High-precision position compound control based on ESO-MPC electro-hydrostatic actuator

Abstract

The invention belongs to the technical field of electro-hydraulic servo control, and discloses a high-precision position compound control method based on an ESO-MPC electro-hydrostatic actuator, and the method comprises the steps: building a nonlinear dynamic model of the electro-hydrostatic actuator based on the working principle and structural composition of the electro-hydrostatic actuator; based on the nonlinear dynamic model of the electro-hydrostatic actuator, constructing a state-space equation of the electro-hydrostatic actuator; designing an extended state observer (ESO), regarding unmodeled dynamics and external disturbance in the system as total disturbance d, and obtaining a total disturbance estimated value through real-time observation; designing a model predictive controller (MPC) to realize rolling optimization; and the model prediction controller dynamically adjusts control input in combination with compensation information of the extended state observer, so that high-precision tracking and strong-robustness control of the displacement of the electro-hydrostatic actuator piston are realized. According to the invention, on the basis of the nonlinear model and the extended state observer, internal and external disturbance of the system is estimated and compensated in real time, and high-precision displacement tracking and control of the electro-hydrostatic actuator are realized.

Description

Technical Field

[0001] This invention belongs to the field of electro-hydraulic servo technology, specifically involving high-precision position composite control based on ESO-MPC electro-hydraulic actuator. Background Technology

[0002] With the continuous advancement of aerospace equipment technology, aircraft control systems are evolving towards high integration, high reliability, and full electrification. Traditional centralized hydraulic systems are complex in structure, have low energy utilization, and are difficult to maintain, making them unable to meet the high efficiency and high precision requirements of modern flight control. Electro-Hydrostatic Actuators (EHAs), as an independent servo system driven by an electric motor, directly convert electrical energy into hydraulic energy to achieve local drive and control of actuators, becoming an important component of the next generation of aircraft servo systems. EHAs combine the advantages of fast response from electric drive and high power density from hydraulic transmission, featuring compact structure, high energy efficiency, and strong self-locking capability. They can operate independently without a centralized hydraulic power source and are widely used in flight control servos, landing gear, and other critical actuators.

[0003] EHA systems typically consist of servo motors, fixed displacement pumps, and hydraulic cylinders. During operation, these systems exhibit significant nonlinearity, parameter coupling, and time-varying characteristics. Factors such as the compressibility, friction, and internal leakage of hydraulic oil, as well as motor inertia, complicate the system's dynamics model. Modeling errors and external disturbances significantly impact control performance. Furthermore, servo motors withstand complex aerodynamic loads during flight, and their execution accuracy and response speed directly affect the stability and safety of the aircraft's attitude. EHA systems are prone to response lag, overshoot, and steady-state errors under varying loads and wide-bandwidth input conditions. Traditional control methods struggle to balance stability and speed under high precision and high dynamic requirements. Therefore, improving the control performance and disturbance rejection capabilities of EHA servo motor systems under complex operating conditions has become a key research focus.

[0004] In summary, the development of EHA (Electro-Hydraulic Actuation) marks the transformation of aircraft actuation systems from centralized hydraulic drive to distributed electro-hydraulic hybrid drive. Its high efficiency, flexibility, and reliability make it a crucial technological direction for future "all-electric" flight control systems. Research on the design and performance optimization of aircraft servo electro-hydraulic actuation systems based on ESO-MPC control can not only improve the dynamic response and steady-state performance of servo systems but also enhance their robustness and disturbance rejection capabilities, which is of great significance for improving the safety and reliability of flight control systems. Furthermore, this research plays a positive role in promoting independent innovation in my country's electro-hydraulic servo technology and facilitating the intelligent and high-performance development of high-end aviation equipment. Summary of the Invention

[0005] This invention aims to address the shortcomings of existing technologies and provides the following solutions: High-precision position composite control based on ESO-MPC electro-hydraulic actuator, characterized by the following steps: Based on the working principle and structural composition of electro-hydraulic actuators, a nonlinear dynamic model of electro-hydraulic actuators is constructed. Based on the nonlinear dynamic model of the electro-hydraulic actuator, the state-space equation of the electro-hydraulic actuator is constructed. Design an extended state observer (ESO) to treat unmodeled dynamics and external disturbances in the system as a total disturbance d, and obtain an estimate of the total disturbance through real-time observation; Design a model predictive controller (MPC) that dynamically adjusts the control input by combining compensation information from an extended state observer, thereby achieving high-precision tracking and robust control of the piston displacement of an electro-hydraulic actuator.

