A voice coil motor direct drive system robust anti-interference control method

Abstract

The application belongs to the technical field of electric-gas servo control, and discloses a control method for enhancing robust anti-interference of a voice coil motor direct drive system. S1, a dynamic equation, a model error and a state equation of the voice coil motor direct drive system are established; S2, the lumped interference is expanded into an additional state variable to update the state equation, a condition that an extended state anti-interference observer and an estimation error thereof satisfy is set on the basis of the updated state equation, and the estimation of the lumped interference is calculated by using the extended state anti-interference observer; S3, a tracking error and an auxiliary error signal are set, a controller for enhancing robust anti-interference is constructed, and a difference between the estimation of the lumped interference and the lumped error is compensated, so as to realize the control of the voice coil motor direct drive system. By the application, the selection limit of a robust gain parameter is reduced, and the control precision and the robustness of the system are ensured in the case that the system suffers from strong interference.

Description

Technical Field

[0001] This invention belongs to the technical field of electrical servo control, and more specifically, relates to a control method for enhancing the robustness and anti-interference of a voice coil motor direct drive system. Background Technology

[0002] High-voltage electro-pneumatic servo control technology is a crucial component of fluid transmission technology and a significant representative of mechatronics. In recent years, as the manufacturing sector's demands have continuously shifted towards higher response, higher precision, higher power-to-weight ratio, and environmental friendliness, my country's electro-pneumatic servo control technology has also made leaps and bounds in progress.

[0003] High-voltage electro-pneumatic servo control technology is a highly sought-after technical field, widely used in aviation, aerospace, military, metallurgy, and engineering machinery. In the field of pneumatic control, high-voltage electro-pneumatic servo control systems offer advantages over traditional low-pressure pneumatic control systems, including higher energy density, larger instantaneous output energy, and faster response speed. However, the increase in gas pressure generates extremely strong aerodynamic interference at the servo valve core, significantly affecting the control accuracy of the high-voltage electro-pneumatic servo valve and thus hindering its further development. Traditional control methods struggle to cope with such severe interference, leading to decreased servo valve performance, reduced response speed, and difficulty in eliminating tracking errors. Therefore, exploring enhanced robust control methods capable of rapidly compensating for strong external disturbances has become an urgent need in practical engineering applications. Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a control method for enhancing robust anti-interference capabilities in a voice coil motor direct drive system, thereby solving the problem of enhanced robust control for rapid compensation of strong external disturbances in a voice coil motor direct drive system.

[0005] To achieve the above objectives, according to one aspect of the present invention, a control method for enhancing robust anti-interference capabilities in a voice coil motor direct drive system is provided, the method comprising the following steps:

[0006] S1 establishes the dynamic equations, model errors, and state equations of the voice coil motor direct drive system;

[0007] S2 extends the lumped disturbance into an additional state variable to update the state equation. Based on the updated state equation, the extended state disturbance robust observer and the conditions satisfied by its estimation error are set, and the extended state disturbance robust observer is used to calculate the estimate of the lumped disturbance.

[0008] S3 sets tracking error and auxiliary error signals, and constructs an enhanced robust anti-interference controller to compensate for the difference between the estimation of lumped interference and the lumped error, thereby realizing the control of the voice coil motor direct drive system.

[0009] More preferably, in step S1, the dynamic equations are performed according to the following relationships:

[0010]

[0011] Where m is the total mass of the driven part (including the sum of the mass of the valve core, the voice coil motor, and the intermediate direct-drive mechanism), and x sv F represents the actual displacement of the valve core. e F is the driving force of the motor. tg For transient aerodynamic forces, F sg For steady-state aerodynamic forces, F f F is the frictional force acting on the system. i For internal disturbances (fluctuations in the driving signal, etc.), F ud For unknown interference, B v t represents the viscous damping coefficient and time.

[0012] More preferably, in step S1, the model error is determined according to the following relationship:

[0013]

[0014] Where m is the unknown exact total mass of the driven part, and K e For unknown accurate voice coil motor parameters, R is the unknown accurate equivalent resistance value of the voice coil motor, and B is... v The exact system damping coefficient is unknown, m0 is the exact total mass of the driven part known, and K is... e0 Given the known parameters of the voice coil motor, R0 is the known equivalent resistance value of the voice coil motor, and B... v0 The known system damping coefficient is given, Δm is the difference between the known total mass and the unknown exact total mass of the driven part, and ΔK is the value of the system damping coefficient. e ΔR is the difference between the known voice coil motor parameters and the unknown accurate voice coil motor parameters, ΔB is the difference between the known equivalent resistance value of the voice coil motor and the unknown equivalent resistance value of the voice coil motor. v This is the difference between the known system damping coefficient and the unknown, accurate system damping coefficient.

[0015] More preferably, in step S1, the state equation is performed according to the following relationship:

[0016]

[0017] Where u is the system input, and the system state variables x1 and x2 are represented as follows: The system damping parameter a1 and gain parameter b0 are:

[0018] Lumped interference Ftd Represented as:

[0019]

[0020] F d =F tg +F sg +F f +F i +F ud

[0021] Where: m is the unknown exact total mass of the driven part, m0 is the known exact total mass of the driven part, and K e0 Given the known parameters of the voice coil motor, R0 is the known equivalent resistance value of the voice coil motor, and B... v0 Given the known system damping coefficient, K e For unknown accurate voice coil motor parameters, R is the unknown accurate equivalent resistance value of the voice coil motor, and B is... v The exact system damping coefficient is unknown, u is the input voltage of the voice coil motor, and F is... tg For transient aerodynamic forces, F sg For steady-state aerodynamic forces, F f F is the frictional force acting on the system. i For internal disturbances (fluctuations in the driving signal, etc.), F ud For unknown interference, F d This represents the total external interference.

