A hydraulic system control method that combines parameter adaptation and neural network learning

Abstract

This invention belongs to the field of electromechanical servo control technology and discloses a hydraulic system control method that combines parameter adaptation and neural network learning. A mathematical model of the hydraulic system is established. Based on this model, a nonlinear controller incorporating parameter adaptation and online neural network learning is designed. Lyapunov stability theory is used to prove the stability of both the parameter adaptation and nonlinear controller, resulting in asymptotic stability of the hydraulic system's tracking error. This invention combines real-time neural network learning with online parameter adaptation, not only using neural networks to approximate the system's unknown nonlinear dynamics but also using parameter adaptation to estimate and compensate for system parameter changes in real time, thus jointly improving the controller's learning and adaptation capabilities to complex uncertainties.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical servo control technology, and relates to a control method for a hydraulic servo system, specifically a hydraulic system control method that takes into account both parameter adaptation and neural network learning. Background Technology

[0002] In critical applications such as aerospace, heavy engineering machinery, and precision robot joint actuation, hydraulic servo systems have consistently played an irreplaceable role due to their outstanding advantages of high power density, large torque output, and rapid dynamic response. However, hydraulic systems are inherently highly nonlinear dynamic systems, and further improvements in their control performance have long been limited by their inherent nonlinear characteristics and multi-source modeling uncertainties. The nonlinearity is mainly manifested in input dead zones and saturation, nonlinearity in the flow-pressure relationship of servo valves, and complex friction effects; modeling uncertainties include time-varying parameters (such as load inertia, viscous damping, leakage coefficient, flow gain, and oil elastic modulus) and unstructured uncertainties (such as unmodeled higher-order dynamics, external disturbances, and residual friction dynamics).

[0003] As modern equipment demands increasingly higher control precision and response frequency, the impact of nonlinearity and uncertainty on system performance becomes more pronounced. Continuing to use traditional linear control methods often leads to performance degradation or even instability due to the difficulty in overcoming model biases. Therefore, developing more advanced nonlinear control strategies to address the complex dynamic characteristics of hydraulic systems has become a crucial pathway to achieving technological breakthroughs.

[0004] To address this challenge, existing control schemes each have their own characteristics and limitations. Adaptive control, through online parameter estimation, can effectively cope with parameter uncertainties in hydraulic systems and achieve tracking compensation. However, its robustness to external loads and disturbances is poor, and it is prone to system divergence or even instability when significant unmodeled dynamics exist, making it difficult to independently adapt to the high-precision control requirements under complex working conditions. As another mainstream method, classical sliding mode control has excellent robustness and can theoretically suppress various bounded disturbances and ensure system convergence. However, chattering problems caused by discontinuous control laws in its controller design not only affect tracking accuracy but may also damage the actuator.

[0005] To balance the advantages of parameter adaptation and robust control, adaptive robust control (ARC) has been proposed. This framework can guarantee the transient and steady-state performance of the system even when parameters are unknown and external disturbances coexist. However, in practical high-precision applications, in order to pursue smaller residual errors, ARC often requires increasing the feedback gain, which amplifies sensor measurement noise, causes high-frequency jitter in the control input, and may even induce system instability. This significantly limits the performance ceiling of this method in high-precision hydraulic control. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a hydraulic system control method that combines parameter adaptation and neural network learning. This method can utilize indirect adaptive real-time estimation of system parameters to resolve the problem of system parameter uncertainty, while simultaneously achieving high-precision motion control performance through real-time learning of unknown system dynamics via neural networks. Furthermore, it avoids the differential explosion problem in traditional backstepping control of hydraulic systems, reducing the impact of measurement noise on control accuracy.

[0007] The technical solution of the present invention is as follows: A hydraulic system control method that combines parameter adaptation and neural network learning includes the following steps: S1, Establish the mathematical model of the hydraulic system; S2, based on the mathematical model of the hydraulic system, designs a nonlinear controller with parameter adaptive law and online neural network learning; S3. Using Lyapunov stability theory, the stability of both the adaptive law of parameters and the nonlinear controller is proved, and the asymptotic stability of the tracking error of the hydraulic system is obtained.

