Intelligent shaft control method of hydraulic valve based on preset time output performance
By designing an intelligent axis control method for hydraulic valves based on preset time output performance, and utilizing neural networks to learn the unknown dynamics of the system, the nonlinearity and modeling uncertainty of the hydraulic valve axis control system are solved, achieving high-precision and stable motion control and avoiding the shortcomings of traditional methods.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2026-04-14
- Publication Date
- 2026-07-14
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Figure CN122014710B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of electromechanical servo control technology, specifically to a hydraulic valve intelligent axis control method (PTOPIAC) based on preset time output performance. Background Technology
[0002] Hydraulic valve axis control systems, with their high power density, large force / torque output, and fast dynamic response, play a crucial role in robotics, heavy machinery, and high-performance loading and testing equipment. However, a hydraulic valve axis control system is a typical nonlinear system, containing numerous nonlinear characteristics and modeling uncertainties. These nonlinear characteristics include input nonlinearities such as hysteresis and saturation, flow and pressure nonlinearities in proportional servo valves, and frictional nonlinearities. Modeling uncertainties include parameter uncertainties and undefined nonlinearities. Parameter uncertainties mainly involve load mass, actuator viscous friction coefficient, leakage coefficient, servo valve flow gain, and hydraulic oil elastic modulus. Undefined nonlinearities mainly include unmodeled frictional dynamics, higher-order system dynamics, external disturbances, and unmodeled leakage. As hydraulic valve axis control systems develop towards higher precision and higher frequency response, the impact of the system's nonlinear characteristics on system performance becomes increasingly significant. Furthermore, the existence of modeling uncertainties can cause instability or order degradation in controllers designed based on the nominal system model. Therefore, the nonlinear characteristics and modeling uncertainties of hydraulic valve axis control systems are important factors limiting performance improvements. With the continuous advancement of technology in the industrial and defense sectors, controllers designed based on traditional linear theory can no longer meet the high-performance requirements of systems. Therefore, it is necessary to study more advanced nonlinear control strategies for the nonlinear characteristics of hydraulic valve shaft control systems.
[0003] Many methods have been proposed to address the nonlinear control problem of hydraulic valve shaft control systems. Among them, adaptive control is very effective in handling parameter uncertainty and can achieve asymptotic tracking steady-state performance. However, it is inadequate for uncertain nonlinearities such as external load disturbances. When the uncertainty nonlinearity is too large, it may cause system instability. Since all practical hydraulic valve shaft control systems have uncertain nonlinearities, adaptive control cannot achieve high-precision control performance in practical applications. As a robust control method, classical sliding mode control can effectively handle any bounded modeling uncertainty and achieve asymptotic tracking steady-state performance. However, the discontinuous controller designed in classical sliding mode control is prone to chattering on the sliding surface, which degrades the system's tracking performance. To simultaneously address parameter uncertainty and uncertain nonlinearity, adaptive robust control has been proposed. This control method can achieve deterministic transient and steady-state performance when both modeling uncertainties exist. To achieve high-precision tracking performance, the feedback gain must be increased to reduce tracking error. Due to the presence of measurement noise, excessively large gains often lead to high-gain feedback, causing chattering of the control input, which further degrades control performance and may even cause system instability. Summary of the Invention
[0004] The purpose of this invention is to provide a hydraulic valve position axis control method that features safe and limited system output performance, active learning compensation, strong anti-interference ability, and high tracking performance. It can achieve preset time control of the system output transient and steady-state performance to ensure the safe and reliable operation of the system. It can also utilize neural networks to learn unknown dynamics of the system in real time to achieve high-precision motion control performance. Furthermore, it can avoid the differential explosion problem in the traditional backstepping control of hydraulic valve axis control systems and reduce the impact of measurement noise on control accuracy.
[0005] The technical solution to achieve the purpose of this invention is: a method for intelligent shaft control of a hydraulic valve based on preset time output performance, comprising the following steps:
[0006] Step 1: Establish the mathematical model of the hydraulic valve position axis control system, then proceed to Step 2.
