Accurate tracking control method and system for finite time of electro-hydraulic servo system

Abstract

The invention discloses an electro-hydraulic servo system finite time accurate tracking control method and system. The method specifically comprises the steps that a mathematical model of a single-rod electro-hydraulic position servo system is established; based on a multilayer feedforward neural network, constructing a finite time neural network extended state observer, and estimating matching and non-matching unknown function disturbances and system states suffered by the single-rod electro-hydraulic servo system; constructing a finite time accurate tracking control algorithm of the single-rod electro-hydraulic servo system for model uncertainty compensation, and designing a finite time multilayer neural network adaptive law with a fractional order; and an initial value of a neural network weight parameter, an adaptive law matrix and a controller parameter are selected to realize the compensation of the uncertainty of a system model, so that the output of the system tracks an expected control target. According to the method, the steady-state tracking error of the single-rod electro-hydraulic servo system controller is reduced in finite time, the uncertainty compensation capability of the model is improved, and the tracking precision and the tracking speed of the single-rod electro-hydraulic servo system are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of electro-hydraulic servo control, and in particular to a finite-time precise tracking control method and system for an electro-hydraulic servo system. Background Art

[0002] An electro-hydraulic control system refers to a control method in hydraulic transmission and control that can receive analog or digital signals and make the output flow or pressure continuously and proportionally controlled, simply referred to as an electro-hydraulic control system. The electro-hydraulic servo system has advantages such as strong load resistance and fast response speed, and is an important type of control equipment in the automation field, being widely used in industrial control fields with high control precision and large output power.

[0003] There are a large number of non-linear factors in the electro-hydraulic servo system, such as servo valve pressure / flow non-linearity, pressure dynamic non-linearity, friction non-linearity, etc., which have gradually become bottleneck factors restricting the improvement of system performance. In addition, the electro-hydraulic servo system is also affected by disturbances such as external disturbances. Due to the existence of the above factors, the high-precision control of the electro-hydraulic servo system becomes quite challenging.

[0004] Currently, for advanced control strategies considering the model uncertainty of the electro-hydraulic servo system, there are mainly methods such as adaptive robust control, active disturbance rejection adaptive control, and neural network-based adaptive control. The research on the combination of neural networks and adaptive control has become a new branch of intelligent control. Adaptive control has strong robustness, while neural networks have good self-learning capabilities and fault tolerance. Neural network adaptive control has powerful advantages due to its better integration of the advantages of both. These control methods can theoretically bring relatively ideal control capabilities, but in engineering applications, due to the relatively complex system working conditions, such as the existence of unmatched disturbances and the non-linear characteristics of system components, the intelligent control algorithms become cumbersome, with a large amount of computation and are not easy to implement in engineering.

[0005] As the controlled system becomes more and more complex, people's requirements for the control system are getting higher and higher, especially requiring the control system to adapt to uncertain and time-varying objects and environments. Control based on neural networks plays an important role in solving the above control problems and is thus increasingly attracting people's attention. However, the precise tracking control based on neural networks is not very perfect, there are still some problems, and it may even seriously affect the control performance of the system.

[0006] However, with the development of technology, people are no longer satisfied with the traditional Lyapunov asymptotic stability and expect to obtain a faster convergence rate. Therefore, the extended finite-time Lyapunov stability theory is proposed. By combining the finite-time neural network extended observer and the finite-time stability theory, global finite-time stability can be achieved, that is, the state observation error, the finite-time command filtering error, and the system tracking error can all be stabilized within a finite time.

[0007] Most of the existing controls are for actuators such as double-rod cylinders or hydraulic motors where the non-linear factors are not very prominent, while there is less research on the control of single-rod electro-hydraulic servo systems with prominent non-linear factors such as non-linear friction, non-linear leakage, and servo valve flow. At the same time, the previous ones are all asymptotic controls and it takes a certain amount of time to reach the stable state. Therefore, there is an urgent need for a control strategy that combines backstepping control, neural network control, and finite-time control methods to be applied to electro-hydraulic servo systems to reduce the steady-state tracking error of the single-rod electro-hydraulic servo system controller, improve the tracking speed, and be able to compensate for model uncertainties. Summary of the Invention

[0008] The purpose of the present invention is to provide a finite-time precise tracking control method and system for an electro-hydraulic servo system, which can reduce the steady-state tracking error of the single-rod electro-hydraulic servo system controller within a finite time, improve the tracking accuracy, and at the same time be able to compensate for model uncertainties.

[0009] The technical solution for achieving the purpose of the present invention is: a finite-time precise tracking control method for an electro-hydraulic servo system, including the following steps:

[0010] Step 1: Establish a mathematical model of a single-rod electro-hydraulic position servo system;

[0011] Step 2: Based on a multi-layer feedforward neural network, construct a finite-time neural network extended state observer to estimate the matching and non-matching unknown function disturbances and system states suffered by the single-rod electro-hydraulic servo system;

[0012] Step 3: Construct a finite-time precise tracking control algorithm for a single-rod electro-hydraulic servo system for model uncertainty compensation;

[0013] Step 4: Design a finite-time multi-layer neural network adaptive law with fractional order;

[0014] Step 5: Select the initial values of the neural network weight parameters, the adaptive law matrix, and the controller parameters to achieve compensation for system model uncertainties and make the output of the system track the desired control target.