[0008] Furthermore, S1 includes the following steps: S11, In the power transmission chain of the hydraulic system, the load and the piston rod of the hydraulic cylinder form a rigid coupling component. The hydraulic cylinder is servo-regulated by the electro-hydraulic proportional servo valve, thereby driving the load to complete the linear motion trajectory. The force balance equation of the hydraulic system is analyzed to obtain the mathematical formulas for the flow rate Q1 of the inlet chamber and the flow rate Q2 of the outlet chamber of the hydraulic system. S12, Define state variables.

[0009] Furthermore, in S11, the force balance equation of the hydraulic system is: (1) In equation (1), m represents the mass of the load, and y represents the displacement of the hydraulic cylinder piston rod. This indicates the speed of the hydraulic cylinder piston rod. The value represents the acceleration of the hydraulic cylinder piston rod, A represents the effective working area of ​​the hydraulic cylinder piston, and the pressure difference between the inlet and outlet oil chambers on both sides of the cylinder. P1 represents the oil pressure in the inlet chamber of the hydraulic cylinder, and P2 represents the oil pressure in the outlet chamber of the hydraulic cylinder. This represents the frictional force acting on the load. This indicates that the system's mechanical disturbances are not modeled, and t represents time; Then equation (1) can be rewritten as: (2) Neglecting external leakage in the hydraulic cylinder, based on the continuity equation of fluid, the dynamic equation of pressure in the two chambers of the hydraulic cylinder is typically expressed as follows: (3) in, Indicates the effective elastic modulus of the oil. This represents the internal leakage coefficient of the hydraulic cylinder and the control volume of the oil inlet chamber. Control volume of oil outlet chamber V 01 V represents the initial volume of the oil inlet chamber. 02 Let Q1 represent the initial volume of the oil inlet chamber, Q2 represent the flow rate of the oil outlet chamber, q1 represent the unmodeled disturbance of Q1, and q2 represent the unmodeled disturbance of Q2. P represents L The first derivative; Q1 and Q2 are respectively related to the valve core displacement x of the electro-hydraulic proportional servo valve. v The following relationship exists: (4) Among them, the valve coefficient of the electro-hydraulic proportional servo valve C d This indicates the flow coefficient of the electro-hydraulic proportional servo valve. This represents the valve core area gradient of an electro-hydraulic proportional servo valve. P represents the density of the oil. s P represents the oil supply pressure. r Indicates the return oil pressure. Indicate intermediate variables The function is defined as: (5) At this time, the valve core displacement x v There is a linear relationship between x and the control voltage input u, which can be expressed as x v = k i u,k i Let the voltage-valve core displacement gain coefficient be represented, then equation (4) becomes: (6) Among them, intermediate variables intermediate variables intermediate variables .

[0010] Furthermore, in S12, state variables are defined:

[0011] Among them, intermediate variables intermediate variables intermediate variables Then equation (2) is transformed into a state-space equation: (7) Equation (7), express The first derivative, express The first derivative, express The first derivative, Unknown system dynamics intermediate variables , , , intermediate variables intermediate variables intermediate variables Unknown system dynamics The superscript T indicates transpose.

[0012] Furthermore, S2 includes the following steps: S21, Define the tracking error of the hydraulic system, and design a nonlinear filter that makes the tracking error of the hydraulic system tend to 0; S22, design the parameter adaptive law for the first channel; S23, Select the Lyapunov function and design the weight update law for the neural network; S24, design the adaptive law for the second channel; S25, using the Lyapunov function, designs a nonlinear controller that balances parameter adaptation and online neural network learning.

[0013] Furthermore, S21 specifically defines the system tracking error. ; in, This is the system's expected tracking position command; Design a nonlinear filter:

[0014] Filter gain , express Virtual control, Filtering error , express The filtered signal, Let f(x) denote a function that is always positive and satisfies the following condition: ,in, Represents the integral variable. Denotes a constant that is always positive. express The first derivative, express The first derivative, The upper realm A constant that is always positive; Tracking error Differentiating, we get: (10) in, express The first derivative, and error ; express first derivative ; Choosing Lyapunov functions ,have to: (11) in, Denotes the first derivative of M1; Design virtual control for: (12) Equation (12), gain .

[0015] Furthermore, S22 specifically refers to: (14) in ,

[0016] Filtering each term on both sides of the formula, we get: (15) In equation (15) Represent the filter coefficients; define the following two variables: (16) Where j represents the variable attenuation factor coefficient, j>0; integrating equation (16) yields: (17) (18) definition: (19) in, To express the error in parameter estimation, the adaptive law for parameters is: (20) Let be a positive definite diagonal matrix representing the adaptive rate gain of the parameters.