[0006] Preferred methods for nonlinear dynamic models include: Construct the hydraulic cylinder piston force balance equation: Where m represents the total mass of the piston, x p Indicates piston displacement. Indicates piston speed. A represents piston acceleration. p P represents the effective area of ​​the hydraulic cylinder piston. L Indicates load pressure, B p F represents the piston viscous damping coefficient, K represents the load spring stiffness, and F represents the piston viscous damping coefficient. L External load force acting on the piston. Construct the dynamic equilibrium equation for system pressure: Where β e V represents the effective bulk modulus. t D represents the total compression volume of the hydraulic cylinder. p K represents the displacement of a fixed displacement pump. v This represents the speed gain, u is the voltage signal, and C tp This represents the total leakage coefficient of the hydraulic cylinder.

[0007] Preferably, based on the nonlinear dynamic model of the electro-hydraulic actuator, the state vector is defined as... The state-space equation of the electro-hydraulic actuator is obtained as follows: To reduce the complexity of the formula derivation in this paper, the following parameters are defined to simplify the equations: The state-space equations can be expressed as:

[0008] Preferably, the extended state observer fourth-order ESO is: in It is the derivative of the perturbation d, assuming d is a bounded function, |d|≤E d Based on the state-space equations, the extended state observer can be designed as follows: Where z = [z1 z2 z3 z4] T This represents x = [x1 x2 x3 x4] T The observed values, β1, β2, β3, and β4 are the error feedback gains. β1 = 4ω0, β2 = 6ω0 2 β3=4ω0 3 β4=ω0 4 ω0 represents the observer bandwidth, which needs to be set according to the system.

[0009] Preferably, the model prediction controller is: u(k) = -K MPC M x x(k)-K MPC M d D(k) Where u(k) represents the control law output by the MPC, K MPC M represents the controller parameter matrix related to the system state. x and M d Let x(k) represent the system controller parameter matrix, x(k) represent the system state at time k, and D(k) represent the external load force.

[0010] Preferably, the dynamic input is: The composite control law consists of the output control law of the MPC controller and the dynamic disturbances observed by the ESO.

[0011] This invention also provides a high-precision position composite control based on an ESO-MPC electro-hydraulic actuator. The control system applies the above-mentioned control method and includes: a model building module, a state-space equation module, an observer and controller module, and a dynamic input module. The model building module constructs a nonlinear dynamic model of the electro-hydraulic actuator based on its working principle and structural composition. The state-space equation module is based on the nonlinear dynamic model of the electro-hydraulic actuator to construct the state-space equation of the electro-hydraulic actuator; the observer and controller module is based on the ESO observer to construct the ESO-MPC controller. The dynamic input module uses a model predictive controller combined with compensation information from an extended state observer to dynamically adjust the control input, thereby achieving high-precision tracking and robust control of the piston displacement of the electro-hydraulic actuator.

[0012] Preferably, the high-precision position composite control based on ESO-MPC electro-hydraulic actuator is characterized in that the workflow of the model building module includes: Construct the hydraulic cylinder piston force balance equation: Where m represents the total mass of the piston, x p Indicates piston displacement. Indicates piston speed. A represents piston acceleration. p P represents the effective area of ​​the hydraulic cylinder piston. L Indicates load pressure, B p F represents the piston viscous damping coefficient, K represents the load spring stiffness, and F represents the piston viscous damping coefficient. L External load force acting on the piston. Construct the dynamic equilibrium equation for system pressure: Where β e V represents the effective bulk modulus. t D represents the total compression volume of the hydraulic cylinder. p K represents the displacement of a fixed displacement pump. v This represents the speed gain, u is the voltage signal, and C tp This represents the total leakage coefficient of the hydraulic cylinder.