[0015] Further, the establishment of the mathematical model of the single-rod electro-hydraulic position servo system in Step 1 is specifically as follows:

[0016] Step 1.1: Define the state variables as where m is the mass of the load and y is the displacement of the load; P 1 , P 2 are the oil pressures in the rodless chamber and the rod chamber of the hydraulic cylinder respectively; A 1 , A 2 are the effective acting areas of the piston rod in the rodless chamber and the rod chamber of the hydraulic cylinder respectively. Then the state - space form of the system's nonlinear model is:

[0017]

[0018] In Equation (1), u is the control input voltage of the system, and the expressions of other parts are as follows:

[0019]

[0020]

[0021] In Equation (2), β e is the elastic modulus of the hydraulic oil, V 1 , V 2 are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder respectively, Q 1 is the hydraulic flow rate entering the rodless chamber of the hydraulic cylinder from the servo valve, Q 2 is the hydraulic flow rate flowing from the rod chamber of the hydraulic cylinder into the servo valve, χ(x 2 ), are unknown functions related to the system state, ε(t), p 1 (t), p 2 (t) are time - varying external disturbances; is the total flow gain of the servo valve, where C q1 , C q2 are the flow coefficients of the throttle orifices of the servo valves in the rodless chamber and the rod chamber respectively, w q1 , w q2 are the area gradients of the throttle orifices in the rodless chamber and the rod chamber respectively, k q1 , k q2 are the flow - displacement gains of the servo - valve spools in the rodless chamber and the rod chamber respectively; ρ o is the density of the oil, P s is the oil - source pressure of the system, P r is the return - oil pressure of the system.

[0022] Furthermore, after Step 1.1, it also includes Step 1.2, which is specifically as follows:

[0023] Step 1.2: To simplify the control - strategy design and the stability analysis of the system, and on the premise of ensuring the system control performance and tracking performance, make the following settings:

[0024] Set 1: Desired trajectory x d Sufficiently smooth and satisfying the following expression:

[0025]

[0026] Set 2: The nonlinear uncertainties d(t) and p(t) in the system and their first-order derivatives are bounded;

[0027] Set 3: Set represents the estimated value of ·, represents the estimation error of ·; variable · i The subscript i in takes values 1, 2, 3; variable · j The subscript j in takes values 2, 3;

[0028] Set 4: The function is defined as follows:

[0029] sig(·) α = |·| α sign(·), where sign is the standard sign function;

[0030] Set 5: For |·| r , r ∈ (0, 1), when · approaches 0, the derivative of |·| r may be singular, so the following framework is set: Here r ∈ Z

[0031] Here r ∈ Z + / {1}, Ω v is defined as: Ω v = {·||·| < η}, 0 < η < 10 -6 ;

[0032] Furthermore, based on the multi-layer feedforward neural network described in step 2, a finite-time neural network extended state observer is constructed to estimate the matching and non-matching unknown function disturbances and system states suffered by the single-rod electro-hydraulic servo system; specifically as follows:

[0033] Step 2.1. For any smooth unknown functions f(x 2 ) and ψ(x 2 , P 1 , P 2 ), which satisfy:

[0034]

[0035] In formula (3), and are the bounded constant ideal weight matrices of the neural network, where M 1 , N 1, M 2 , N 2 , where M and N are the number of neurons; is the input vector and represents the activation function; β 2 (δ 2 ), β 3 (δ 3 ) represents the function reconstruction error;

[0036] Define the estimator of the smooth unknown function as:

[0037]

[0038] Step 2.2: Apply the smooth unknown function f(x 2 ) and ψ(x 2 , P 1 , P 2 ) to the system nonlinear model, we get:

[0039]

[0040] Further expand the state variables of the system to be:

[0041]

[0042] In Equation (6), x δ2 , x δ3 represent the system reconstruction error;

[0043] Set: According to Set 2, D 2 (t), D 3 (t) are both bounded. Convert the system nonlinear model to:

[0044]

[0045] Step 2.3: Based on the smooth unknown function (4) and the system nonlinear model (7), construct a finite-time neural network extended state observer as:

[0046]

[0047] In Equation (8), ω o2 , ω o3 are adjustable parameters; Define as follows:

[0048]

[0049] In Equation (9), μ j,1 , μ j,2 , β j,3is an adjustable positive constant, 0 < Δ < 10 -4 ;

[0050] Step 2.4. According to the system nonlinear model (7) and the finite-time neural network extended state observer (8), the observation error of the finite-time neural network extended state observer is obtained as follows:

[0051]

[0052] Based on (10), the observation error term ζ 1 , ζ 2 is:

[0053]

[0054] Furthermore, the finite-time accurate tracking control algorithm for the single-rod electro-hydraulic servo system constructed in Step 3 for model uncertainty compensation is as follows:

[0055] Step 3.1. Define e 1 = x 1 - x 1d as the tracking error of the system, and define e 2 and e 3 as:

[0056] e 2 = x 2 - α 1,c , e 3 = x 3 - α 2,c (12)

[0057] In equation (12), α 1,c and α 2,c are the filtered values of the virtual control laws α 1 and α 2 respectively, and are obtained through the following filter:

[0058]

[0059] In equation (13), r j-1,1 , r j-1,2 are adjustable positive constants;

[0060] The dynamic equation of the filtering error is defined as:

[0061]

[0062] Step 3.2. Define the vector v = [v 1 , v 2 , v3 T = [e 1 -k 1 , e 2 -k 2 , e 3 -k 3 T , where k i is an auxiliary variable generated by the following auxiliary system:

[0063]

[0064] In Equation (15), c 1 , c 2 , c 3 , l 1 , l 2 , l 3 are adjustable positive constants;

[0065] Step 3.3. Design the virtual control laws α 1 , α 2 and the actual control law u as follows:

[0066]

[0067] In Equation (16), s 1 , s 2 , s 3 are adjustable positive gains;

[0068] Note: When α j-1 passes through the command filter, the derivative of |v j-1 | r will be singular, so the method of setting 5 is used to handle it;

[0069] Furthermore, the design of the fractional-order finite-time multi-layer neural network adaptive law described in Step 4 is as follows:

[0070] Design the fractional-order finite-time multi-layer neural network adaptive law. The update formula for the weight parameters of the multi-layer feedforward neural network is:

[0071]

[0072] In Equation (17), is represented by the following formula:

[0073]

[0074] Proj(·) is a continuous projection mapping function, Γ j is the adaptive law matrix of the weight parameter W j , Υ j ​​is the weight parameter V j of the adaptive law matrix, e NNj is the additional term of the multi-layer neural network, ω oj is an adjustable positive constant;

[0075] Furthermore, the initial values of the neural network weight parameters, the adaptive law matrix, and the controller parameters described in step 5 are selected to compensate for the system model uncertainty and make the output of the system track the desired control target, specifically as follows:

[0076] Select the initial values of the neural network weight parameters and the adaptive law matrix Γ j > 0, Υ j > 0 values, and adjust the parameters c 1 、c 2 、c 3 、l 1 、l 2 、l 3 、s 1 、s 2 、s 3 、a 1 、a 2 、b 1 、b 2 values to ensure the effect of compensating the system model uncertainty and at the same time make the output of the system y = x 1 track the desired smooth command y d = x 1d , where c 1 、c 2 、c 3 、l 1 、l 2 、l 3 、s 1 、s 2 、s 3 、a 1 、a 2 、b 1 、b 2 are all greater than 0;

[0077] A finite-time precise tracking control system for an electro-hydraulic servo system, which is used to implement the finite-time precise tracking control method of the electro-hydraulic servo system. The system includes a model establishment module, an observer construction module, an algorithm construction module, an adaptive law construction module, and a compensation module, where:

[0078] The model establishment module is used to establish the mathematical model of the single-rod electro-hydraulic position servo system;

[0079] The observer construction module constructs a finite-time neural network extended state observer based on a multi-layer feedforward neural network to estimate the unknown non-linearity inside the single-rod electro-hydraulic servo system, external disturbances, and system states.

[0080] The algorithm construction module is used to construct a finite-time precise tracking control algorithm for the single-rod electro-hydraulic servo system for model uncertainty compensation.

[0081] The adaptive law construction module is used to design a finite-time multi-layer neural network adaptive law with fractional order.

[0082] The compensation module is used to select the initial values of the neural network weight parameters, the adaptive law matrix, and the controller parameters to achieve the compensation of system model uncertainty and make the output of the system track the desired control target.

[0083] A mobile terminal includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the finite-time precise tracking control method of the electro-hydraulic servo system described above.

[0084] A computer-readable storage medium stores a computer program, and when the program is executed by a processor, it implements the steps in the finite-time precise tracking control method of the electro-hydraulic servo system.

[0085] Compared with the prior art, the significant advantages of the present invention are: (1) For the unknown function non-linearity of the single-rod electro-hydraulic servo system, a finite-time multi-layer neural network observer is introduced for rapid estimation and feedforward compensation. For the time-varying external disturbances suffered by the system, approximation and compensation are carried out through a hyper-torque function with fractional order, reducing the steady-state tracking error of the controller within a finite time and improving the tracking accuracy; (2) Adopting a multi-layer neural network structure, a finite-time precise control algorithm for model uncertainty compensation is designed, improving the model uncertainty compensation ability while ensuring that the position output of the single-rod electro-hydraulic servo system can accurately track the desired position command within a finite time. Brief Description of the Drawings

[0086] Figure 1 is a schematic flow chart of a finite-time precise tracking control method for an electro-hydraulic servo system of the present invention.

[0087] Figure 2 is a schematic structural diagram of the electro-hydraulic servo system in an embodiment of the present invention.

[0088] Figure 3 is the state x of the system in an embodiment of the present invention using the method of the present invention 1 The curve graph of the change with time.

[0089] Figure 4It is a curve graph showing the variation of the tracking error of the system adopting the method of the present invention with time in an embodiment of the present invention.

[0090] Figure 5 It is the state x of the system in an embodiment of the present invention 2 Curve graph showing the variation of the estimation performance with time.

[0091] Figure 6 It is the state x of the system in an embodiment of the present invention 3 Curve graph showing the variation of the estimation performance with time.