[0007] Step 2: Based on the mathematical model of the hydraulic valve position axis control system, design an intelligent axis controller with output performance based on preset time, and proceed to Step 3.
[0008] Step 3: Using Lyapunov stability theory, the stability of the intelligent axis controller based on the preset time output performance is proven, and the asymptotic stability of the system tracking error is obtained.
[0009] Compared with the prior art, the significant advantages of this invention are: (1) It realizes the preset time control of the transient and steady-state performance of the system output, ensuring the safe and reliable operation of the system; (2) It uses neural networks to learn the unknown dynamics of the system in real time, realizing high-precision motion control performance; (3) It avoids the differential explosion problem in the traditional backstep control of the hydraulic valve shaft control system, reduces the impact of measurement noise on control accuracy, realizes high-precision tracking performance, and the simulation results verify its effectiveness. Attached Figure Description
[0010] Figure 1 This is a schematic diagram illustrating the principle of the intelligent shaft control method for hydraulic valves based on preset time output performance according to the present invention.
[0011] Figure 2 This is a simplified schematic diagram of the hydraulic valve shaft control system of the present invention.
[0012] Figure 3 This is a graph showing the tracking process of the system output to the desired command under the action of the PTOPIAC controller designed in this invention.
[0013] Figure 4 This is a graph showing the change of the tracking error of the system over time under the action of the PTOPIAC controller designed in this invention.
[0014] Figure 5 This is a comparison curve of the tracking error of the system under the action of the PTOPIAC controller designed in this invention and the traditional PID controller.
[0015] Figure 6 This is a control input curve of the system under the action of the PTOPIAC controller designed in this invention. Detailed Implementation
[0016] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0017] Combination Figure 1 and Figure 2 The present invention provides a method for intelligent shaft control of hydraulic valves based on preset time output performance, comprising the following steps:
[0018] Step 1: Establish a mathematical model of the hydraulic valve position axis control system.
[0019] Step 1-1: The hydraulic valve position axis control system is applied to the linear motion of large industrial heavy-duty machinery and equipment, wherein the load is fixedly connected to the piston rod on the hydraulic cylinder, and the hydraulic valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move.
[0020] According to Newton's second law, the force balance equation of the hydraulic valve position control system is:
[0021] (1),
[0022] In equation (1), Indicates the quality of the load. This indicates the displacement of the piston rod in a hydraulic cylinder. This indicates the speed of the hydraulic cylinder piston rod. This indicates the acceleration of the piston rod in the hydraulic cylinder. This indicates the effective working area of the hydraulic cylinder piston; P1 represents the oil pressure in the hydraulic cylinder inlet chamber; and P2 represents the oil pressure in the hydraulic cylinder outlet chamber. This represents the frictional force acting on the load. This indicates that the system's mechanical disturbances are not modeled, and t represents time.
[0023] Then equation (1) can be rewritten as:
[0024] (2),
[0025] In a hydraulic valve position control system, ignoring external oil leakage from the cylinder, the pressure dynamic equation is:
[0026] (3),
[0027] In equation (3), Indicates the effective elastic modulus of the oil. This represents the internal leakage coefficient of the hydraulic cylinder, and the pressure difference between the inlet and outlet oil chambers on both sides of the cylinder. Control volume of oil inlet chamber Control volume of oil outlet chamber V 01 V represents the initial volume of the oil inlet chamber. 02 This indicates the initial volume of the oil outlet cavity. This indicates the flow rate of the oil inlet chamber. This indicates the flow rate of the oil cavity. express Unmodeled interference, express Unmodeled interference, express The first derivative, express The first derivative.