[0013] Preferably, the workflow of the state-space equation module includes: Based on the nonlinear dynamic model of the electro-hydraulic actuator, the state vector is defined as The state-space equation of the electro-hydraulic actuator is obtained as follows: To reduce the complexity of the formula derivation in this paper, the following parameters are defined to simplify the equations: The state-space equations can be expressed as:

[0014] Preferably, the high-precision position composite control based on ESO-MPC electro-hydraulic actuator is characterized in that the observer is: in It is the derivative of the perturbation d, assuming d is a bounded function, |d|≤Ed Based on the state-space equations, the extended state observer can be designed as follows: Where z = [z1 z2 z3 z4] T This represents x = [x1 x2 x3 x4] T The observed values, β1, β2, β3, and β4 are the error feedback gains. β1 = 4ω0, β2 = 6ω0 2 β3=4ω0 3 β4=ω0 4 ω0 represents the observer bandwidth, which needs to be set according to the system.

[0015] Preferably, in the high-precision position composite control based on ESO-MPC electro-hydraulic actuator according to claim 10, the model predictive controller is: u(k) = -K MPC M x x(k)-K MPC M d D(k) Where u(k) represents the control law output by the MPC, K MPC M represents the controller parameter matrix related to the system state. x and M d Let x(k) represent the system controller parameter matrix, x(k) represent the system state at time k, and D(k) represent the external load force.

[0016] Preferably, the dynamic input is: The composite control law consists of the output control law of the MPC controller and the dynamic disturbances observed by the ESO.

[0017] The controller designed in this invention employs a structure combining an extended state observer and model predictive control. The extended state observer is used to estimate unmodeled dynamics and external disturbances in the hydraulic system, and the estimation results are used as feedforward compensation inputs. Model predictive control, based on the system prediction model, generates control variables through rolling optimization under constraints, and corrects the prediction results by incorporating compensation information from the extended state observer. The two work together to form a comprehensive control input u, which acts on the electro-hydraulic actuator, achieving high-precision tracking and enhanced robust control performance. Attached Figure Description

[0018] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the controller structure according to an embodiment of the present invention; Figure 3 This is a simulation diagram of an embodiment of the present invention; Detailed Implementation

[0020] The technical solutions in the embodiments are clearly described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0022] Example 1:

[0023] In this embodiment, as Figure 1 As shown, high-precision position composite control based on ESO-MPC electro-hydraulic actuator includes the following steps: S1. Based on the working principle and structural composition of the electro-hydraulic actuator, a nonlinear dynamic model of the electro-hydraulic actuator is constructed; based on the nonlinear dynamic model of the electro-hydraulic actuator, the state-space equation of the electro-hydraulic actuator is constructed.

[0024] Methods for nonlinear dynamic models include: Constructing the piston force balance equation for a hydraulic cylinder: The dynamic characteristics of hydraulic power components are affected by load characteristics. Load forces generally include inertial forces, viscous damping forces, and external load forces. Where m represents the total mass of the piston, x p Indicates piston displacement. Indicates piston speed. A represents piston acceleration. p P represents the effective area of ​​the hydraulic cylinder piston. L Indicates load pressure, B p F represents the piston viscous damping coefficient, K represents the load spring stiffness, and F represents the piston viscous damping coefficient. L External load force acting on the piston.

[0025] The system pressure dynamic balance equation is constructed as follows: In this embodiment, the following assumptions are made: there is laminar leakage between the plunger variable pump and the actuating hydraulic cylinder; the pump casing returns oil through zero pressure; and the leakage from the low-pressure chamber to the pump casing is negligible. Due to the sufficiently short connecting pipeline design, pressure loss along the pipeline, transient hydraulic forces, and pipeline dynamic effects are all negligible, and the replenishing valve possesses ideal operating characteristics. The two pipelines are completely identical; the pump, hydraulic cylinder, and pipeline form two chambers with the same total volume; the oil temperature and bulk modulus of elasticity remain constant in each chamber, and the pressure is uniformly distributed within the chambers. There is no lag in the replenishing system's operation, and the replenishing pressure remains constant. During operation, the low-pressure chamber pressure equals the replenishing pressure; only the high-pressure chamber pressure changes. The flow rate q1 flowing into the oil inlet chamber of the hydraulic cylinder is: The flow rate q2 flowing out of the hydraulic cylinder return chamber is: Where q1 and q2 represent inflow and outflow volumes; A p —Effective area of ​​the hydraulic cylinder piston; x p —Piston displacement; C ip and C ep — Hydraulic cylinder internal leakage coefficient; p1 and p2 — Hydraulic cylinder inlet and outlet pressures; V1 and V2 — Hydraulic cylinder inlet and outlet oil volumes; β e —Effective bulk modulus. Load flow can be defined as: Among them: Q L —Load traffic. The volume of the two chambers of a hydraulic cylinder during operation can be expressed as: Where: V 01 and V 01 —Initial volume of the oil inlet and return chambers. From equations (2)-(5), the flow continuity equation can be obtained: To achieve the same compression flow rate, the initial volumes of the two chambers must be equal, that is: V 01 =V 02 =V t (7) Where V t — This indicates the total compression volume of the hydraulic cylinder. P L =p1-p2 (9) Q L =D p K v u (10) According to equations (6)-(10), the dynamic equilibrium equations of pressure can be obtained: Where D p K represents the displacement of a fixed displacement pump. v This represents the speed gain, u is the voltage signal, and C tp This represents the total leakage coefficient of the hydraulic cylinder. Based on the above-derived hydraulic cylinder piston force balance equation (1) and pressure dynamic balance equation, the dynamic model of the electro-hydraulic actuator is as follows: S2. Based on the nonlinear dynamic model of the electro-hydraulic actuator, construct the state-space equation of the electro-hydraulic actuator.