[0022] More preferably, in step S2, the updated state equation is expressed according to the following relationship:

[0023]

[0024] Where u is the system input, and Let x1, x2, and x3 be the rates of change of system state variables, a1 be the known system damping parameter, and b0 be the known gain parameter. The acceleration of the servo valve displacement. F represents the velocity of the servo valve displacement. td =f represents lumped interference. The rate of change of the lumped disturbance.

[0025] More preferably, in step S2, the anti-spreading state anti-interference observer is configured according to the following relationship:

[0026]

[0027]

[0028]

[0029] Wherein, the observer estimation matrix z = [z1 z2 z3] T z1, z2, and z3 are the observed estimates output by the extended state observer, corresponding to the servo valve displacement x, respectively. sv The speed of servo valve displacement The lumped disturbance is f, a1 is the system damping, b0 is the known gain parameter, A is the system state matrix, B is the observer gain matrix, C is the observer output matrix; L is the feedback matrix that needs to be designed for the extended state observer, which includes the system damping a1 and the observer bandwidth w0.

[0030] More preferably, in step S2, the error estimation satisfies the following conditions:

[0031] When the observer bandwidth w0 satisfies The estimation error of ESO is bounded and its upper bound exists, i.e. Where φ1 is the maximum value of the ESO's estimation error for system state and external disturbances, and λ max (P) is the largest eigenvalue of the intermediate matrix variable P, M f-1 The maximum value of the rate of change of the lumped disturbance f is represented by w0, where w0 is the observer bandwidth (observer parameter), and a1 is the known system damping parameter.

[0032] More preferably, in step S3, the tracking error and auxiliary error signals are determined according to the following relationship:

[0033] e c1 =x d -x sv

[0034]

[0035]

[0036] Where, x d For target instructions, For the speed target command, x sv For servo valve displacement, For the servo valve's movement speed, α and k r For controller parameters, e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2 The corrected speed difference of the high-pressure electro-pneumatic servo valve. To correct the acceleration difference of the high-pressure electro-pneumatic servo valve, r is the correction value for the velocity difference of the high-pressure electro-pneumatic servo valve, e.c2 It is the corrected acceleration difference The auxiliary intermediate variable of the sum.

[0037] More preferably, the enhanced robust anti-interference controller is configured according to the following relationship:

[0038]

[0039] Where k1,k2,k3,k r b0 is the controller parameter; α and β are both controller parameters and are positive real numbers, sgn(e c2 ) for e c2 The standard symbolic function, tanh(k3e c1 ) is e c1 The hyperbolic tangent function, e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This indicates the correction of the speed difference between the high-voltage electro-pneumatic servo valve and z3, which is the lumped interference estimate output by the extended state anti-interference observer.

[0040] More preferably, the control parameter β satisfies the following relationship:

[0041] β≥γ1-χ1(e c2 )and

[0042] Where γ1 and γ2 are intermediate variables, χ1(e c2 ) and χ2(e c1 ) represents the parameter selection constraint function proposed in the invention, k r These are the controller parameters.

[0043] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0044] 1. This invention effectively combines Interference Reduction (ERC) and Interference Estimation Compensation (ESO). The use of ERC further ensures compensation for external disturbances when there are estimation residuals in ESO, thereby improving control performance. Simultaneously, the nonlinear robust feedback gain term of the improved ERC can provide multiple compensations for external disturbances, reducing the limitations on the selection of robust gain parameters. The parameter selection is related to the derivative of the disturbance estimation error and the strong disturbance compensation gain parameter, making it easier to meet the conditions than the original RISE-ESO. The controller tracking performance is significantly improved compared to traditional robust control methods LADRC and RIES-ESO. Experimental results verify its effectiveness.

[0045] 2. This invention utilizes Lyapunov stability theory to prove the stability of a composite enhanced robust control method for a voice coil motor-driven high-voltage electro-pneumatic servo valve with an additional extended state anti-interference observer. The result is a theoretical assessment of the system's large-scale asymptotic stability and its anti-interference performance. This invention can guarantee the system's control accuracy and robustness even under strong disturbances.

[0046] 3. This invention ensures the system's wide-range asymptotic stability and rapid recovery to a stable state even under conditions of varying system model parameters and strong external interference; it achieves excellent tracking performance and anti-interference capability, and experiments have verified the effectiveness of the invention; the controller structure is novel, clear, and well-defined, and the control method is reliable and stable, with broad application prospects. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the anti-interference control principle of a voice coil motor direct-drive high-voltage electro-pneumatic pressure servo valve constructed according to a preferred embodiment of the present invention;

[0048] Figure 2 This is a schematic diagram of the structure of a voice coil motor direct-drive high-voltage electro-pneumatic pressure servo valve constructed according to a preferred embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of a step response constructed according to a preferred embodiment of the present invention;

[0050] Figure 4 The graph shows the tracking error of the system constructed according to the preferred embodiment of the present invention over time, wherein (a) is a schematic diagram of the ERC-ESO error curve, (b) is a schematic diagram of the RISE-RSO error curve, and (c) is a schematic diagram of the LADRC error curve. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0052] This invention proposes a novel enhanced robust control method (ERC-ESO) based on an integrated extended state anti-interference observer (ESO). The ESO estimates unmodeled dynamics and external disturbances in the system and incorporates these estimates as feedforwards into the controller. The ERC further compensates for the disturbance estimation residuals of the ESO, reducing its observation burden. The newly proposed ERC (Enhanced Robust Controller) method further improves the anti-interference capability of the controller compared to traditional RISE controllers and significantly reduces the parameter selection restrictions for nonlinear robust terms. This ensures good system performance even when the system is sensitive to integral robust structures and the observation capability of the anti-interference observer is limited. Finally, the stability of a voice coil motor direct-drive high-voltage electric servo valve position servo system is proven using Lyapunov stability theory, demonstrating that the system can achieve asymptotic stability even with significant external disturbances.