[0017] Furthermore, in S23, the nonlinear filter is: (twenty one) Filter gain , express Virtual control, Filtering error , express The filtered signal, express The first derivative, express The first derivative, The upper realm A constant that is always positive; For error Differentiating, we get: (twenty two) in, express The first derivative, and error ; Choosing Lyapunov functions We can obtain: (twenty three) in, This represents the first derivative of M². Design virtual control for: (twenty four) Equation (24), gain , Indicates intermediate variables. It is a constant that is always positive. express The estimated value, The specific form is as follows: (25) Equation (25), T represents a The estimated value, T a Represents the weights of the neural network. X represents the activation function of a neural network. a This represents the input to the neural network; The weight update law of the neural network is designed as follows: (26) in express The first derivative, Let Proj represent the weight gain matrix of the neural network, and let Proj represent the discontinuous mapping function. Substituting equation (26) into equation (25), we get: (27) Equation (27), neural network weights T a estimation error , This represents the approximation error of the neural network.

[0018] Furthermore, S24 specifically refers to: (28) in , ; (29) In equation (29), the filter gain , representing the filter coefficients; define the following two variables: (30) Where j represents the variable attenuation factor coefficient, j > 0. Integrating (30) yields: (31) (32) definition: (33) in, To express the error in parameter estimation, the adaptive law for parameters is: (34) This indicates the adaptive rate gain of the parameters.

[0019] Furthermore, in S25, regarding Differentiating, we get: (35) in, , express The first derivative; Choosing Lyapunov functions ,have to: (36) in, This represents the first derivative of M3; According to equation (36), the control input of the valve core, i.e., the nonlinear controller u that takes into account both parameter adaptation and online neural network learning, is: (37) Equation (37), gain , Indicates intermediate variables. A constant that is always positive; Substituting equation (37) into equation (36), we get: (38).

[0020] Furthermore, S3 specifically defines the Lyapunov function M as follows: (39) Differentiating equation (39) and substituting equations (9), (20), (21), (27), (34), and (38) into the equation, we get: (40) in, Let M be the first derivative.

[0021] The advantages of this invention are as follows: 1. This invention combines real-time neural network learning with online parameter adaptation mechanism. It not only uses neural network to approximate the unknown nonlinear dynamics of the system, but also uses parameter adaptation law to estimate and compensate for changes in system parameters in real time, thereby improving the controller's ability to learn and adapt to complex uncertainties.

[0022] 2. This invention effectively overcomes the structural defects of traditional backstepping control. By combining dynamic surface control methods, it avoids the "differential explosion" problem and reduces the sensitivity to measurement noise. At the same time, the parameter adaptive design further enhances the robustness of the system under parameter perturbation.

[0023] 3. This invention also achieves high-precision and robust position tracking control. The neural network and parameter adaptive work together to significantly improve the system's comprehensive suppression ability against unknown dynamics, parameter uncertainties and external disturbances. Simulation results show that the method has superior tracking accuracy and stability. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. 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.

[0025] Figure 1This is a schematic diagram illustrating the principle of the hydraulic system control method of the present invention, which combines parameter adaptation and online neural network learning.

[0026] Figure 2 This is a simplified schematic diagram of the hydraulic system of the present invention.

[0027] Figure 3 This is a graph showing the tracking process of the system output to the desired command under the action of the PANNC controller designed in this invention.

[0028] Figure 4 This is a graph showing the change of tracking error of the system over time under the action of the PANNC controller designed in this invention.

[0029] Figure 5 This is a comparison curve of the tracking error of the system under the action of the PANNC controller designed in this invention and the traditional PID controller. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0031] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setups and methods set forth below, but covers any improvements, substitutions, and modifications to structures, methods, and devices without departing from the spirit of the invention. Well-known structures and techniques are not shown in the drawings and the following description to avoid unnecessarily obscuring the invention.

[0032] In the description of this invention, it should be noted that the directions or positional relationships indicated by terms such as "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer" are based on the directions or positional relationships shown in the accompanying drawings and are only for the convenience of describing and simplifying the invention, and should not be construed as limiting the invention. Furthermore, the use of ordinal numbers (e.g., "first and second," etc.) is for distinguishing objects and is not limited to this order, and should not be construed as indicating or implying relative importance.

