A hydraulic valve position axis control method that is not limited by initial performance

Abstract

The application discloses a hydraulic valve position shaft control method without initial performance limitation, which innovatively introduces a preset time performance safety function without initial performance limitation, fuses a dynamic surface control thought, and designs a position shaft controller with output preset time performance. For the hydraulic valve position shaft control problem, the application can realize preset time control of system output transient performance and steady-state performance, is free from initial performance limitation, guarantees safe and reliable operation of the system, avoids the problem of differential explosion in traditional backstepping control of the hydraulic valve shaft control system, reduces the influence of measurement noise on control precision, and realizes high-precision tracking performance.

Description

Technical Field

[0001] This invention relates to the field of electromechanical servo control technology, and specifically to a hydraulic valve position axis control method (FIPRAC) that is not limited by initial 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 is safe and unrestricted in terms of system output performance, is not limited by initial performance, has strong anti-interference ability, and has high tracking performance. It can achieve preset time control of the transient and steady-state performance of the system output, avoid initial performance limitations, ensure the safe and reliable operation of the system, and avoid the differential explosion problem in the traditional backstepping control of hydraulic valve axis control system, reduce the impact of measurement noise on control accuracy, and achieve high-precision tracking performance.

[0005] The technical solution to achieve the objective of this invention is: a hydraulic valve position axis control method not limited by initial 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 a position axis controller with output preset time performance, and proceed to Step 3.

[0008] Step 3: Use Lyapunov stability theory to prove the stability of the position axis controller and obtain the result that the system tracking error is asymptotically stable.

[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; (2) it ensures that the system output is free from initial performance limitations and guarantees the safe and reliable operation of the system; (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, and achieves high-precision tracking performance. The simulation results verify its effectiveness. Attached Figure Description

[0010] Figure 1 This is a schematic diagram illustrating the principle of the hydraulic valve position axis control method of the present invention, which is not limited by initial performance.

[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 FIPRAC controller designed in this invention.

[0013] Figure 4 This is a graph showing the change of tracking error of the system over time under the action of the FIPRAC 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 FIPRAC controller designed in this invention and the traditional PID controller.

[0015] Figure 6 This is a control input curve diagram of the system under the action of the FIPRAC 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 hydraulic valve position axis control method that is not limited by initial 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 viscous damping coefficient of the hydraulic cylinder. 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 a position axis controller with preset output time performance. 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. Indicate intermediate variables The preset time performance transformation function, 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 first-ever preset time performance safety function is introduced. 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. Represents the tangent 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; express The first derivative; express 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 .

[0073] Substituting equation (19) into equation (18), we get:

[0074] (20)

[0075] 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:

[0076] right Differentiating, we get:

[0077] (twenty one),

[0078] Choosing Lyapunov functions ,have to:

[0079] (twenty two),

[0080] According to equation (22), the control input of the valve core, i.e., the position axis controller u with preset output time performance, is:

[0081] (twenty three),

[0082] Equation (23), 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 .

[0083] Substituting equation (23) into equation (22), we get:

[0084] (twenty four),

[0085] Proceed to step 3.

[0086] Step 3: Apply Lyapunov stability theory to prove the stability of the position axis controller, and obtain the result that the system tracking error is asymptotically stable, as follows:

[0087] The Lyapunov function is defined as follows:

[0088] (25),

[0089] Differentiating equation (25) and substituting equations (11), (16), and (24) into the equation, we obtain:

[0090] (26)

[0091] Considering , , and The expression can be obtained as follows:

[0092] (27)

[0093] Note:

[0094] (28)

[0095] Substituting equation (28) into equation (27), we get

[0096] (29)

[0097] Equation (29), intermediate variable Intermediate variables .

[0098] Integrating both sides of equation (29) respectively, we get:

[0099] (30)

[0100] Equation (30), intermediate variable .

[0101] From equation (30), 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.

[0102] Therefore, we can conclude that by adjusting the gains k1, k2, k3, and the filter gain... , A hydraulic valve position axis controller, designed for hydraulic valve position axis control systems and not limited by initial performance, can innovatively achieve asymptotic convergence of tracking error to zero. A schematic diagram of the hydraulic valve position axis control system position axis controller is shown below. Figure 1 As shown.

[0103] Example

[0104] 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:

[0105] Table 1 System Physical Parameters

[0106]

[0107] Given the desired instructions of the system m.

[0108] The following controller is used for comparison in the simulation:

[0109] Hydraulic valve position axis controller (FIPRAC) without initial performance limitations: gain take , , , , , , , , .

[0110] 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... , , .

[0111] The system's expected command, FIPRAC controller tracking error, and a comparison of the tracking errors of the FIPRAC 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 FIPRAC 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 FIPRAC controller proposed in this invention is much smaller than that of the PID controller, and its tracking performance is superior.

[0112] 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 FIPRAC 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 controlling the position of a hydraulic valve without initial performance limitations, characterized in that, Includes the following steps: Step 1: Establish the mathematical model of the hydraulic valve position axis control system, 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. 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 viscous damping coefficient of the hydraulic cylinder. 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. This 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 ; 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; Proceed to step 2; Step 2: Based on the mathematical model of the hydraulic valve position axis control system, design a position axis controller u with preset output time performance: ， in, This represents the model-based compensation term. Indicates robustness. Represents the linear robust term, Represents the nonlinear robust term. Represents a function that is always positive. , , Both represent intermediate variables. Represents a nonlinear filter; , Both represent error and gain. Unknown system dynamics The upper realm ; Proceed to step 3; Step 3: Use Lyapunov stability theory to prove the stability of the position axis controller and obtain the result that the system tracking error is asymptotically stable.

2. The hydraulic valve position axis control method according to claim 1, which is not limited by initial performance, is 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.

3. The hydraulic valve position axis control method according to claim 2, which is not limited by initial performance, is 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.

4. The hydraulic valve position axis control method according to claim 3, which is not limited by initial performance, is characterized in that, In step 2, based on the mathematical model of the hydraulic valve position axis control system, a position axis controller with preset output time performance is designed, as follows: Step 2-1, Define the error ,in, Indicates the system tracking error. This is the system's expected position tracking command. Indicate intermediate variables The preset time performance transformation function, 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; 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.

5. The hydraulic valve position axis control method according to claim 4, which is not limited by initial performance, is characterized in that, In step 2-1, the specific details are 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. Represents the cotangent function. Represents pi (π). Indicates time; 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; express The first derivative; express The first derivative; Choosing Lyapunov functions ,in Representing the logarithmic function, we get: （13）， Design virtual control for: （14）， Equation (14), gain ,but （15）。 6. The hydraulic valve position axis control method according to claim 5, which is not limited by initial performance, is 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 ; Substituting equation (19) into equation (18), we get: （20）。 7. The hydraulic valve position axis control method according to claim 6, which is not limited by initial performance, is 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: （21）， Choosing Lyapunov functions ,have to: （22）， According to equation (22), the control input of the valve core, i.e., the position axis controller u with preset output time performance, is: （23）， Equation (23), 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 (23) into equation (22), we get: （24）， Proceed to step 3.

8. The hydraulic valve position axis control method according to claim 7, which is not limited by initial performance, is characterized in that, Step 3 describes the application of Lyapunov stability theory to prove the stability of the position axis controller, resulting in the asymptotic stability of the system tracking error, as detailed below: The Lyapunov function is defined as follows: （25）， The stability was proven using Lyapunov stability theory, and the asymptotic stability of the system tracking error was obtained.

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