[0053] like Figure 1 As shown, the enhanced robust anti-interference control algorithm for a voice coil motor direct-drive high-voltage electro-pneumatic servo valve proposed in this invention mainly comprises two parts: interference estimation using an extended state anti-interference observer and enhanced robust compensation. These two parts are coupled together to achieve state regulation of the high-voltage electro-pneumatic servo valve. The target command and displacement information acquired by the sensor are ultimately input into the enhanced robust compensation term for calculation. The calculation result of the enhanced robust compensation term is combined with the interference estimation result, and after gain transformation, it is input into the high-voltage electro-pneumatic servo valve to achieve online adjustment of the valve. During this process, sensor acquisition and control algorithm calculation are continuously performed, achieving continuous adjustment and control of the high-voltage electro-pneumatic servo valve.

[0054] like Figure 2 As shown, the working principle of the high-voltage electro-pneumatic servo valve control system mainly consists of three parts: a servo controller, a servo driver, and a high-voltage electro-pneumatic servo valve. The servo controller utilizes an enhanced robust anti-interference control algorithm for a voice coil motor direct-drive high-voltage electro-pneumatic servo valve proposed in this invention. Its specific working process is described in [link to documentation]. Figure 2 The relevant description is as follows: A reference signal is input to the servo controller. After processing, the servo controller outputs a corresponding control signal. This signal is amplified by the servo driver and has driving capability, enabling the drive of the voice coil motor, thereby controlling the movement of the valve core of the high-voltage electro-pneumatic servo valve.

[0055] A high-pressure electro-servo valve mainly consists of three parts. First, the voice coil motor, permanent magnet, and magnet housing constitute the drive part of the servo valve, providing the driving force for the valve core's movement. Driven by the voice coil motor, the valve core moves, controlling the valve opening. The external servo valve body constrains the movement of the valve core. During the operation of a high-pressure electro-servo valve, it is constantly subjected to complex interference forces, mainly including: the frictional force between the magnet outer housing and the permanent magnet, the frictional force between the valve core and the valve body, and the high-pressure aerodynamic force generated by the high-pressure gas on the valve core. Therefore, an anti-interference control algorithm is needed to ensure the control accuracy of the high-pressure electro-pneumatic pressure servo valve.

[0056] The present invention provides an enhanced robust anti-interference control method for a voice coil motor direct-drive high-voltage electric servo valve, comprising the following steps:

[0057] S1. Establish a mathematical model for a voice coil motor high-voltage electric servo valve system.

[0058] S11, the voice coil motor high-voltage electric servo valve system considered in this invention maintains a constant voltage across the voice coil motor, controls the magnitude of the current across the voice coil motor to drive the voice coil motor to move in parallel, thereby driving the servo valve core to move and controlling the opening and closing of the servo valve.

[0059] The equivalent circuit of the voice coil motor is as follows:

[0060]

[0061] In the formula, R is the equivalent resistance of the voice coil motor, L is the coil inductance of the voice coil motor, i is the current, and e is the current. m It is the back electromotive force generated in the voice coil motor.

[0062] The driving force F of the voice coil motor e Expressed as:

[0063] F e =K e i = Bli (2)

[0064] Wherein: F e K is the Ampere force of the motor. e Here are the motor parameters: B is the magnetic field strength, l is the equivalent total length of the conductor in the magnetic field for the voice coil motor, and i is the current.

[0065] Therefore, based on the force balance equation, the dynamic equation of the voice coil motor direct-drive high-voltage electro-pneumatic servo valve can be obtained as follows:

[0066]

[0067] Where m is the unknown total mass of the driven part (including the sum of the mass of the valve core, the voice coil motor, and the intermediate direct-drive mechanism), and x svF represents the actual displacement of the valve core. e F is the driving force of the motor. tg For transient aerodynamic forces, F sg For steady-state aerodynamic forces, F f F is the frictional force acting on the system. i For internal disturbances (fluctuations in the driving signal, etc.), F ud For unknown interference, B v The exact system damping coefficient is unknown, and t represents time.

[0068] Considering the uncertainty in system modeling, the model error of the system can be expressed as:

[0069]

[0070] Where m is the unknown exact total mass of the driven part, and K e For unknown accurate voice coil motor parameters, R is the unknown accurate equivalent resistance value of the voice coil motor, and B is... v The exact system damping coefficient is unknown, m0 is the exact total mass of the driven part known, and K is... e0 Given the known parameters of the voice coil motor, R0 is the known equivalent resistance value of the voice coil motor, and B... v0 The known system damping coefficient is given, Δm is the difference between the known total mass and the unknown exact total mass of the driven part, and ΔK is the value of the system damping coefficient. e ΔB is the difference between the known voice coil motor parameters and the unknown accurate voice coil motor parameters, ΔR is the difference between the known equivalent resistance value of the voice coil motor and the unknown accurate equivalent resistance value of the voice coil motor, and ΔB is the difference between the known and unknown accurate equivalent resistance values ​​of the voice coil motor. v This is the difference between the known system damping coefficient and the unknown, accurate system damping coefficient.

[0071] According to equations (1)-(4), the system state equation of the voice coil motor direct-drive high-voltage electric servo valve can be expressed as:

[0072]

[0073] Where: system state variables x2 represents the servo valve's movement speed. Let F be the acceleration of the servo valve. a1 is the known system damping parameter, b0 is the known gain parameter, and F is the acceleration of the servo valve. td For lumped interference, F d Let m be the total external disturbance, m be the unknown exact total mass of the driven part, m0 be the known exact total mass of the driven part, and K be the total external disturbance. e0 Given the known parameters of the voice coil motor, R0 is the known equivalent resistance value of the voice coil motor, and B... v0 Given the known system damping coefficient, K eFor unknown accurate voice coil motor parameters, R is the unknown accurate equivalent resistance value of the voice coil motor, and B is... v F represents the unknown, accurate system damping coefficient, and u represents the input voltage of the voice coil motor. tg For transient aerodynamic forces, F sg For steady-state aerodynamic forces, F f F is the frictional force acting on the system. i For internal disturbances (fluctuations in the driving signal, etc.), F ud For unknown interference.