[0033] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly, encompassing both direct connection and indirect connection via an intermediate medium. Those skilled in the art can understand the specific meaning of these terms in this invention based on the specific circumstances.

[0034] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited in each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] First embodiment: Step 1: Establish a mathematical model of the hydraulic system.

[0036] Step 1-1: The system is used to drive the linear feed mechanism of large, heavy-duty industrial equipment. In its power transmission chain, the load and the hydraulic cylinder piston rod form a rigid coupling assembly. The hydraulic cylinder is servo-regulated via an electro-hydraulic proportional servo valve, thereby driving the load to complete a linear motion trajectory.

[0037] According to Newton's second law, the force balance equation of a hydraulic system is: (1) In equation (1), m represents the mass of the load, and y represents the displacement of the hydraulic cylinder piston rod. This indicates the speed of the hydraulic cylinder piston rod. The value represents the acceleration of the hydraulic cylinder piston rod, A represents the effective working area of ​​the hydraulic cylinder piston, and the pressure difference between the inlet and outlet oil chambers on both sides of the cylinder. P1 represents the oil pressure in the inlet chamber of the hydraulic cylinder, and P2 represents the oil pressure in the outlet chamber of the hydraulic cylinder. This represents the frictional force acting on the load. This indicates that the system's mechanical disturbances are not modeled, and t represents time; Then equation (1) can be rewritten as: (2) Neglecting external leakage in the hydraulic cylinder, based on the continuity equation of fluid, the dynamic equation of pressure in the two chambers of the hydraulic cylinder is typically expressed as follows: (3) in, Indicates the effective elastic modulus of the oil. This represents the internal leakage coefficient of the hydraulic cylinder and the control volume of the oil inlet chamber. Control volume of oil outlet chamber V 01 V represents the initial volume of the oil inlet chamber. 02Let Q1 represent the initial volume of the oil inlet chamber, Q2 represent the flow rate of the oil outlet chamber, q1 represent the unmodeled disturbance of Q1, and q2 represent the unmodeled disturbance of Q2. P represents L The first derivative; Q1 and Q2 are respectively related to the valve core displacement x of the electro-hydraulic proportional servo valve. v The following relationship exists: (4) Among them, the valve coefficient of the electro-hydraulic proportional servo valve C d This indicates the flow coefficient of the electro-hydraulic proportional servo valve. This represents the valve core area gradient of an electro-hydraulic proportional servo valve. P represents the density of the oil. s P represents the oil supply pressure. r Indicates the return oil pressure. Indicate intermediate variables The function is defined as: (5) Given that the response frequency of an electro-hydraulic proportional servo valve is typically much higher than the natural mechanical frequency of a hydraulic system, it is treated as a high-frequency proportional element, and its dynamic hysteresis is ignored. At this point, the valve spool displacement x... v There is a linear relationship between x and the control voltage input u, which can be expressed as x v = k i u,k i Let the voltage-valve core displacement gain coefficient be represented, then equation (4) becomes: (6) Among them, intermediate variables intermediate variables intermediate variables .

[0038] Step 1-2: Define state variables: intermediate variables intermediate variables intermediate variables Then equation (2) is transformed into a state-space equation: (7) Equation (7), express The first derivative, express The first derivative, express The first derivative, Unknown system dynamics intermediate variables , , , intermediate variables intermediate variables intermediate variables Unknown system dynamics The superscript T indicates transpose.

[0039] To facilitate controller design, the following assumptions are made here: Assumption 1: The desired tracking trajectory xd is sufficiently smooth and has continuity of the second derivative; at the same time, the desired position signal and its first derivative (velocity) and second derivative (acceleration) both satisfy the boundedness condition.

[0040] Assumption 2: The system has unknown dynamics and a set of uncertainties. and satisfy: (8) Equation (8), and All of them are unknown positive constants.

[0041] Proceed to step 2.