[0028] , Relative to the displacement x of the hydraulic valve core v The following relationship exists:
[0029] (4),
[0030] Among them, the hydraulic valve coefficient , This indicates the flow coefficient of the hydraulic valve. This represents the valve core area gradient of a hydraulic valve. Indicates the density of the oil. Indicates the oil supply pressure. Indicates the return oil pressure. Indicate intermediate variables The function is defined as:
[0031] (5),
[0032] Ignoring the dynamics of the hydraulic valve spool, assume the control input u and the spool displacement x acting on the spool. v A proportional relationship, that is, satisfying x v = k i u, where k i This represents the voltage-valve core displacement gain coefficient, therefore equation (4) is rewritten as:
[0033] (6),
[0034] Equation (6), intermediate variables intermediate variables intermediate variables .
[0035] Step 1-2: Define state variables: Among them, intermediate variables intermediate variables intermediate variables Then equation (2) is transformed into a state-space equation:
[0036] (7),
[0037] Equation (7), express The first derivative, express The first derivative, express First derivative, unknown dynamics of the system intermediate variables intermediate variables intermediate variables Unknown system dynamics , T represents transpose.
[0038] To facilitate controller design, the following assumptions are made:
[0039] Assumption 1: The system expects to track position commands. It is second-order continuous, and the system expects the position command, velocity command, and acceleration command to be bounded.
[0040] Assumption 2: Unknown system dynamics and satisfy:
[0041] (8),
[0042] Equation (8), and All of them are unknown positive constants.
[0043] Proceed to step 2.
[0044] Step 2: Based on the mathematical model of the hydraulic valve position axis control system, design an intelligent axis controller with output performance based on a preset time. The specific steps are as follows:
[0045] Step 2-1, Define the error ,in, Indicates the system tracking error. This is the system's expected position tracking command. This represents a preset time-performance safety function, used to facilitate the monitoring of system states under the control of the designed controller. Track the desired position command as accurately as possible. And let Always satisfied Tracking error must be guaranteed It tends towards 0, specifically as follows:
[0046] Tracking error Meets preset range:
[0047] (9),
[0048] In equation (9), the preset time performance safety function is... Defined as:
[0049] (10)
[0050] in, Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Represents the cotangent function. It represents pi (π).
[0051] To facilitate controller design, the following nonlinear filter is designed:
[0052] (11),
[0053] Equation (11), Filtering gain , Filtering error , 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 .
[0054] Tracking error Differentiating, we get:
[0055] (12)
[0056] in, Indicates error; express The first derivative; express The first derivative; Indicates the preset time performance safety function The first derivative.
[0057] Choosing Lyapunov functions ,in Representing the logarithmic function, we get:
[0058] (13)
[0059] Design virtual control for:
[0060] (14)
[0061] Equation (14), gain ,but:
[0062] (15)
[0063] Step 2-2, Define the error ,in, express The filtered signal, express Virtual control, to ensure tracking error Approaching 0, the error must be guaranteed. It tends towards 0, specifically as follows:
[0064] Design the following nonlinear filter:
[0065] (16)
[0066] Equation (16), Filtering gain , Filtering error , 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 ;right Differentiating, we get:
[0067] (17)
[0068] Choosing Lyapunov functions We can obtain:
[0069] (18)
[0070] Design virtual control for:
[0071] (19)
[0072] Equation (19), gain , This represents the model-based compensation term. Indicates robustness. Represents the linear robust term, Represents the nonlinear robust term. 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. The upper realm ; express The estimated value, The specific form is:
[0073] (20)
[0074] Equation (20), express The estimated value, Represents the weights of the neural network. Represents the activation function of a neural network. This represents the input to the neural network.
[0075] The weight update law of the neural network is designed as follows:
[0076] (twenty one),
[0077] Equation (21), express The first derivative, This represents the weight gain matrix of the neural network. Represents a discontinuous mapping function;
[0078] Substituting equation (19) into equation (18), we get:
[0079] (twenty two),
[0080] Equation (22), neural network weights estimation error , This represents the approximation error of the neural network.