[0074] Assumption 1: In engineering practice, although it is difficult to obtain accurate model information, their values ​​must be continuous and bounded. Furthermore, although various disturbances may change drastically, they are also continuous and bounded. Therefore, the lumped disturbance F... td Belongs to C 2 ,satisfy and and These represent the rate of change and acceleration of the lumped disturbance, respectively, with intermediate variable M. f-1 M f-2 Positive values ​​represent the rate of change of lumped disturbance, respectively. The rate of change and acceleration of the lumped disturbance The maximum value.

[0075] S2 is based on the design of the anti-interference controller for the above-mentioned voice coil motor direct-drive high-voltage electric servo valve;

[0076] Interference compensation design based on extended state-resistant observer with model information:

[0077] The lumped interference F td Extended to an additional state variable x3 of the system, i.e., x3 = f = F td Then equation (5) can be rewritten as:

[0078]

[0079] Where u is the system input, x2 represents the servo valve's movement speed. Let a be the acceleration of the servo valve, a1 be the known system damping parameter, and b0 be the known gain parameter. The acceleration of the servo valve displacement. F represents the velocity of the servo valve displacement. td =f represents lumped interference. The rate of change of the lumped disturbance.

[0080] The ESO design with model information is as follows:

[0081]

[0082] The observer estimation matrix z = [z1 z2 z3] T z1, z2, and z3 are the observed estimates output by the extended state anti-interference observer, and they correspond to the servo valve displacement x, respectively. sv The speed of servo valve displacement The lumped disturbance is f; a1 is the system damping; A is the observer state matrix; B is the observer gain matrix (which can be calculated based on the system parameters); C is the observer output matrix; L is the feedback matrix that needs to be designed for the extended state observer, which includes the system damping a1 and the observer bandwidth (observer parameters) w0.

[0083] The feedback matrix L is designed as follows:

[0084]

[0085] Where a1 is the known system damping and w0 is the observer bandwidth (observer parameter) that needs to be set.

[0086] The lemma is given as follows: When the observer bandwidth w0 satisfies The estimation error of ESO is bounded and its upper bound exists, i.e. φ1 is the maximum value of the ESO's estimation error for the system state and external disturbances. Furthermore, the first and second derivatives of the disturbance estimation error are also bounded (φ2 and φ3, respectively).

[0087]

[0088] in: Let λ be the scaled observer matrix. max (P) represents the largest eigenvalue of the intermediate matrix P; w0 is the observer bandwidth; intermediate variable M f-1 and M f-2 φ1 and φ2 are positive values, representing the maximum values ​​of the rate of change of the lumped disturbance f and the acceleration of the change of the lumped disturbance f, respectively; φ2 and φ3 are intermediate variables, where φ2 represents the maximum value of the rate of change of the ESO's estimation error of the system state and external disturbances, and φ3 represents the maximum value of the acceleration of the ESO's estimation error of the system state and external disturbances.

[0089] The verification process for the above estimation error is as follows:

[0090] The proof of this lemma is as follows:

[0091] The state estimation error matrix E of the extended state-intolerant observer is defined as follows:

[0092]

[0093] Where z1, z2, z3 are the observation estimates of the extended state anti-interference observer, and x sv For servo valve displacement, Let z1 be the velocity of the servo valve displacement, and f be the lumped disturbance. e1, e2, and e3 are the observed values ​​z1 and x1 of the extended state anti-interference observer, respectively. sv The error between them, the extended state anti-interference observer observation value z2 on the servo valve movement speed The error between the observations; the error between the extended state anti-interference observer observation value z3 and the lumped interference f.

[0094] Definition: Scaling state estimation error matrix of an extended state robust observer e1, e2, and e3 are the observed values ​​z1 and servo valve displacement x of the extended state anti-interference observer, respectively. sv The error between them, the extended state anti-interference observer observation value z2 on the servo valve movement speed The error between the observations; the error between the extended state anti-interference observer observation value z3 and the lumped interference f.

[0095] Equation (7) can then be rewritten as:

[0096]

[0097] Where: ε is the scaling state estimation error matrix. These are the scaled observer matrix and the scaled gain matrix, respectively. Let w0 be the rate of change of the lumped disturbance, w0 be the observer bandwidth, and a1 be the known system damping.

[0098] According to the criterion theorem for Hurwitz matrices, a matrix is ​​a Hurwitz matrix when all its eigenvalues ​​lie in the complex half-plane of the complex plane. Therefore, we take:

[0099]

[0100] The intermediate variables λ, λ1, λ2, and λ3 are the scaled observer matrices. The matrix eigenvalues, where I is the identity matrix and a1 is the known damping parameter of the system.

[0101] When the observer bandwidth Observer matrix If the matrix is ​​a Herwitz matrix, then there exists an intermediate matrix variable P that satisfies... Where I is the identity matrix, and the Lyapunov function V is defined. ε :

[0102] V ε =ε T Pε (12)

[0103] Taking its derivative, we get:

[0104]

[0105] V ε Let P be a Lyapunov function, and P be an intermediate matrix variable. Here, denoted by , we have the scaled observer matrix and the scaled gain matrix, and ε is the scaled state estimation error matrix. To estimate the rate of change of the error matrix in the scaled state, For lumped interference F td The rate of change, intermediate variable M f-1 and M f-2 The positive values ​​represent the maximum values ​​of the rate of change of the lumped disturbance f and the acceleration of the change of the lumped disturbance f, respectively.