[0042] Step 2: Based on the mathematical model of the hydraulic system, design a nonlinear controller that balances parameter adaptation and online neural network learning. The specific steps are as follows: Step 2-1: To facilitate controller design, define the system tracking error. ,in, The system expects to track position commands, and to facilitate the control of the system state under the design of the controller. Track the desired position command as accurately as possible. Tracking error must be guaranteed The nonlinear filter is designed to approach 0, and the specific design is as follows: (9) Equation (9), Filtering gain , express Virtual control, Filtering error , express The filtered signal, Let f(x) denote a function that is always positive and satisfies the following condition: ,in, Represents the integral variable. Denotes a constant that is always positive. express The first derivative, express The first derivative, The upper realm A constant that is always positive; Tracking error Differentiating, we get: (10) in, express The first derivative, and error ; express The first derivative; Choosing Lyapunov functions We can obtain: (11) in, Denotes the first derivative of M1; Design virtual control for: (12) Equation (12), gain ,but (13) Step 2-2: To design the adaptive law for the first channel, ignoring the interference term, transform the second formula in (7) into: (14) in ,

[0043] Filtering each term on both sides of the formula, we get: (15) In equation (15) , representing the filter coefficients. Define the following two variables: (16) Where j represents the variable attenuation factor coefficient, j > 0. Integrating (16) yields: (17) Therefore (18) definition (19) in, This represents the error in parameter estimation. The adaptive law for the parameters can be derived as follows: (20) Let be a positive definite diagonal matrix representing the adaptive rate gain of the parameters.

[0044] Steps 2-3: Design the following nonlinear filter: (twenty one) Equation (21), Filter gain , express Virtual control, Filtering error , express The filtered signal, express The first derivative, express The first derivative, The upper realm A constant that is always positive; For error Differentiating, we get: (twenty two) in, express The first derivative, and error ; Choosing Lyapunov functions We can obtain: (twenty three) in, This represents the first derivative of M². Design virtual control for: (twenty four) Equation (24), gain , Indicates intermediate variables. It is a constant that is always positive. express The estimated value, The specific form is as follows: (25) Equation (25), T represents a The estimated value, T a Represents the weights of the neural network. X represents the activation function of a neural network. a This represents the input to the neural network; The weight update law of the neural network is designed as follows: (26) Equation (26), express The first derivative, Let Proj represent the weight gain matrix of the neural network, and let Proj represent the discontinuous mapping function. Substituting equation (26) into equation (25), we get: (27) Equation (27), neural network weights T a estimation error , This represents the approximation error of the neural network.

[0045] Step 2-4: To design the adaptive law for the second channel, the third formula in (7) is transformed into: (28) in , ; Filtering each term on both sides of the formula, we get: (29) In equation (29), the filter gain , representing the filter coefficients. Define the following two variables: (30) Where j represents the variable attenuation factor coefficient, j > 0. Integrating (30) yields: (31) Therefore (32) definition (33) in, This represents the error in parameter estimation. The adaptive law for the parameters can be derived as follows: (34) This indicates the adaptive rate gain of the parameters.

[0046] Steps 2-5, for Differentiating, we get: (35) in, , express The first derivative; Choosing Lyapunov functions ,have to: (36) in, This represents the first derivative of M3; According to equation (36), the control input of the valve core, i.e., the nonlinear controller u that takes into account both parameter adaptation and online neural network learning, is: (37) Equation (37), gain , Indicates intermediate variables. A constant that is always positive; Substituting equation (37) into equation (36), we get: (38) Proceed to step 3.

[0047] Step 3: Using Lyapunov stability theory, the stability of the nonlinear controller that balances parameter adaptation and online neural network learning is proven, yielding the asymptotically stable result of the system tracking error, as detailed below: The Lyapunov function M is defined as follows: (39) Differentiating equation (39) and substituting equations (9), (20), (21), (27), (34), and (38) into the equation, we obtain: (40) in, Let M be the first derivative.

[0048] Considering , , and , , Let be a positive definite diagonal matrix, representing the adaptive gain, and we can obtain the expression: (41) in: (42) Substituting equation (42) into equation (41), we get (43) Equation (43), intermediate variable .

[0049] Integrating both sides of equation (43) respectively, we get: (44) From equation (44), we can see that M is bounded. Since the integral is bounded, it can be concluded that all signals in the system are bounded. Therefore, It is consistent and continuous. Applying Barbalat's lemma, we can conclude that as time approaches positive infinity, the tracking error... It will gradually approach zero.

[0050] In summary, the following conclusions can be drawn: For the proposed hydraulic nonlinear controller that combines parameter adaptive law and neural network compensation mechanism, as long as the feedback gain k1, k2, k3 and the filter gain are properly tuned... , This ensures that the tracking error of the closed-loop system asymptotically converges to zero. The overall principle architecture of this control strategy is as follows: Figure 1 As shown.