[0092] Figure 7 It is the estimation of the reconstruction error x of the non - linear function f of the system and the sum of their estimations and the curve graph showing the variation with time of the result of adding them to the true unknown function f plus the unknown perturbation d(t) in an embodiment of the present invention. δ2 And the curve graph showing the variation with time of the sum of them and the true unknown function f plus the unknown perturbation d(t).

[0093] Figure 8 It is the estimation of the reconstruction error x of the non - linear function ψ of the system and the sum of their estimations and the curve graph showing the variation with time of the result of adding them to the true unknown function ψ plus the unknown perturbation p(t) in an embodiment of the present invention. δ3 And the curve graph showing the variation with time of the sum of them and the true unknown function ψ plus the unknown perturbation p(t).

[0094] Figure 9 It is the curve graph showing the variation of the control input voltage with time in an embodiment of the present invention. Specific implementation manners

[0095] The following combines the attached drawings and specific embodiments to make a further detailed description of the present invention.

[0096] Combined with Figure 1 , a finite - time precise tracking control method for an electro - hydraulic servo system of the present invention includes the following steps:

[0097] Step 1: Establish the mathematical model of a single - rod electro - hydraulic position servo system;

[0098] Step 2: Based on a multi - layer feed - forward neural network, construct a finite - time neural network extended state observer to estimate the internal unknown non - linearity, external perturbation and system state of the single - rod electro - hydraulic servo system;

[0099] Step 3: Construct a finite - time precise tracking control algorithm for the single - rod electro - hydraulic servo system for model uncertainty compensation;

[0100] Step 4: Design a finite - time multi - layer neural network adaptive law with fractional - order;

[0101] Step 5: Select the initial values of the neural network weight parameters, the adaptive law matrix and the controller parameters to achieve the compensation of the system model uncertainty and make the output of the system track the desired control target.

[0102] As a specific example, the mathematical model of a single-rod electro-hydraulic position servo system is established in Step 1 as follows:

[0103] Step 1.1 Figure 2 As the structural schematic diagram of the electro-hydraulic servo system, according to Newton's second law, the kinematic equation of the load can be obtained as:

[0104]

[0105] In Equation (1), y represents the load displacement; m represents the inertial load; P 1 , P 2 respectively represent the pressures of the rodless chamber and the rod chamber, A 1 , A 2 respectively represent the effective working areas of the rodless chamber and the rod chamber; represents the unknown non-linear uncertainty regarding the load displacement and velocity, and ε(t) represents the external disturbance of the system;

[0106] The pressure dynamic equations of the rodless chamber and the rod chamber of the hydraulic cylinder are:

[0107]

[0108] In Equation (2), β e is the elastic modulus of the hydraulic oil, V 1 , V 2 respectively represent the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, Q 1 is the hydraulic flow rate entering the rodless chamber of the hydraulic cylinder from the servo valve, Q 2 is the hydraulic flow rate flowing from the rod chamber of the hydraulic cylinder into the servo valve, is an unknown function related to the system state, p 1 (t), p 2 (t) are time-varying external disturbances;

[0109] The load flow equation of the servo valve is:

[0110] Q 1 = K Q1 R 1 u, Q 2 = K Q2 R 2 u (3)

[0111] In Equation (3), u is the control input voltage of the system; are the total flow rate gains of the servo valves of the rodless chamber and the rod chamber respectively, where are the flow coefficient of the throttle holes of the servo valves of the rodless chamber and the rod chamber respectively, are the area gradients of the throttle holes of the rodless chamber and the rod chamber respectively, They are the spool displacement flow gains of the rodless chamber and the rod chamber respectively, ρ 0 is the density of the hydraulic oil; R 1 、R 2 The expressions of are:

[0112]

[0113] In Equation (4), P s is the oil source pressure of the system, P r is the return oil pressure of the system;

[0114] Define the system state variables as Set the modeling nonlinear uncertainty is continuously differentiable, then according to Equations (1)-(4), establish the dynamic equation, and the system model can be expressed in the following state space form:

[0115]

[0116] In Equation (5), the definitions of each symbol are as follows:

[0117]

[0118]

[0119] The control objective of the single-rod electro-hydraulic servo system is: for the single-rod hydraulic cylinder actuator servo system, design a finite-time precise tracking control algorithm for model uncertainty compensation to improve the effect of compensating the system model uncertainty, and at the same time make the output of the system y = x 1 accurately track the desired smooth command y d = x 1d ;

[0120] Step 1.2: To simplify the control strategy design and the stability analysis of the system, make the following settings on the premise of ensuring the system control performance and tracking performance:

[0121] Setting 1: The command signal x 1d (t) that the system expects to track is continuously differentiable of the first order, and the system state desired command and its first derivative are both bounded;

[0122] Setting 2: The unknown function disturbances suffered by the system are all continuous functions; and the time-varying disturbances suffered by the system and their first derivatives are both bounded;

[0123] Setting 3: Set to represent the estimated value of ·, represents the estimation error of ·; · min and · maxrepresent the minimum and maximum values of · respectively; the variable · i in the subscript i takes values 1, 2, 3; the variable · j in the subscript j takes values 2, 3;

[0124] Assumption 4: The function is defined as follows:

[0125] sig(·) α = |·| α sign(·), where sign is the standard sign function;

[0126] Assumption 5: For |·| r , r ∈ (0, 1), when · approaches 0, the derivative of |·| r may be singular. To solve this problem, the following framework is set: Here r ∈ Z

[0127] / {1}, Ω + is defined as: Ω v = {·||·| < η}, 0 < η < 10 v ; -6 ;

[0128] As a specific example, in step 2, based on a multi-layer feedforward neural network, a finite-time neural network extended state observer is constructed to estimate the matched and unmatched unknown function disturbances and system states suffered by a single-rod electro-hydraulic servo system, as follows:

[0129] Step 2.1. For any smooth unknown functions f(x 2 ) and ψ(x 2 , P 1 , P 2 ), which satisfy:

[0130]

[0131] In equation (7), and are the bounded constant ideal weight matrices of the neural network, where M 1 , N 1 , M 2 , N 2 , M and N are the numbers of neurons; is the input vector and represents the activation function; β 2 (δ 2 ), β 3 (δ 3 ) represent the function reconstruction errors;

[0132] The estimator of the smooth unknown function can be defined by Equation (7) as follows:

[0133]

[0134] Step 2.2: Applying Equation (7) to (5) gives:

[0135]

[0136] The state variables of the further expanded system are changed to:

[0137]

[0138] In Equation (10), x δ2 , x δ3 represent the system reconstruction error;

[0139] Set According to Setting 2, both D 2 (t) and D 3 (t) are bounded, and the following equation can be obtained:

[0140]

[0141] Step 2.3: According to Equations (8) and (11), a finite-time neural network extended state observer can be constructed as:

[0142]

[0143] In Equation (12), ω o2 , ω o3 are adjustable parameters; Define as follows:

[0144]

[0145]

[0146] In Equation (13), μ j,1 , μ j,2 , β j,3 are adjustable positive constants, 0 < Δ < 10 -4 ;

[0147] Step 2.4: According to Equations (11) and (12), the observation error of the finite-time neural network extended state observer can be expressed as:

[0148]

[0149] The observation error terms ζ 1 , ζ 2 can be constructed from Equation (14) as follows:

[0150]

[0151] According to (15), it can be calculated that as follows:

[0152]

[0153] In formula (16),

[0154] After integration, the following formula can be obtained:

[0155]

[0156] In formula (17), A o , C 1 , C 2 can be expressed as:

[0157]

[0158] Similarly, it can be obtained that as follows:

[0159]

[0160] As a specific example, in step 3, a finite-time exact tracking control algorithm for a single-rod electro-hydraulic servo system for model uncertainty compensation is constructed as follows:

[0161] Step 3.1: Define e 1 = x 1 - x 1d as the tracking error of the system, and define e 2 and e 3 as:

[0162]

[0163] In formula (20), α 1,c and α 2,c are the filtered values of the virtual control laws α 1 and α 2 respectively, and are obtained through the following filters:

[0164]

[0165] In formula (21), r j-1,1 , r j-1,2 are adjustable positive constants;

[0166] The dynamic equation of the filtering error is defined as:

[0167]

[0168] In formula (22), r j-1,2 , r j-1,1 are positive constants;

[0169] Step 3.2: Define the vector v = [v 1 , v 2 , v 3 T = [e 1 - k 1 , e 2 - k 2 , e 3 - k 3 T , where k i is an auxiliary variable generated by the following auxiliary system:

[0170]

[0171] In equation (23), c 1 , c 2 , c 3 , l 1 , l 2 , l 3 are adjustable positive constants;

[0172] Step 3.3: Design the virtual control law α 1 , α 2 and the actual control law u:

[0173] Differentiate x 1 , and based on formulas (9), (20), and (23), we get:

[0174]

[0175] According to equation (24), design the virtual control law α 1 as:

[0176]

[0177] Substitute (25) into (24) to get:

[0178]

[0179] Similarly, differentiate v 2 , and design the virtual control law α 2 as:

[0180]

[0181] Note: When α​​j-1 When passing through the instruction filter, the derivative of |v j-1 | r will be singular, so the method of setting 5 is adopted for processing.

[0182] Based on formulas (9), (20), (23), and (27), it can be obtained that:

[0183]

[0184] Similarly, for v 3 derivative is taken, and the actual control law u is designed as:

[0185]

[0186] Based on formulas (9), (20), (23), and (29), it can be obtained that:

[0187]

[0188] From formula (29), the control law u can be obtained as:

[0189]

[0190] As a specific example, in step 4, a finite-time multi-layer neural network adaptive law with fractional order is designed, specifically as follows:

[0191] Based on the designed controller (31), a finite-time multi-layer neural network adaptive law with fractional order is designed, and the weight parameters of its multi-layer feedforward neural network are updated by the following formula:

[0192]

[0193] In formula (32), is the additional term of the multi-layer neural network and can be expressed by the following formula:

[0194]

[0195] In formula (32), Proj(·) is the continuous projection mapping function, Γ j is the adaptive law matrix of the weight parameter W j , Υ j is the adaptive law matrix of the weight parameter V j , a j-1 , b j-1 are both adjustable positive constants;