[0106] therefore, φ1 is an intermediate variable, representing the maximum value of the ESO's estimation error for system state and external disturbances; intermediate variable M f-1 λ represents the rate of change of the lumped disturbance f; w0 represents the observer bandwidth. max (P) is the largest eigenvalue of the intermediate matrix P. Meanwhile, based on (10) and (12), it can be calculated that:

[0107]

[0108]

[0109] Where: ε is the scaling state estimation error matrix. The scaling state estimation error matrix represents the rate of change, and P is an intermediate matrix variable. Let F be the scaled observer matrix and the scaled gain matrix. td This is to prevent centralized interference.

[0110] It has been proven that by and These represent the rate of change and acceleration of the lumped disturbance, respectively, with intermediate variable M. f-1 M f-2 Positive values ​​represent the rate of change of lumped disturbance, respectively. The rate of change and acceleration of the lumped disturbance The maximum value of . We can conclude that the estimated state is always bounded, and after any time, and Where: ε is the scaling state estimation error matrix; λ max (P) is the largest eigenvalue of the intermediate matrix P; The scaled observer matrix, where w0 is the observer bandwidth; intermediate variable M f-1 and M f-2 φ1, φ2, and φ3 are positive values, representing the maximum values ​​of the rate of change of the lumped disturbance f and the acceleration of the change of the lumped disturbance f, respectively; φ1, φ2, and φ3 are intermediate variables, where φ1 is the maximum value of the ESO's estimation error of the system state and external disturbance, φ2 is the maximum value of the rate of change of the ESO's estimation error of the system state and external disturbance, and φ3 is the maximum value of the acceleration of the ESO's estimation error of the system state and external disturbance.

[0111] Design of S3 Enhanced Robust Interference Suppression Controller

[0112] S31 defines the tracking error e c1 e c2 The auxiliary error signal r is as follows:

[0113] e c1 =x d -x sv (16)

[0114]

[0115]

[0116] Where, x d For target instructions, For the speed target command, x sv For servo valve displacement, For the servo valve's movement speed, α and k r For controller parameters, e is an intermediate variable c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2 This indicates the correction of the speed difference between the high-pressure electro-pneumatic servo valve. This represents the difference in motion acceleration of the high-pressure electro-pneumatic servo valve, where r represents the auxiliary intermediate variable representing the sum of the high-pressure electro-pneumatic servo valve's velocity and its corrected acceleration.

[0117] The control law of the S32 enhanced robust anti-interference controller is as follows:

[0118]

[0119] Where: k1, k2, k3, k r Here are the controller parameters; α and β are both controller parameters and are positive real numbers, b0 is a known gain parameter, and sgn(e c2 ) for ec2 The standard symbolic function, tanh(k3e c1 ) is e c1 The hyperbolic tangent function. c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This indicates the corrected speed difference of the high-pressure electro-pneumatic servo valve. t represents the speed of the servo valve and t represents time.

[0120] Considering equation (18), the expansion of the auxiliary intermediate variable r is as follows:

[0121]

[0122] Where: k i (i = 1, 2, 3, r) are the controller parameters; α, k r Both β and b0 are controller parameters and are positive real numbers, b0 is a known gain parameter, u is the system input, and sgn(e c2 ) for e c2 The standard symbolic function, tanh(k3e c1 ) is e c1 The hyperbolic tangent function. This indicates the rate of change of the target command's acceleration. This represents the acceleration value of the servo valve's movement. This represents the speed value of the servo valve's movement. intermediate variables The rate of change, e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 The value represents the difference in motion speed of the high-pressure electro-pneumatic servo valve, r represents the auxiliary intermediate variable of the sum of the corrected speed and the corrected acceleration of the high-pressure electro-pneumatic servo valve; t is time; w1 = f - z3 is the total disturbance error, f is the system lumped disturbance, and z3 is the estimated value of the system lumped disturbance obtained from the extended state anti-interference observer.

[0123] Then, differentiating both sides of equation (20), we get:

[0124]

[0125] Where: k i (i = 1, 2, 3, r) are controller parameters; α and β are both controller parameters and are positive real numbers, sgn(e c2 ) for e c2 The standard symbolic function, tanh(k3e c1 ) is e c1 The hyperbolic tangent function. This indicates the rate of change of the target command's acceleration. Indicates the target command acceleration value. Let α and k be the acceleration values ​​of the servo valve's motion. r For controller parameters, intermediate variables The acceleration value, e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. This is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. e is the difference between the actual acceleration of the high-voltage electro-pneumatic servo valve and the actual acceleration of the target. c2 This indicates the correction of the speed difference between the high-pressure electro-pneumatic servo valve. This represents the difference in corrected motion acceleration of the high-pressure electro-pneumatic servo valve; r represents the auxiliary intermediate variable representing the sum of the corrected velocity and the corrected acceleration of the high-pressure electro-pneumatic servo valve; t represents time. w1 is an intermediate variable, and w1 is the total disturbance error.

[0126] In the intermediate variable N, x d It is a command signal, therefore Both are continuous and bounded. For any system, the change in system state is also continuous and bounded. Therefore... It is also continuous and bounded. This is the difference between the actual acceleration of the high-pressure electro-pneumatic servo valve and the actual acceleration of the target. To correct the motion acceleration difference of the high-voltage electro-pneumatic servo valve, the intermediate variable δ1 is defined as follows: The intermediate variable δ2 is This is the difference between the actual acceleration of the high-pressure electro-pneumatic servo valve and the actual acceleration of the target. The rate of change of the difference between the actual acceleration of the high-pressure electro-pneumatic servo valve and the actual acceleration of the target. This indicates the correction value of the motion acceleration difference by the high-pressure electro-pneumatic servo valve. x represents the rate of change of the difference in motion acceleration corrected by the high-voltage electro-pneumatic servo valve. d For target instructions, For speed target instructions, An intermediate variable representing the rate of change of the target command's acceleration. Indicate intermediate variables The speed of change.