[0026] State-space equations are constructed: To facilitate the design of the extended state observer and controller in subsequent processes, the state vector is defined as follows: The state-space equations of the system model described by (1)-(2) are: To reduce the complexity of the formula derivation in this paper, the following parameters are defined to simplify the equations: The state-space equation (3) can be expressed as equation (5): S3. Design an extended state observer (ESO) to treat unmodeled dynamics and external disturbances in the system as a total disturbance d, and obtain an estimate of the total disturbance through real-time observation; design a model predictive controller (MPC) to achieve rolling optimization.

[0027] The method for constructing a state observer includes: treating the disturbance d as the system state and creating a four-dimensional state-space equation; and designing an observer based on the expanded state-space equation. In this embodiment, the expanded state observer chooses to use the disturbance d as the state variable for its construction. Considering the disturbance being converted into a spatial state equation, it is expanded into a four-dimensional spatial state equation: in It is the derivative of the perturbation d, assuming d is a bounded function, |d|≤E d .

[0028] Based on the state-space equation (15), the extended state observer can be designed as follows: Where z = [z1 z2 z3 z4] T This represents x = [x1 x2 x3 x4] T The observed values, β1, β2, β3, and β4, are the error feedback gains. β1 = 4ω0, β2 = 6ω0 2 β3=4ω0 3 β4=ω0 4 ω0 represents the observer bandwidth, which needs to be set according to the system.

[0029] Model predictive control (MDC) is a class of optimization control methods based on system models. Its basic idea is to use a predictive model to predict future outputs within a finite prediction time domain and obtain the optimal control sequence through rolling optimization. At each sampling time, only the first control variable is applied to the system, and the remaining variables are recalculated at the next time step, thus achieving dynamic optimization and online correction. To implement MDC, the state-space equations need to be... Discretization, the discrete model equations are as follows: x(k+1)=Ax(k)+Bu(k)+D(k) (17) Where x(k) is the system state at time k; A and B are the parameter matrices of the discrete model; u(k) is the system input; and D(k) is the external load.

[0030] MPC obtains the optimal control sequence by solving an optimal control problem that includes a control objective and a system model, and then... An optimal control is applied to the system. The calculation of the control law can be transformed into solving a quadratic programming problem online: Where J is the objective function; N is the prediction interval length; i represents the i-th control time domain; Q and R are positive definite weight matrices. Where I is the identity matrix; D(k) is the external load force, which remains unchanged in the prediction time domain. definition: X k =[x(k|k),x(k+1|k),x(k+2|k),…,x(k+N|k)] T (20) U k =[u(k|k),u(k+1|k),u(k+2|k), …,u(k+N-1|k)] T (twenty one) By further deriving equation (20) and (21), we can obtain equation (19): X k=M x x(k)+M u U k +M d D(k) (22) M x =(A,A) 2 ,…,A N ) T ; M d =(I,A+I,…,A) N-1 +A N-2 +A+I) T In the formula M x M u and M d This represents the system controller parameter matrix. Substituting formulas (20) and (21) into formula (18), we get: in X k =M x x(k)+M u U k +M d Substituting D(k) into (23) gives: make Thus, we obtain the standard unconstrained QP:

[0031] In the unconstrained case, Given: Right now: Let E p (k)=-(M x x(k)+M d D(k)), we can obtain: In MPC control, the controller only applies the control law obtained at the first moment, that is: u(k) = [1,0, …,0]·U * (k)=K MPC ·E p (k) (29) in This represents the controller parameter matrix related to the system state.