[0051] Second embodiment: To evaluate the performance of the designed controller, the physical parameters of the hydraulic system in the simulation are shown in Table 1: Table 1 System Physical Parameters

[0052] Given the desired instructions of the system .

[0053] The following controller is used for comparison in the simulation: A hydraulic system control method that combines parameter adaptation and online neural network learning: taking the gain , , , , , , .

[0054] PID Controller: The steps for selecting PID controller parameters are as follows: First, ignoring the nonlinear dynamics of the hydraulic system, obtain a set of controller parameters using the PID parameter self-tuning function in Matlab. Then, after adding the nonlinear dynamics of the system, fine-tune the obtained self-tuning parameters to achieve optimal tracking performance. The selected controller parameters are... , , .

[0055] The system's expected command, PANNC controller tracking error, and a comparison of the tracking errors of the PANNC controller and the PID controller are as follows: Figure 3 , Figure 4 and Figure 5 As shown. By Figure 4It can be seen that, under the action of the PANNC controller, the position output of the hydraulic system tracks the command with high accuracy, and the amplitude of the steady-state tracking error is approximately... m. From Figure 5 A comparison of the tracking errors of the two controllers shows that the tracking error of the PANNC controller proposed in this invention is much smaller than that of the PID controller, and its tracking performance is superior.

[0056] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A hydraulic system control method that combines parameter adaptation and neural network learning, characterized in that, Includes the following steps: S1, Establish the mathematical model of the hydraulic system; S2, based on the mathematical model of the hydraulic system, designs a nonlinear controller with parameter adaptive law and online neural network learning; S3. Using Lyapunov stability theory, the stability of both the adaptive law of parameters and the nonlinear controller is proved, and the asymptotic stability of the tracking error of the hydraulic system is obtained.

2. The hydraulic system control method that combines parameter adaptation and neural network learning according to claim 1, characterized in that, S1 includes the following steps: S11, In the power transmission chain of the hydraulic system, the load and the piston rod of the hydraulic cylinder form a rigid coupling component. The hydraulic cylinder is servo-regulated by the electro-hydraulic proportional servo valve, thereby driving the load to complete the linear motion trajectory. The force balance equation of the hydraulic system is analyzed to obtain the mathematical formulas for the flow rate Q1 of the inlet chamber and the flow rate Q2 of the outlet chamber of the hydraulic system. S12, Define state variables.

3. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 2, characterized in that, In S11, the force balance equation of the hydraulic system is: （1） In equation (1), m represents the mass of the load, and y represents the displacement of the hydraulic cylinder piston rod. This indicates the speed of the hydraulic cylinder piston rod. The value represents the acceleration of the hydraulic cylinder piston rod, A represents the effective working area of ​​the hydraulic cylinder piston, and the pressure difference between the inlet and outlet oil chambers on both sides of the cylinder. P1 represents the oil pressure in the inlet chamber of the hydraulic cylinder, and P2 represents the oil pressure in the outlet chamber of the hydraulic cylinder. This represents the frictional force acting on the load. This indicates that the system's mechanical disturbances are not modeled, and t represents time; Then equation (1) can be rewritten as: （2） Neglecting external leakage in the hydraulic cylinder, based on the fluid continuity equation, the pressure dynamic equations for the two chambers of the hydraulic cylinder are typically expressed as follows: （3） in, Indicates the effective elastic modulus of the oil. This represents the internal leakage coefficient of the hydraulic cylinder and the control volume of the oil inlet chamber. Control volume of oil outlet chamber V 01 V represents the initial volume of the oil inlet chamber. 02 Let Q1 represent the initial volume of the oil inlet chamber, Q2 represent the flow rate of the oil outlet chamber, q1 represent the unmodeled disturbance of Q1, and q2 represent the unmodeled disturbance of Q2. P represents L The first derivative; Q1 and Q2 are respectively related to the valve core displacement x of the electro-hydraulic proportional servo valve. v The following relationship exists: （4） Among them, the valve coefficient of the electro-hydraulic proportional servo valve C d This indicates the flow coefficient of the electro-hydraulic proportional servo valve. This represents the valve core area gradient of an electro-hydraulic proportional servo valve. P represents the density of the oil. s P represents the oil supply pressure. r Indicates the return oil pressure. Indicate intermediate variables The function is defined as: （5） At this time, the valve core displacement x v There is a linear relationship between x and the control voltage input u, which can be expressed as x v = k i u,k i Let the voltage-valve core displacement gain coefficient be represented, then equation (4) becomes: （6） Among them, intermediate variables intermediate variables intermediate variables .

