0226] in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. This indicates the external load force.

[0227] The matching uncertainty acquisition module obtains the matching uncertainty based on a nonlinear dynamics model.

[0228] The workflow of the uncertainty acquisition module includes: obtaining the state-space equations of the uncertain electro-hydraulic servo system based on the nonlinear dynamic model.

[0229] , (69)

[0230] , (70)

[0231] in, express The derivative of express The derivative of express The derivative of , , Represents the system's state variables. This represents the known part of the model. , and This represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, The matching uncertainty is represented; based on the state-space equations, the matching uncertainty is obtained as follows:

[0232] , (71)

[0233] in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

[0234] The observer and controller construction module is based on the RBF neural network to build an RCFO observer and a filtered backstepping sliding mode controller.

[0235] The RCFO observer is:

[0236] , (72)

[0237] in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the observation error vector. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. express The observation error, This represents the Gaussian function.

[0238] The filtered backstepping sliding mode controller is:

[0239] , (73)

[0240] in, This represents the first virtual control law. , , Indicates a positive design parameter. , Indicates tracking error. express The derivative of This represents the second virtual control law. This represents the output of a second-order filter. Indicates the input voltage of the servo valve. , Represents a positive constant. This represents the output of a second-order filter. This represents the sliding mode function.

[0241] The compensation control module uses the RCFO observer to compensate for the matching uncertainty in the system and performs tracking control of the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

[0242] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A filtering backstepping sliding mode control method for an electro-hydraulic servo system based on RCFO, characterized in that, 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 aforementioned nonlinear dynamic model, the matching uncertainty is obtained; An RCFO observer is constructed based on an RBF neural network, and then a filter backstepping sliding mode controller is constructed. The matching uncertainty in the system is compensated by the RCFO observer, and the electro-hydraulic servo system is tracked and controlled based on the filtered backstepping sliding mode controller; The methods for constructing the nonlinear dynamic model include: Construct the pressure-flow characteristic equation for the servo valve: ， ， in, This indicates the load flow rate of an asymmetric hydraulic cylinder. This indicates the flow gain of the hydraulic cylinder. Indicates the input voltage of the servo valve. Indicates the oil supply pressure. This indicates the load pressure of the asymmetric hydraulic cylinder. Represents a symbolic function. To represent a positive integer, Represents the flow coefficient. This represents the area gradient of the servo valve. Indicates the density of the oil; Construct the flow continuity equation for valve-controlled hydraulic cylinders: ， in, Indicates the total leakage coefficient. This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder. Indicates the effective oil bulk modulus. The derivative representing the load pressure difference; Construct the equilibrium equation for the load force of an asymmetric hydraulic cylinder: ， in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. This indicates the external load force.

2. The method for filtering, backstepping, and sliding mode control of an electro-hydraulic servo system based on RCFO according to claim 1, characterized in that, The methods for obtaining the matching uncertainty include: Based on the aforementioned nonlinear dynamic model, the state-space equations of the uncertain electro-hydraulic servo system are obtained as follows: ， ， in, express The derivative of express The derivative of express derivative , , Represents the system's state variables. This represents the known part of the model. , and This represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, This indicates uncertainty in the matching process; Based on the state-space equation, the matching uncertainty is obtained: ， in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

3. The method for filtering, backstepping, and sliding mode control of an electro-hydraulic servo system based on RCFO according to claim 2, characterized in that, The RCFO observer is: ， in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the observation error vector. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. express The observation error, This represents the Gaussian function.

4. The filtering backstepping sliding mode control method for an electro-hydraulic servo system based on RCFO according to claim 3, characterized in that, The filtered backstepping sliding mode controller is: ， in, This represents the first virtual control law. , , Indicates a positive design parameter. , Indicates tracking error. express The derivative of This represents the second virtual control law. This represents the output of a second-order filter. Indicates the input voltage of the servo valve. , Represents a positive constant. This represents the output of a second-order filter. This represents the sliding mode function.

5. A filter-backstepping sliding mode control system for an electro-hydraulic servo system based on RCFO, wherein the control system applies the control method described in any one of claims 1-4, characterized in that, include: The module includes a model building module, a matching uncertainty acquisition module, an observer and controller building module, and a compensation control module. The model building module constructs a nonlinear dynamic model of the electro-hydraulic servo system based on its working principle and structural composition. 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 an RBF neural network, and then constructs a filtered backstepping sliding mode controller. The compensation control module uses the RCFO observer to compensate for the matching uncertainty in the system, and performs tracking control of the electro-hydraulic servo system based on the filtered backstepping sliding mode controller.

6. The RCFO-based electro-hydraulic servo system filter backstepping sliding mode control system according to claim 5, characterized in that, The workflow of the model building module includes: Construct the pressure-flow characteristic equation for the servo valve: ， ， in, This indicates the load flow rate of an asymmetric hydraulic cylinder. This indicates the flow gain of the hydraulic cylinder. Indicates the input voltage of the servo valve. Indicates the oil supply pressure. This indicates the load pressure of the asymmetric hydraulic cylinder. Represents a symbolic function. To represent a positive integer, Represents the flow coefficient. This represents the area gradient of the servo valve. Indicates the density of the oil; Construct the flow continuity equation for valve-controlled hydraulic cylinders: ， in, Indicates the total leakage coefficient. This represents the average working area of ​​the left and right chambers of the hydraulic cylinder. Indicates speed, Indicates the total volume of the hydraulic cylinder. Indicates the effective oil bulk modulus. The derivative representing the load pressure difference; Construct the equilibrium equation for the load force of an asymmetric hydraulic cylinder: ， in, This indicates the total mass of the load and the piston. Indicates displacement acceleration. B Indicates the coefficient of viscous friction. Indicates the elastic stiffness coefficient. Indicates the output displacement. This indicates the external load force.

7. The RCFO-based electro-hydraulic servo system filter backstepping sliding mode control system according to claim 6, characterized in that, The workflow of the matching uncertainty acquisition module includes: Based on the aforementioned nonlinear dynamic model, the state-space equations of the uncertain electro-hydraulic servo system are obtained as follows: ， ， in, express The derivative of express The derivative of express The derivative of , , Represents the system's state variables. This represents the known part of the model. , and This represents a constant related to the parameters of the electro-hydraulic servo system. i =1, 2, 3, This indicates uncertainty in the matching process; Based on the state-space equation, the matching uncertainty is obtained: ， in, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters The perturbation item, Indicates parameters b The perturbation item.

8. The RCFO-based electro-hydraulic servo system filter backstepping sliding mode control system according to claim 7, characterized in that, The RCFO observer is: ， in, express The derivative of express The derivative of express The derivative of This represents the adaptive weight adjustment law. express The estimated value, , , Represents the state variables of the observer. Indicates the gain of the observer. Represents the observation error vector. Represents the compensation function. Indicates the regulating factor. Represents the sliding surface function. express The observation error, This represents the Gaussian function.

9. The RCFO-based electro-hydraulic servo system filter backstepping sliding mode control system according to claim 8, characterized in that, The filtered backstepping sliding mode controller is: ， in, This represents the first virtual control law. , , Indicates a positive design parameter. , Indicates tracking error. express The derivative of This represents the second virtual control law. This represents the output of a second-order filter. Indicates the input voltage of the servo valve. , Represents a positive constant. This represents the output of a second-order filter. This represents the sliding mode function.

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