[0032] The control law of the controller can be derived as follows: u(k) = -K MPC M x x(k)-K MPC M d D(k) (30) Where u(k) represents the control law output by the MPC, K MPC M represents the controller parameter matrix related to the system state. x and M d Let x(k) represent the system controller parameter matrix, x(k) represent the system state at time k, and D(k) represent the external load force. S4. The model predictive controller dynamically adjusts the control input by combining the compensation information from the extended state observer, thereby achieving high-precision tracking and robust control of the piston displacement of the electro-hydraulic actuator.

[0033] The controller designed in this invention adopts a structure that combines an extended state observer with model predictive control, such as... Figure 2 As shown, the extended state observer is used to estimate unmodeled dynamics and external disturbances in the hydraulic system, and the estimation results are used as feedforward compensation inputs. Model predictive control is based on the system predictive model, and generates control quantities through rolling optimization under constraints, and corrects the prediction results by combining the compensation information from the extended state observer. The two work together to form a comprehensive control input u, which acts on the electro-hydraulic actuator to achieve high-precision tracking and enhanced robust control performance.

[0034] Example 2:

[0035] The high-precision position composite control based on the ESO-MPC electro-hydraulic actuator proposed in Example 1 aims to improve system tracking performance by estimating and compensating for uncertainties in the system. Building upon the control method proposed in Example 1, this example verifies the results through simulation, setting external disturbances and unmodeled system errors as... 5%-10%, that is, d = 3 × 10 7 sin(10πt)+10 8 sin(t+π / 3). Three control signals are input to the system: a step signal, a sine signal, and a stepped signal, to simulate the actual working state of the EHA, including smoothed displacement abrupt changes. Three control schemes are compared and analyzed: a global predictive controller based on an extended state observer, traditional global predictive control, and PID control.

[0036] Simulation results are as follows Figure 3As shown, the ESO can accurately estimate the amplitude, phase, and trend of disturbance signals. Especially when disturbances change drastically, the observer can respond quickly and synchronize with the actual disturbance. This indicates that the ESO has strong dynamic response capabilities and can effectively suppress uncertainties caused by modeling errors and external disturbances, providing a reliable basis for feedforward compensation in model predictive control, thereby improving the system's disturbance rejection capability and control accuracy.

[0037] To verify the effectiveness of the ESO-MPC control strategy, this paper compares it with traditional PID control and conventional MPC control. Simulation results show that ESO-MPC outperforms PID and MPC control in terms of dynamic response, settling time, and steady-state error. Especially under multi-step input conditions, ESO-MPC exhibits faster dynamic convergence and no steady-state error. Furthermore, in sinusoidal signal tracking simulations, ESO-MPC also demonstrates higher tracking accuracy and phase synchronization capability. Overall, the ESO-MPC controller exhibits excellent dynamic performance and robustness under various input conditions, proving the advantages of this strategy in practical applications.

[0038] Example 3:

[0039] In this embodiment, as Figure 1 , Figure 2 As shown, the high-precision position composite control based on ESO-MPC electro-hydraulic actuator includes: a model building module, a state-space equation module, an observer and controller module, and a dynamic input module.

[0040] Based on the working principle and structural composition of the electro-hydraulic actuator, a nonlinear dynamic model of the electro-hydraulic actuator is constructed; based on the nonlinear dynamic model of the electro-hydraulic actuator, the state-space equation of the electro-hydraulic actuator is constructed.

[0041] The model building module workflow includes: Construct the hydraulic cylinder piston force balance equation: Where m represents the total mass of the piston, x p Indicates piston displacement. Indicates piston speed. A represents piston acceleration. p P represents the effective area of ​​the hydraulic cylinder piston. L Indicates load pressure, B p F represents the piston viscous damping coefficient, K represents the load spring stiffness, and F represents the piston viscous damping coefficient. L External load force acting on the piston. Construct the dynamic equilibrium equation for system pressure: Where βe V represents the effective bulk modulus. t D represents the total compression volume of the hydraulic cylinder. p K represents the displacement of a fixed displacement pump. v This indicates the speed gain.