4. The hydraulic system control method that combines parameter adaptation and neural network learning according to claim 3, characterized in that, In S12, state variables are defined as follows: Among them, intermediate variables intermediate variables intermediate variables Then equation (2) is transformed into a state-space equation: （7） Equation (7), express The first derivative, express The first derivative, express The first derivative, Unknown system dynamics intermediate variables , , , intermediate variables intermediate variables intermediate variables Unknown system dynamics The superscript T indicates transpose.

5. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 1, characterized in that, S2 includes the following steps: S21, Define the tracking error of the hydraulic system, and design a nonlinear filter that makes the tracking error of the hydraulic system tend to 0; S22, design the parameter adaptive law for the first channel; S23, Select the Lyapunov function and design the weight update law for the neural network; S24, design the adaptive law for the second channel; S25, using the Lyapunov function, designs a nonlinear controller that balances parameter adaptation and online neural network learning.

6. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 5, characterized in that, S21 specifically defines the system tracking error. ; in, This is the system's expected tracking position command; Design a nonlinear filter: Filter gain , express Virtual control, Filtering error , express The filtered signal, Let f(x) denote a function that is always positive and satisfies the following condition: ,in, Represents the integral variable. Denotes a constant that is always positive. express The first derivative, express The first derivative, The upper realm A constant that is always positive; Tracking error Differentiating, we get: （10） in, express The first derivative, and error ; express first derivative ; Choosing Lyapunov functions ,have to: （11） in, Denotes the first derivative of M1; Design virtual control for: （12） Equation (12), gain .

7. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 6, characterized in that, S22 specifically refers to: （14） in , Filtering each term on both sides of the formula, we get: （15） In formula (15) Represent the filter coefficients; define the following two variables: （16） Where j represents the variable attenuation factor coefficient, j>0; integrating equation (16) yields: （17） （18） definition: (19) in, To express the error in parameter estimation, the adaptive law for parameters is: （20） Let be a positive definite diagonal matrix representing the adaptive rate gain of the parameters.

8. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 7, characterized in that, In S23, the nonlinear filter is: （21） Filter gain , express Virtual control, Filtering error , express The filtered signal, express The first derivative, express The first derivative, The upper realm A constant that is always positive; For error Differentiating, we get: （22） in, express The first derivative, and error ; Choosing Lyapunov functions We can obtain: （23） in, This represents the first derivative of M². Design virtual control for: （24） Equation (24), gain , Indicates intermediate variables. It is a constant that is always positive. express The estimated value, The specific form is as follows: （25） Equation (25), T represents a The estimated value, T a Represents the weights of the neural network. X represents the activation function of a neural network. a This represents the input to the neural network; The weight update law of the neural network is designed as follows: （26） in express The first derivative, Let Proj represent the weight gain matrix of the neural network, and let Proj represent the discontinuous mapping function. Substituting equation (26) into equation (25), we get: （27） Equation (27), neural network weights T a estimation error , This represents the approximation error of the neural network.

9. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 8, characterized in that, S24 specifically refers to: （28） in , ; （29） In equation (29), the filter gain , representing the filter coefficients; define the following two variables: （30） Where j represents the variable attenuation factor coefficient, j>0; then integrating (30) yields: （31） （32） definition: (33) in, To express the error in parameter estimation, the adaptive law for parameters is: （34） This indicates the adaptive rate gain of the parameters.

10. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 9, characterized in that, In S25, for Differentiating, we get: （35） in, , express The first derivative; Choosing Lyapunov functions ,have to: （36） in, This represents the first derivative of M3; According to equation (36), the control input of the valve core, i.e., the nonlinear controller u that takes into account both parameter adaptation and online neural network learning, is: （37） Equation (37), gain , Indicates intermediate variables. A constant that is always positive; Substituting equation (37) into equation (36), we get: （38）。 11. A hydraulic system control method that combines parameter adaptation and neural network learning according to claim 10, characterized in that, S3 specifically refers to the following definition of the Lyapunov function M: （39） Differentiating equation (39) and substituting equations (9), (20), (21), (27), (34), and (38) into the equation, we get: （40） in, Let M be the first derivative.

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