[0127] Combining equations (14) and (15), intermediate variables and satisfy and Therefore, intermediate variable N and intermediate variable The following inequalities must be satisfied:

[0128]

[0129]

[0130] In the formula, γ1 and γ2 are intermediate variables. This indicates the rate of change of the target command's acceleration. This represents the target command acceleration value, where δ1 and δ2 are intermediate variables, and w0 is the observer bandwidth (observer parameter).

[0131] To ensure that the controlled system can achieve asymptotic stability under the presence of disturbances and system uncertainties, the controller parameter β needs to satisfy the following conditions:

[0132] β≥γ1-χ1(e c2 )and

[0133]

[0134] χ1(e c2 ) and χ2(e c1 (Regarding e) c2 and e c1 Parameter selection constraint function, k i (i = 2, 3) are the controller parameters; k r α and β are controller parameters; e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e is the difference between the actual movement speed and the target movement speed of the high-pressure electro-pneumatic servo valve. c2 This indicates the correction of the speed difference between the high-pressure electro-pneumatic servo valve. tanh(·) is the hyperbolic tangent function.

[0135] S4 uses Lyapunov's stability theory to prove the stability of a closed-loop control system for a voice coil motor-driven high-voltage electric servo valve, and uses Barbalat's lemma to show that the system can achieve asymptotic stability, as detailed below:

[0136] The following theorem is given first:

[0137] Define the auxiliary function L(t):

[0138]

[0139] k i (i = 2, 3) are the controller parameters, k r α and β are controller parameters, sgn(e c2) is the standard symbolic function of e2, tanh(k3e c1 ) is e c1 The hyperbolic tangent function, e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e represents the speed difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2 This indicates the corrected speed difference of the high-pressure electro-pneumatic servo valve. The value represents the difference in corrected motion acceleration of the high-pressure electro-pneumatic servo valve, r represents the auxiliary intermediate variable that is the sum of the corrected velocity and the corrected acceleration of the high-pressure electro-pneumatic servo valve; N is the intermediate variable, and t is time.

[0140] Among them, respectively ① , ② , ③ and ④ Calculation yields:

[0141]

[0142] ②≤∫k r |e c2 |Ndt≤∫k r |e c2 |γ1dt (28)

[0143] ③=β(|e c2 (t)|-|e c2 (0)|) (29)

[0144] ④=∫βk r |e c2 (t)|dt (30)

[0145]

[0146] in:

[0147]

[0148] k i (i = 2, 3) are the controller parameters, k r α and β are controller parameters, sgn(e c2 ) is the standard symbolic function of e2, tanh(k3e c1 ) is e c1 The hyperbolic tangent function, e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e represents the speed difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2This indicates the correction of the speed difference between the high-pressure electro-pneumatic servo valve. The value represents the difference in corrected motion acceleration of the high-pressure electro-pneumatic servo valve, r represents the auxiliary intermediate variable that is the sum of the corrected velocity and the corrected acceleration of the high-pressure electro-pneumatic servo valve; N is an intermediate variable, γ1 and γ2 are intermediate variables, and t is time.

[0149] therefore:

[0150]

[0151] Where, k i (i = 2, 3) are the controller parameters, k r And α are controller parameters, tanh(k3e c1 ) is k3e c1 The hyperbolic tangent function, e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2 This indicates the corrected speed difference of the high-pressure electro-pneumatic servo valve. This represents the difference in motion acceleration corrected by the high-pressure electro-pneumatic servo valve, where c1 is a constant related to the initial state of the integral, and t is time.

[0152] definition:

[0153]

[0154]

[0155] Where: χ1(e c2 ) and χ2(e c1 ) is the parameter selection constraint function, k i (i = 2, 3) are controller parameters, α is a controller parameter, and e c1 This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. e is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. c2 This represents the corrected speed difference of the high-pressure electro-pneumatic servo valve, where c1 is a constant related to the initial state of the integral, and tanh(k3e c1 ) is k3e c1 The hyperbolic tangent function.

[0156] The combined equations (33-35), ⑤ can be rewritten as:

[0157] ⑤=χ1(e c2 )|e c2 |+∫k r χ2(ec1 )|e c2 |dt (36)

[0158] Where: χ1(e c2 ) and χ2(e c1 ) is the parameter selection constraint function, k r For controller parameters, e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This represents the corrected speed difference of the high-pressure electro-pneumatic servo valve, where t is time.

[0159] Combining equations ①-⑤, equation (26) can be rewritten as:

[0160]

[0161] L(t) is an auxiliary function; k r β and e are controller parameters; c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This indicates the corrected speed difference of the high-pressure electro-pneumatic servo valve; e c1 (0) represents the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve at the initial moment; e c2 (0) represents the difference in motion speed of the high-pressure electro-pneumatic servo valve after initial correction; N and γ1 and γ2 are intermediate variables; N(0) is the initial value of intermediate variable N; γ1 and γ2 are intermediate variables, χ1(e c2 ) and χ2(e c1 ) is the parameter to select the constraint function, and t is the time.

[0162] Combining the conditions that need to be satisfied in equations (24-25), we have:

[0163] L(t)≤β|e c2 (0)|-N(0)e c2 (0) (38)

[0164] Where: L(t) is the auxiliary function, β is the controller parameter, N(0) is the initial time value of the intermediate variable N, and e c2 (0) indicates the initial correction of the speed difference of the high-pressure electro-pneumatic servo valve.

[0165] Define an auxiliary function P such that when β satisfies the condition in equation (24), then we have

[0166] P=β|e c2 (0)|-N(0)e c2 (0)-L(t)≥0 (39)

[0167] Where: L(t) is the auxiliary function, β is the controller parameter, N(0) is the initial time value of the intermediate variable N, and e c2 (0) represents the difference in the movement speed of the high-pressure electro-pneumatic servo valve after the initial time correction.