[0081] Steps 2-3: Define the error ,in, express The filtered signal, express Virtual control, to ensure error Approaching 0, the error must be guaranteed. It tends towards 0, specifically as follows:
[0082] right Differentiating, we get:
[0083] (twenty three),
[0084] Choosing Lyapunov functions ,have to:
[0085] (twenty four),
[0086] According to equation (24), the control input of the valve core, i.e., the intelligent axis controller u based on the preset time output performance, is:
[0087] (25),
[0088] Equation (25), gain , This represents the model-based compensation term. Indicates robustness. Represents the linear robust term, Represents the nonlinear robust term. 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. The upper realm Substituting equation (25) into equation (24), we get:
[0089] (26)
[0090] Proceed to step 3.
[0091] Step 3: Apply Lyapunov stability theory to prove the stability of the intelligent axis controller based on the preset time output performance, and obtain the asymptotically stable result of the system tracking error, as follows:
[0092] The Lyapunov function L is defined as follows:
[0093] (27)
[0094] Differentiating equation (27) and substituting equations (11), (18), and (26) into the equation, we obtain:
[0095] (28)
[0096] Considering , , and The expression can be obtained as follows:
[0097] (29)
[0098] Note:
[0099] (30)
[0100] Substituting equation (30) into equation (29), we get
[0101] (31),
[0102] Equation (31), intermediate variable Intermediate variables Integrating both sides of equation (31) respectively, we get:
[0103] (32),
[0104] Equation (32), intermediate variable .
[0105] From equation (32), we can see that It 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. According to Barbalat's lemma, as time approaches positive infinity, the tracking error... It tends towards 0.
[0106] Therefore, we can conclude that by adjusting the gains k1, k2, k3, and the filter gain... , A hydraulic valve position axis control system based on a preset time output performance intelligent axis controller can innovatively achieve asymptotic convergence of tracking error to 0. A schematic diagram of the hydraulic valve position axis control system position axis controller is shown below. Figure 1 As shown.
[0107] Example
[0108] To evaluate the performance of the designed controller, the physical parameters of the hydraulic valve position axis control system in the simulation are shown in Table 1:
[0109] Table 1 System Physical Parameters
[0110]
[0111] Given the desired instructions of the system m.
[0112] The following controller is used for comparison in the simulation:
[0113] Hydraulic valve intelligent shaft control method based on preset time output performance (PTOPIAC): taking gain , , , , , , , , .
[0114] PID Controller: The steps for selecting PID controller parameters are as follows: First, ignoring the nonlinear dynamics of the hydraulic valve shaft control 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... , , .
[0115] The system's expected command, PTOPIAC controller tracking error, and a comparison of the tracking errors of the PTOPIAC controller and the PID controller are as follows:Figure 3 , Figure 4 and Figure 5 As shown. By Figure 4 It can be seen that, under the action of the PTOPIAC controller, the position output of the hydraulic valve shaft control system has a very high tracking accuracy to the command, 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 PTOPIAC controller proposed in this invention is much smaller than that of the PID controller, and its tracking performance is superior.
[0116] Figure 6 This is a graph showing the change of control input of the hydraulic valve shaft control system over time under the action of the PTOPIAC controller. As can be seen from the graph, the obtained control input is a low-frequency continuous signal, which is more conducive to execution in practical applications.