[0196] As a specific example, in step 5, the initial values of the neural network weight parameters, the adaptive law matrix, and the controller parameters are selected to achieve the effect of compensating for model uncertainties while accurately tracking the control objective, specifically as follows:

[0197] Obtain the initial values of the neural network weight parameters and the adaptive law matrix Γ j > 0, Υ j Values greater than 0 and adjust the parameter c 1 、c 2 、c 3 、l 1 、l 2 、l 3 、s 1 、s 2 、s 3 、a 1 、a 2 、b 1 、b 2 The value of, ensure the effect of compensating for the system model uncertainty while making the output of the system y = x 1 Precisely track the desired smooth command y within a finite time d = x 1d , where c 1 、c 2 、c 3 、l 1 、l 2 、l 3 、s 1 、s 2 、s 3 、a 1 、a 2 、b 1 、b 2 Are all greater than 0;

[0198] According to the stability analysis of the system in control theory, select the Lyapunov function V as:

[0199]

[0200] tr(·) represents the trace of a certain matrix ·;

[0201] Substitute equations (17), (18), (19), (22), (23), (26), (28), (30), (32) and (33) into the differential equation of equation (34), and through a series of transformations, we can obtain:

[0202]

[0203] Since the Young's inequality is applied:

[0204]

[0205] According to setting 1 and setting 2, we can obtain:

[0206]

[0207] By applying Young's inequality, we have:

[0208]

[0209] Substituting (36), (37), and (38) into (35), we get:

[0210]

[0211]

[0212] In formula (39):

[0213]

[0214] In (40) is a bounded value, and the other parameters in (39) and (40) have been defined above.

[0215] Define Furthermore, the following conclusion can be obtained:

[0216]

[0217] Define as follows:

[0218]

[0219] From the above formula, it can be summarized that all the above signals are finite-time stable, that is, e 1 、e 2 、e 3 、v 1 、v 2 、v 3 、k 1 、k 2 、k 3 、η 1 、η 2 、 are all bounded. Therefore is also bounded; according to Assumption 1 and formula (37), the virtual control laws α 1 、 α 2 、 are all bounded; according to formulas (22), (34), and (41), α 1,c 、α 2,c 、 are all bounded; according to Assumption 1, the control input u is bounded; therefore all signals are bounded;

[0220] It can be seen from formula (41) that by selecting appropriate parameter values, making and If each term in

[0221] is a positive value, then its Lyapunov function V satisfies the finite-time stability criterion of the control system, and V can converge to 0 within a finite time, that is, the system will converge to 0 under any initial state. When the Lyapunov function V converges, the tracking error e of the system will also converge to 0, proving the stability of the system; r According to the analysis of the finite-time stability theory, V will reach stability within a finite time T r , and the range of T

[0222]

[0223] Equation (42) means that the state x 1 will track x r within time T 1 , where V(x 0 ) is the initial state value of the system.

[0224] The present invention also provides a finite-time precise tracking control system for an electro-hydraulic servo system, which is used to implement the finite-time precise tracking control method of the electro-hydraulic servo system. The system includes a model establishment module, an observer construction module, an algorithm construction module, an adaptive law construction module, and a compensation module, where:

[0225] The model establishment module is used to establish a mathematical model of a single-rod electro-hydraulic position servo system;

[0226] The observer construction module constructs a finite-time neural network extended state observer based on a multi-layer feedforward neural network to estimate the internal unknown nonlinearity, external disturbance, and system state of the single-rod electro-hydraulic servo system;

[0227] The algorithm construction module is used to construct a finite-time precise tracking control algorithm for a single-rod electro-hydraulic servo system for model uncertainty compensation;

[0228] The adaptive law construction module is used to design a finite-time multi-layer neural network adaptive law with fractional order;

[0229] The compensation module is used to select the initial values of the neural network weight parameters, the adaptive law matrix, and the controller parameters to achieve the compensation of the system model uncertainty and make the output of the system track the desired control target.

[0230] The present invention also provides a mobile terminal, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the finite-time precise tracking control method of the electro-hydraulic servo system.

[0231] The present invention also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps in the finite-time precise tracking control method of the electro-hydraulic servo system are implemented.

[0232] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0233] Embodiment

[0234] Build a third-order electro-hydraulic servo system simulation model as follows:

[0235]

[0236] Here, the system symbols are defined as shown above. In addition, B is the effective viscous damping coefficient, and A f is the Coulomb friction amplitude;

[0237] The parameters of the single-rod electro-hydraulic servo system provided in this embodiment are as follows:

[0238] Table 1 Electro-hydraulic servo system simulation parameters

[0239]

[0240]

[0241] Desired command: x 1d (t) = 0.05sin(π*t)*(1 - e -0.5t ), with the unit of m. Set the sampling time interval of the simulation to 0.001 s, the running time to 30 s, and the added disturbance to p 1 (t) = sin(t); p 2 (t) = 1.2sin(t); ε(t) = 1000sin(t), and the initial position of the system is 0.02 m.

[0242] Table 2 Controller parameters

[0243]

[0244] Figure 3 is the curve of the system state x 1 changing with time under the action of the controller designed by the present invention. It can be seen from Figure 3 that under the action of the controller designed by the present invention, the state of its system can track the command signal within 0.4 seconds and achieve a relatively high tracking accuracy, thus verifying the effectiveness of the controller designed by the present invention.