[0168] The Lyapunov function V is defined as follows:

[0169]

[0170] Where: P is an auxiliary function, e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This represents the corrected speed difference of the high-pressure electro-pneumatic servo valve, and r represents the auxiliary intermediate variable representing the sum of the corrected speed and the corrected acceleration of the high-pressure electro-pneumatic servo valve.

[0171] Differentiating equation (40) and simultaneously solving equations (17-18) and (39), we get:

[0172]

[0173] in: The value of the rate of change of the Lyapunov function V; k represents the rate of change of the auxiliary function P. i (i = 1, 2, 3) are the controller parameters; k r α and β are controller parameters; e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 This represents the corrected difference in the high-pressure electro-pneumatic servo valve's motion speed; r represents the auxiliary intermediate variable representing the sum of the corrected high-pressure electro-pneumatic servo valve's speed and its corrected acceleration. This is the speed difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. This indicates the correction value of the motion acceleration difference by the high-voltage electro-pneumatic servo valve; This represents the rate of change of the auxiliary intermediate variable r; N is an intermediate variable.

[0174] The intermediate variable matrices η and Λ are defined as follows:

[0175] η=[e c1 e c2 r] T (42)

[0176]

[0177] Where: k1 is the controller parameter; k r α and e are controller parameters; c1e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 represents the corrected difference in the motion speed of the high-pressure electro-pneumatic servo valve; r represents the auxiliary intermediate variable representing the sum of the corrected speed and the corrected acceleration of the high-pressure electro-pneumatic servo valve.

[0178] By adjusting the parameter controller parameters α,k r If k1 makes the intermediate variable matrix Λ positive definite, then:

[0179]

[0180] in: Let V be the rate of change of the Lyapunov function, η and Λ be intermediate variable matrices, and λ be the value of the change of the Lyapunov function. min (Λ) is the smallest eigenvalue of the intermediate variable matrix Λ, e c1 e is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. c2 represents the corrected difference in the motion speed of the high-pressure electro-pneumatic servo valve; r represents the auxiliary intermediate variable representing the sum of the corrected speed and the corrected acceleration of the high-pressure electro-pneumatic servo valve; W is an intermediate variable.

[0181] Integrating both sides of equation (44), we have:

[0182]

[0183] Where W is an intermediate variable. Let V be the rate of change of the Lyapunov function V, τ be an intermediate variable, V(0) be the exact value of the Lyapunov function V at the initial time, and V(t) be the exact value of the Lyapunov function V at time t.

[0184] Due to the difference e between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve c1 The corrected speed difference e of the high-pressure electro-pneumatic servo valve c2 The auxiliary intermediate variable r all belong to the L2 norm, and according to the assumption, the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target is... High-voltage electro-pneumatic servo valve corrects motion acceleration difference The rate of change of the auxiliary intermediate variable r Belongs to L ∞ Norm, therefore the intermediate variable W is uniformly continuous. By Barbalat's lemma, as time t→∞, the difference e between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve is... c1 →0.

[0185] therefore:

[0186] Conclusion 1: The enhanced robust anti-interference control designed for the voice coil motor direct-drive high-voltage electro-pneumatic pressure servo valve (5) can achieve asymptotic stability of the system by adjusting the gain α,k r k1 enables the system's tracking error to approach zero as time approaches infinity; the enhanced robust anti-interference control principle diagram for the voice coil motor direct-drive high-voltage electro-pneumatic pressure servo valve (5) is shown below. Figure 2 As shown.

[0187] The present invention will be further described below with reference to specific embodiments.

[0188] Example

[0189] To evaluate the performance of the designed controller, the following physical prototypes were used for experimental comparison and analysis. Table 1 shows the relevant parameters of the servo valve.

[0190] Table 1

[0191] <![CDATA[K e ]]> 23.5 N / A Motor parameters I 4A maximum current of voice coil motor R 3Ω Voice coil motor resistor L 1Mh@1kHz Voice coil motor inductance <![CDATA[x vmax ]]> ±1.5mm Maximum range of motion of valve core <![CDATA[x max ]]> ±1mm Effective movement range of valve core M 0.6kg Total mass driven by voice coil motor

[0192] Implementation method: Since step response speed and steady-state tracking error are the most important performance indicators for servo valves, the evaluation method is as follows: under the same external alternating disturbance force, the step response speed and steady-state tracking error of different controllers are compared.

[0193] like Figure 3 As shown, the same step signal control command is input to a high-pressure electro-pneumatic servo valve under different control methods, and the corresponding step response curves are compared to compare the response performance of the control algorithms. Experimental results show that the enhanced robust controller algorithm enables the high-pressure electro-pneumatic servo valve to track the target command in the shortest time and remain stable, achieving the best response performance.

[0194] like Figure 4 As shown, when the voice coil motor-driven high-voltage electro-pneumatic servo valve is stable, the same alternating disturbance is applied to it. Then, the anti-interference performance of the control algorithm is compared based on the tracking error of the high-voltage electro-pneumatic servo valve under different control methods. Experimental results show that under the same disturbance, the enhanced robust controller algorithm can guarantee the best anti-interference performance and the smallest steady-state tracking error.

[0195] Figure 4 In the case of a voice coil motor direct-drive high-voltage electro-pneumatic servo valve subjected to the same interference, when the enhanced robust anti-interference control method proposed in this invention is used, such as... Figure 4 As shown in (a), it has the smallest tracking error, with an error range of approximately ±0.005 mm. When the RISE-ESO control method is used, as shown in Figure (a), the tracking error is the smallest. Figure 4As shown in (b), the voice coil motor direct-drive high-voltage electro-pneumatic servo valve exhibits a large tracking error under the same interference conditions, with an error range approaching ±0.01 mm. When the LADRC control method is adopted, as shown in Figure (b), Figure 4 As shown in (c), the voice coil motor direct-drive high-voltage electro-pneumatic servo valve has the largest tracking error under the same interference, with the error range exceeding ±0.015mm.