[0042] Based on the nonlinear dynamic model of the electro-hydraulic actuator, the state-space equation of the electro-hydraulic actuator is constructed.

[0043] The workflow of the state-space equations module includes: Based on the nonlinear dynamic model of the electro-hydraulic actuator, the state vector is defined as The state-space equation of the electro-hydraulic actuator is obtained as follows: To reduce the complexity of the formula derivation in this paper, the following parameters are defined to simplify the equations: The state-space equations can be expressed as:

[0044] The workflow of the observer and controller module includes:

[0045] The observer is: in It is the derivative of the perturbation d, assuming d is a bounded function, |d|≤E d Based on the state-space equations, the extended state observer can be designed as follows: Where z = [z1 z2 z3 z4] T This represents x = [x1 x2 x3 x4] T The observed values, β1, β2, β3, and β4 are the error feedback gains. β1 = 4ω0, β2 = 6ω0 2 β3=4ω0 3 β4=ω0 4 ω0 represents the observer bandwidth, which needs to be set according to the system.

[0046] The model predictive controller is: u(k) = -K MPC M x x(k)-K MPC M d D(k) (37) Where u(k) represents the control law output by the MPC, K MPC M represents the controller parameter matrix related to the system state.x and M d Let x(k) represent the system controller parameter matrix, x(k) represent the system state at time k, and D(k) represent the external load force.

[0047] The dynamic input module works as follows:

[0048] like Figure 2 As shown, the extended state observer is used to estimate unmodeled dynamics and external disturbances in the hydraulic system, and the estimation results are used as feedforward compensation inputs. Model predictive control is based on the system predictive model, and generates control quantities through rolling optimization under constraints, and corrects the prediction results by combining the compensation information from the extended state observer. The two work together to form a comprehensive control input u, which acts on the electro-hydraulic actuator to achieve high-precision tracking and enhanced robust control performance.

[0049] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A high-precision position compound control based on ESO-MPC electro-hydraulic actuator, characterized in that, The method comprises the following steps: A nonlinear dynamic model of the electro-hydraulic actuator is constructed based on the working principle and structural composition of the electro-hydraulic actuator; A state space equation of the electro-hydraulic actuator is constructed based on the nonlinear dynamic model of the electro-hydraulic actuator; An extended state observer (ESO) is designed, the unmodeled dynamics and external disturbances in the system are regarded as total disturbances d, and the total disturbance estimation value is obtained through real-time observation; A model predictive controller (MPC) is designed. The model predictive controller dynamically adjusts the control input in combination with the compensation information of the extended state observer, so as to realize high-precision tracking and strong robust control of the piston displacement of the electro-hydraulic actuator.

2. The high-precision position compound control of the ESO-MPC-based electro-hydraulic actuator according to claim 1, wherein, The method of the nonlinear dynamic model comprises: A piston force balance equation of the hydraulic cylinder is constructed: where m represents the total mass of the piston, x p represents the piston displacement, represents the piston velocity, represents the piston acceleration, A p represents the effective area of the hydraulic cylinder piston, P L represents the load pressure, B p represents the viscous damping coefficient of the piston, K represents the load spring stiffness, F L the external load force acting on the piston, A system pressure dynamic balance equation is constructed: where β e represents the effective bulk modulus, V t represents the total compression volume of the hydraulic cylinder, D p represents the displacement of the fixed displacement pump, K v represents the rotational speed gain, u is the voltage signal, C tp represents the total leakage coefficient of the hydraulic cylinder.