[0245] Figure 4 is the curve of the tracking error of the system changing with time under the action of the controller designed by the present invention. The tracking error of the controller can be reduced to 3×10-4 near m and reach a bounded stable state in a short time.

[0246] Figure 5 is the curve of the estimation performance of the system x under the action of the controller designed by the present invention. 2 It can be seen from the Figure 5 that under the action of the controller designed by the present invention, the estimated value of the system x 2 is bounded, and the estimated value of x 2 can completely track the system state x 2 .

[0247] Figure 6 is the curve of the estimation performance of the system x under the action of the controller designed by the present invention. 3 It can be seen from the Figure 6 that under the action of the controller designed by the present invention, the estimated value of the system x 3 is bounded, and the estimated value of x 3 can completely track the system state x 3 .

[0248] Figure 7 is the estimation of the unknown nonlinear function f by the multi-layer neural network under the action of the controller designed by the present invention, the estimation of the reconstruction error term x δ2 and the comparison between the estimation of the multi-layer neural network plus the reconstruction error term and the true unknown function f plus the unknown disturbance d(t). It can be seen that the unknown nonlinear function term and the uncertainty term of the system can be well estimated.

[0249] Figure 8 is the estimation of the unknown nonlinear function ψ by the multi-layer neural network under the action of the controller designed by the present invention, the estimation of the reconstruction error term x δ3 and the comparison between the estimation of the multi-layer neural network plus the reconstruction error term and the true unknown function ψ plus the unknown disturbance p(t). It can be seen that the unknown nonlinear function term and the uncertainty term of the system can be well estimated.

[0250] Figure 9 is the curve of the control input voltage of the controller designed by the present invention changing with time. It can be seen from the figure that the obtained control input signal of the present invention is continuously differentiable and bounded, which is beneficial to the application in engineering practice.

[0251] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A finite time precise tracking control method for an electro-hydraulic servo system, characterized in that: The following steps are involved: Step 1, establishing a mathematical model of a single-rod electro-hydraulic position servo system; Step 2: Based on a multi-layer feedforward neural network, a finite-time neural network extended state observer is constructed to estimate the matching and non-matching unknown function disturbances and system states of the single-rod electro-hydraulic servo system; Step 3, construct a finite time precise tracking control algorithm for a single-rod electro-hydraulic servo system for model uncertainty compensation; Step 4: Design a finite-time multilayer neural network adaptive law with fractional order; Step 5: Select the initial values ​​of the neural network weight parameters, the adaptive law matrix and the controller parameters to compensate for the uncertainty of the system model so that the output of the system tracks the desired control target.

2. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 1 is characterized in that: The mathematical model of establishing the single-rod electro-hydraulic position servo system described in step 1 is as follows: Step 1.1, define the state variable as Where m is the mass of the load, y is the displacement of the load; P1 and P2 are the oil pressures of the rodless and rod chambers of the hydraulic cylinder respectively; A1 and A2 are the effective action areas of the piston rods of the rodless and rod chambers of the hydraulic cylinder, then the state space form of the nonlinear model of the system is: In formula (1), u is the control input voltage of the system, and the expressions of other parts are as follows: In formula (2), β e is the elastic modulus of hydraulic oil, V1 and V2 are the volumes of the rodless chamber and rod chamber of the hydraulic cylinder respectively, Q1 is the hydraulic flow from the servo valve into the rodless chamber of the hydraulic cylinder, Q2 is the hydraulic flow from the rod chamber of the hydraulic cylinder into the servo valve, χ(x2), g1(x2,P1,P2), g2(x2,P1,P2) are unknown functions related to the system state, ε(t), p1(t), p2(t) are time-varying external disturbances; is the total flow gain of the servo valve, where C q1 , C q2 is the flow coefficient of the throttle hole of the rodless cavity and rod cavity servo valve, w q1 、w q2 are the throttle area gradients of the rodless cavity and the rod cavity, k q1 , k q2 They are the displacement flow gains of the servo valve cores of the rodless and rod-type servo valves; ρ o is the density of the oil, P s is the oil source pressure of the system, P r The system return oil pressure.

3. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 2 is characterized in that: Step 1.1 also includes step 1.2, which is as follows: Step 1.2: In order to simplify the control strategy design and the stability analysis of the system, the following settings are made under the premise of ensuring the system control performance and tracking performance: Setting 1: Expected trajectory x d is smooth enough and satisfies the following expression: Setting 2: The nonlinear uncertainties d(t) and p(t) in the system and their first-order derivatives are bounded; Setting 3: Setting represents the estimated value of , represents the estimated error of ; variable · i The subscript i in the variable is 1, 2, or 3; j The subscript j in is 2 or 3; Setting 4: Define the function as follows: sig(·) α =|·| α sign(·), sign is the standard sign function; Setting 5: For |·| r , r∈(0,1), when · approaches 0, |·| r The derivative of There may be some weirdness, so here is the framework: Here r∈Z + / {1},Ω v Defined as: Ω v ={·||·|<η},0<η<10 -6 .

4. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 3 is characterized in that: Based on the multi-layer feedforward neural network described in step 2, a finite-time neural network extended state observer is constructed to estimate the matching and non-matching unknown function disturbances and system states of the single-rod electro-hydraulic servo system, as follows: Step 2.1: For any smooth unknown function f(x2) and ψ(x2,P1,P2), it satisfies: In formula (3), and is the bounded constant ideal weight matrix of the neural network, where M1, N1, M2, N2, M and N are the number of neurons; is the input vector and represents the activation function; β2(δ2) and β3(δ3) represent the function reconstruction errors; The estimation formula for defining a smooth unknown function is: Step 2.2: Apply the smooth unknown function f(x2) and ψ(x2, P1, P2) to the nonlinear model of the system, and we get: The state variables of the further expanded system are: The variable x in formula (6) δ2 、x δ3 represents the system reconstruction error; set up: According to setting 2, D2(t) and D3(t) are both bounded, and the system nonlinear model (5) is transformed into: Step 2.3: Based on the smooth unknown function (4) and the system nonlinear model (7), a finite-time neural network extended state observer is constructed as: In formula (8), ω o2 ,ω o3 is an adjustable parameter; The definition is as follows: In formula (9), μ j,1 , μ j,2 , β j,3 It is an adjustable positive constant, 0<Δ<10 -4 ; Step 2.4: According to the system nonlinear model (7) and the finite time neural network extended state observer (8), the observation error of the finite time neural network extended state observer is obtained as: Based on (10), the observation error terms ζ1 and ζ2 are constructed as follows:

5. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 4 is characterized in that: The finite time precise tracking control algorithm for the single-rod electro-hydraulic servo system for model uncertainty compensation described in step 3 is as follows: Step 3.1: Define e1 = x1 - x 1d is the tracking error of the system, and e2 and e3 are defined as: e2=x2-a 1,c ,e3=x3-a 2,c (12) In formula (12), α 1,c and α 2,c are the filtered values ​​of the virtual control laws α1 and α2, respectively, obtained by the following filters: In formula (13), r j-1,1 ,r j-1,2 is an adjustable positive constant; Filter Error The dynamic equation of Defined as: Step 3.2, define vector v = [v1, v2, v3] T =[e1-k1,e2-k2,e3-k3] T , where k i is an auxiliary variable, generated by the following auxiliary systems: In formula (15), c1, c2, c3, l1, l2, l3 are adjustable positive constants; Step 3.3, design the virtual control laws α1, α2 and the actual control law u as: In formula (16), s1, s2, and s3 are adjustable positive gains; When α j-1 When passing through the command filter, |v j-1 | r The derivative of will appear singular, so we use the method of setting 5 to deal with it.

6. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 5, characterized in that: The design of the fractional-order finite-time multilayer neural network adaptive law described in step 4 is as follows: Design a fractional-order finite-time multilayer neural network adaptive law. The update formula of the weight parameters of the multilayer feedforward neural network is: In the formula, It is expressed by the following formula: Proj(·) is the continuous projection mapping function, Γ j is the weight parameter W j The adaptive law matrix, Υ j is the weight parameter V j The adaptive law matrix, is an additional term for the multi-layer neural network, ω oj is an adjustable positive constant.

7. The finite time precise tracking control method for an electro-hydraulic servo system according to claim 6, characterized in that: The initial values ​​of the neural network weight parameters, the adaptive law matrix and the controller parameters are selected in step 5 to compensate for the uncertainty of the system model so that the output of the system tracks the desired control target, as follows: Select the initial value of the neural network weight parameter and the adaptive law matrix Γ j >0, Υ j >0, and adjust the values ​​of parameters c1, c2, c3, l1, l2, l3, s1, s2, s3, a1, a2, b1, b2 to ensure the effect of compensating the uncertainty of the system model and making the system output y=x1 track the expected smooth command y in a finite time d =x 1d , among which c1, c2, c3, l1, l2, l3, s1, s2, s3, a1, a2, b1, and b2 are all greater than 0.

8. A finite time precision tracking control system for an electro-hydraulic servo system, characterized in that: The system is used to implement the finite time precise tracking control method of the electro-hydraulic servo system according to any one of claims 1 to 7, and the system includes a model building module, an observer building module, an algorithm building module, an adaptive law building module and a compensation module, wherein: Model building module, used to build a mathematical model of a single-rod electro-hydraulic position servo system; The observer construction module builds a finite-time neural network extended state observer based on a multi-layer feedforward neural network to estimate the unknown nonlinearity, external disturbance and system state of the single-rod electro-hydraulic servo system. Algorithm building module, used to build a finite time precise tracking control algorithm for a single-rod electro-hydraulic servo system for model uncertainty compensation; Adaptive law building block for designing adaptive laws for finite-time multilayer neural networks with fractional order; The compensation module is used to select the initial values ​​of the neural network weight parameters, the adaptive law matrix and the controller parameters to compensate for the uncertainty of the system model and make the system output track the desired control target.

9. A mobile terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the finite-time precise tracking control method for an electro-hydraulic servo system as claimed in any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by the processor, the steps of the finite time precise tracking control method for an electro-hydraulic servo system as claimed in any one of claims 1 to 7 are implemented.

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