[0196] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A voice coil motor direct drive system robust anti-interference control method, characterized in that, The method includes the following steps: S1 Establish the dynamic equations, model errors, and state equations of the voice coil motor direct drive system; S2 extends the lumped disturbance into an additional state variable to update the state equation. Based on the updated state equation, the extended state disturbance robust observer and the conditions satisfied by its estimation error are set, and the extended state disturbance robust observer is used to calculate the estimate of the lumped disturbance. S3 sets the tracking error and auxiliary error signals, and constructs an enhanced robust anti-interference controller to compensate for the difference between the estimation of lumped interference and the lumped error, thereby realizing the control of the voice coil motor direct drive system; In step S2, the extended state anti-interference observer is configured according to the following relationship: where the observer estimation matrix , , , are the observed estimation values of the extended state observer output, which correspond to the servo valve displacement , the velocity of the servo valve displacement , the lumped disturbance , is the system damping, is the known gain parameter, is the system state matrix, is the observer gain matrix, is the observer output matrix; is the feedback matrix that needs to be designed for the extended state observer, which contains the system damping and the observer bandwidth ; In step S2, the error estimation satisfies the following conditions: When the observer bandwidth When satisfied The estimation error of ESO is bounded and its upper bound exists, i.e. ,in, This represents the maximum value of the ESO's estimation error for system state and external disturbances. intermediate matrix variables The largest eigenvalue, Indicates lumped interference The maximum rate of change, The observer bandwidth is a parameter of the observer. Given the system damping parameters; In step S3, the tracking error and auxiliary error signals are determined according to the following relationship: in, For target instructions, For speed target instructions, For servo valve displacement, For the movement speed of the servo valve, and For controller parameters, This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. This is the difference between the actual movement speed of the high-pressure electro-pneumatic servo valve and the actual movement speed of the target. The corrected speed difference of the high-pressure electro-pneumatic servo valve. To correct the difference in motion acceleration between the high-voltage electro-pneumatic servo valve, To correct the speed difference of the high-pressure electro-pneumatic servo valve It is the corrected acceleration difference The auxiliary intermediate variable of the sum; The enhanced robust anti-interference controller is configured according to the following relationship: in, For controller parameters; The gain parameter is known. and All are controller parameters and are positive real numbers. for Standard symbolic functions, yes The hyperbolic tangent function, This is the difference between the actual displacement and the target displacement of the high-pressure electro-pneumatic servo valve. This indicates the correction of the speed difference between the high-pressure electro-pneumatic servo valve. To extend the lumped disturbance estimate output by the state-resistant observer.

2. The control method for enhancing robust anti-interference in a voice coil motor direct drive system as described in claim 1, characterized in that, In step S1, the dynamic equations are performed according to the following relationships: in, m The total mass of the driven parts includes the sum of the mass of the valve core, the mass of the voice coil motor, and the mass of the intermediate direct-drive mechanism. xsv This represents the actual displacement of the valve core. Fe For the driving force of the motor, Ftg For transient aerodynamic forces, Fsg For steady-state aerodynamic forces, Ff The frictional force acting on the system, Fi This refers to internal disturbances, including fluctuations in the drive signal. Fud Due to unknown interference, Bv The viscous damping coefficient, t Indicates time.

3. The control method for enhancing robust anti-interference in a voice coil motor direct drive system as described in claim 2, characterized in that, In step S1, the model error is determined according to the following relationship: in, m For the unknown total mass of the driven part, K e For unknown accurate voice coil motor parameters, R For the unknown voice coil motor accurate equivalent resistance value and B v The exact system damping coefficient is unknown. m 0 represents the known exact total mass of the driven part. K e0 Given the parameters of the voice coil motor, R 0 represents the known equivalent resistance value of the voice coil motor. B v0 Given the system damping coefficient, m The difference between the known total mass and the unknown exact total mass of the driven part. K e The difference between the known voice coil motor parameters and the unknown accurate voice coil motor parameters. R The sum of the differences between the known and unknown equivalent resistance values ​​of the voice coil motor. B v This is the difference between the known system damping coefficient and the unknown, accurate system damping coefficient.

4. The control method for enhancing robust anti-interference in a voice coil motor direct drive system as described in claim 3, characterized in that, In step S1, the state equation is performed according to the following relationship: in, System input, system state variables and Represented as System damping parameters and gain parameters for , Centralized interference Represented as: in: m For the unknown total mass of the driven part. m 0 represents the known, accurate total mass of the driven portion. K e0 Given the parameters of the voice coil motor, R 0 represents the known equivalent resistance value of the voice coil motor. B v0 Given the system damping coefficient, K e For unknown accurate voice coil motor parameters, R For the unknown accurate equivalent resistance value of the voice coil motor. B v The exact system damping coefficient is unknown. u This is the input voltage for the voice coil motor. F tg For transient aerodynamic forces, F sg For steady-state aerodynamic forces, F f The frictional force acting on the system. F i This refers to internal disturbances, including fluctuations in the drive signal. F ud Due to unknown interference, F d This represents the total external interference.

5. A control method for enhancing robust anti-interference in a voice coil motor direct drive system as described in claim 1 or 4, characterized in that, In step S2, the updated state equation is expressed according to the following relationship: in, For system input, , and System state variables System state variables and system state variables The rate of change Given the system damping parameters, Given the gain parameters, The acceleration of the servo valve displacement. The speed of the servo valve displacement. To centralize interference, The rate of change of the lumped disturbance.

6. A control method for enhancing robust anti-interference in a voice coil motor direct drive system as described in claim 1, characterized in that, The controller parameters The following relationship must be satisfied: and in, and As an intermediate variable, and Choose a constraint function for the parameters proposed in the invention. These are the controller parameters.

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