Claims
1. A method for intelligent shaft control of a hydraulic valve based on preset time output performance, characterized in that, Includes the following steps: Step 1: Establish the mathematical model of the hydraulic valve position axis control system: , in, Indicates the quality of the load. This indicates the displacement of the piston rod in a hydraulic cylinder. This indicates the speed of the hydraulic cylinder piston rod. This indicates the acceleration of the piston rod in the hydraulic cylinder. This indicates the effective working area of the hydraulic cylinder piston; P1 represents the oil pressure in the hydraulic cylinder inlet chamber; and P2 represents the oil pressure in the hydraulic cylinder outlet chamber. This represents the frictional force acting on the load. This indicates that the system's mechanical disturbances are not modeled, and t represents time; Proceed to step 2; Step 2: Based on the mathematical model of the hydraulic valve position axis control system, design an intelligent axis controller with output performance based on a preset time: Step 2-1, Define the error ,in, Indicates the system tracking error. This is a system command to track position. This represents a preset time-performance safety function, used to facilitate the monitoring of system states under the control of the designed controller. Track the desired position command as accurately as possible. And let Always satisfied Tracking error must be guaranteed It tends towards 0; Among them, the preset time performance safety function Defined as: (10), in, Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Represents the cotangent function. Represents pi; Step 2-2, Define the error ,in, express The filtered signal, express Virtual control, to ensure tracking error Approaching 0, the error must be guaranteed. It tends towards 0; Steps 2-3: Define the error ,in, express The filtered signal, express Virtual control, to ensure error Approaching 0, the error must be guaranteed. It tends towards 0; , Among them, gain , This represents the model-based compensation term. Indicates robustness. Represents the linear robust term. Represents the nonlinear robust term. Let f(x) denote a function that is always positive and satisfies the following condition: ,in, Represents the integral variable. Represents a constant that is always positive, where the system dynamics are unknown. The upper realm ; , , Both represent intermediate variables. Represents a nonlinear filter; , All represent errors; Proceed to step 3; Step 3: Using Lyapunov stability theory, the stability of the intelligent axis controller based on the preset time output performance is proven, and the asymptotic stability of the system tracking error is obtained.
2. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 1, characterized in that, In step 1, a mathematical model of the hydraulic valve position axis control system is established, as follows: Step 1-1: The hydraulic valve position axis control system is applied to the linear motion of large industrial heavy-duty machinery and equipment. The load is fixedly connected to the piston rod on the hydraulic cylinder. The hydraulic valve controls the movement of the piston rod on the hydraulic cylinder, thereby driving the load to move. Based on the dynamic characteristics of the load, hydraulic cylinder and electro-hydraulic valve, the mathematical model of the hydraulic valve position axis control system is obtained. Steps 1-2: To facilitate controller design, define state variables and convert the mathematical model of the hydraulic valve position axis control system into state-space equations.
3. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 2, characterized in that, Step 1-1: The hydraulic valve position control system is applied to the linear motion of large industrial heavy-duty machinery. The load is fixedly connected to the piston rod on the hydraulic cylinder, and the hydraulic valve controls the movement of the piston rod, thereby driving the load. Based on the dynamic characteristics of the load, hydraulic cylinder, and hydraulic valve, the mathematical model of the hydraulic valve position control system is obtained, as follows: According to Newton's second law, the force balance equation of the hydraulic valve position control system is: (1), In equation (1), Indicates the quality of the load. This indicates the displacement of the piston rod in a hydraulic cylinder. This indicates the speed of the hydraulic cylinder piston rod. This indicates the acceleration of the piston rod in the hydraulic cylinder. This indicates the effective working area of the hydraulic cylinder piston; P1 represents the oil pressure in the hydraulic cylinder inlet chamber; and P2 represents the oil pressure in the hydraulic cylinder outlet chamber. 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), In a hydraulic valve position control system, ignoring external oil leakage from the cylinder, the pressure dynamic equation is: (3), In equation (3), Indicates the effective elastic modulus of the oil. This represents the internal leakage coefficient of the hydraulic cylinder, and the pressure difference between the inlet and outlet oil chambers on both sides of the cylinder. Control volume of oil inlet chamber Control volume of oil outlet chamber V 01 V represents the initial volume of the oil inlet chamber. 02 This indicates the initial volume of the oil outlet cavity. This indicates the flow rate of the oil inlet chamber. Indicates the flow rate of the oil cavity. express Unmodeled interference, express Unmodeled interference, express The first derivative, express The first derivative; , Relative to the displacement x of the hydraulic valve core v The following relationship exists: (4), Among them, the hydraulic valve coefficient , This indicates the flow coefficient of the hydraulic valve. This represents the valve core area gradient of a hydraulic valve. Indicates the density of the oil. Indicates the oil supply pressure. Indicates the return oil pressure. Indicate intermediate variables The function is defined as: (5), Ignoring the dynamics of the hydraulic valve spool, assume the control input u and the spool displacement x acting on the spool. v A proportional relationship, that is, satisfying x v = k i u, where k i This represents the voltage-valve core displacement gain coefficient, therefore equation (4) is rewritten as: (6), Equation (6), intermediate variables intermediate variables intermediate variables .
4. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 3, characterized in that, Steps 1-2: To facilitate controller design, define state variables and convert the obtained mathematical model of the hydraulic valve position axis control system into state-space equations, as follows: Define state variables: 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 First derivative, unknown dynamics of the system intermediate variables intermediate variables intermediate variables Unknown system dynamics , T represents transpose.
5. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 4, characterized in that, In step 1, for the convenience of controller design, the following assumptions are made: Assumption 1: The system expects to track position commands. It is second-order continuous, and the system expects the position command, velocity command, and acceleration command to be bounded; Assumption 2: Unknown system dynamics and satisfy: (8), Equation (8), and All are unknown positive constants; Proceed to step 2.
6. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 5, characterized in that, In step 2-1, the error is defined. ,in, Indicates the system tracking error. This is a system command to track position. This represents a preset time-performance safety function, used to facilitate the monitoring of system states under the control of the designed controller. Track the desired position command as accurately as possible. And let Always satisfied Tracking error must be guaranteed It tends towards 0, specifically as follows: Tracking error Meets preset range: (9), In equation (9), the preset time performance safety function is... Defined as: (10), in, Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Denotes a constant that is always positive. Represents the cotangent function. Represents pi; To facilitate controller design, the following nonlinear filter is designed: (11), Equation (11), Filter gain , Filtering error , 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 ; Tracking error Differentiating, we get: (12), in, Indicates error; express The first derivative; express The first derivative; Indicates the preset time performance safety function The first derivative; Choosing Lyapunov functions ,in Representing the logarithmic function, we get: (13), Design virtual control for: (14), Equation (14), gain ,but (15)。 7. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 6, characterized in that, In step 2-2, the error is defined. ,in, express The filtered signal, express Virtual control, to ensure tracking error Approaching 0, the error must be guaranteed. It tends towards 0, specifically as follows: Design the following nonlinear filter: (16), Equation (16), Filtering gain , Filtering error , 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 ;right Differentiating, we get: (17), Choosing Lyapunov functions We can obtain: (18), Design virtual control for: (19), Equation (19), gain , This represents the model-based compensation term. Indicates robustness. Represents the linear robust term. Represents the nonlinear robust term. 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. The upper realm ; express The estimated value, The specific form is as follows: (20), Equation (20), express The estimated value, Represents the weights of the neural network. Represents the activation function of a neural network. This represents the input to the neural network; The weight update law of the neural network is designed as follows: (21), Equation (21), express The first derivative, This represents the weight gain matrix of the neural network. Represents a discontinuous mapping function; Substituting equation (19) into equation (18), we get: (22), Equation (22), neural network weights estimation error , This represents the approximation error of the neural network.
8. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 7, characterized in that, In steps 2-3, the error is defined. ,in, express The filtered signal, express Virtual control, to ensure error Approaching 0, the error must be guaranteed. It tends towards 0, specifically as follows: right Differentiating, we get: (23), Choosing Lyapunov functions ,have to: (24), According to equation (24), the control input of the valve core, i.e., the intelligent axis controller u based on the preset time output performance, is: (25), Equation (25), gain , This represents the model-based compensation term. Indicates robustness. Represents the linear robust term. Represents the nonlinear robust term. 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. The upper realm ; Substituting equation (25) into equation (24), we get: (26), Proceed to step 3.
9. The intelligent shaft control method for hydraulic valves based on preset time output performance according to claim 8, characterized in that, Step 3 describes the application of Lyapunov stability theory to prove the stability of the intelligent axis controller based on the preset time output performance, yielding the asymptotically stable result of the system tracking error, as detailed below: The Lyapunov function is defined as follows: (27), The stability was proven using Lyapunov stability theory, and the asymptotic stability of the system tracking error was obtained.