3. The high-precision position compound control of the ESO-MPC-based electro-hydraulic actuator according to claim 2, characterized in that, Based on the nonlinear dynamic model of the electro-hydrostatic actuator, the state vector is defined as The state space equation of the electro-hydrostatic actuator is obtained as In order to reduce the complexity of formula derivation in the present application, the following parameters are defined to simplify the equation: The state space equation can be expressed as equation:

4. The high-precision position compound control of the ESO-MPC based electro-hydraulic actuator according to claim 3, wherein, The fourth-order ESO of the extended state observer is: where is the derivative of the disturbance d, assuming d is a bounded function, |d|≤E d , based on the state-space equation, the extended state observer can be designed as: where z = [z1z2z3z4] T represents x = [x1x2x3x4] T The observation value, β1, β2, β3, and β4 are error feedback gains. β1 = 4ω0, β2 = 6ω0 2 , β3 = 4ω0 3 , β4 = ω0 4 . ω0 represents the observer bandwidth, and a specific value needs to be set according to the system.

5. The high-precision position compound control of the ESO-MPC based electro-hydraulic actuator according to claim 4, wherein, The model predictive controller and the dynamic input are: u(k) = -K MPC M x x(k) - K MPC M d D(k) where u(k) represents the control rate of the MPC output, K MPC represents the controller parameter matrix related to the system state, M x and M d represents the system controller parameter matrix, x(k) represents the system state at the kth time, and D(k) represents the external load force, The composite control rate composed of the control rate output by the MPC controller and the dynamic disturbance observed by the ESO.

6. The high-precision position compound control of the ESO-MPC electro-hydraulic actuator based on the control system of claim 5, wherein the control system applies the control method of any one of claims 1-5. It comprises: A model construction module, a state space equation module, an observer and controller module, and a dynamic input module; The model construction module constructs a nonlinear dynamic model of the electro-hydraulic actuator based on the working principle and structural composition of the electro-hydraulic actuator; The state space equation module constructs a state space equation of the electro-hydraulic actuator based on the nonlinear dynamic model of the electro-hydraulic actuator; The observer and controller module is based on the ESO observer, and further constructs an ESO-MPC controller; The dynamic input module dynamically adjusts the control input in combination with the compensation information of the extended state observer, so as to realize high-precision tracking and strong robust control of the piston displacement of the electro-hydraulic actuator.

7. The high-precision position compound control of the ESO-MPC based electro-hydrostatic actuator according to claim 6, characterized in that, The working process of the model construction module comprises: A piston force balance equation of the hydraulic cylinder is constructed: where m represents the total mass of the piston, x p represents the piston displacement, represents the piston velocity, represents the piston acceleration, A p represents the effective area of the hydraulic cylinder piston, P L represents the load pressure, B p represents the piston viscous damping coefficient, K represents the load spring stiffness, F L the external load force acting on the piston, A system pressure dynamic balance equation is constructed: where β e represents the effective bulk modulus, V t represents the total compression volume of the hydraulic cylinder, D p represents the displacement of the fixed displacement pump, K v represents the rotational speed gain, u is the voltage signal, C tp represents the total leakage coefficient of the hydraulic cylinder.

8. The high-precision position compound control of the ESO-MPC based electro-hydrostatic actuator according to claim 7, wherein, The working process of the state space equation module comprises: Based on the nonlinear dynamic model of the electro-hydrostatic actuator, the state vector is defined as The electro-hydrostatic actuator state space equation is obtained: In order to reduce the complexity of formula derivation in the present application, the following parameters are defined to simplify the equation: The state space equation can be expressed as equation:

9. The high-precision position compound control of the ESO-MPC based electro-hydrostatic actuator according to claim 8, wherein, The working process of the observer and controller module comprises: where is the derivative of the disturbance d, assuming d is a bounded function, |d|≤E d , based on the state-space equation, the extended state observer can be designed as: where z = [z1z2z3z4] T represents x = [x1x2x3x4] T The observation value, β1, β2, β3, and β4 are error feedback gains. β1 = 4ω0, β2 = 6ω0 2 , β3 = 4ω0 3 , β4 = ω0 4 . ω0 represents the observer bandwidth, and a specific value needs to be set according to the system. The model predictive control is: u(k) = -K MPC M x x(k) - K MPC M d D(k) where u(k) represents the control rate of the MPC output, K MPC represents the controller parameter matrix related to the system state, M x and M d represents the system controller parameter matrix, x(k) represents the system state at the kth time, and D(k) represents the external load force.

10. The high-precision position compound control method for the ESO-MPC electro-hydraulic actuator based on claim 9, characterized in that, The working process of the dynamic input module is: The composite control rate composed of the control rate output by the MPC controller and the dynamic disturbance observed by the ESO.

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