Fixed time optimal synchronous control method for aero-engine electro-hydraulic actuating mechanism

Abstract

The invention belongs to the field of electro-hydraulic system motion control, and discloses a fixed time optimal synchronous control method for an aero-engine electro-hydraulic actuating mechanism. Constructing a double-cylinder hydraulic system dynamic model, and defining a tracking error and a synchronous coupling error; designing an optimal synchronous controller based on a reinforcement learning actor-commentator architecture, and introducing a fixed time convergence mechanism; and a self-adaptive robust compensation item of the enhanced neural network is designed, and unmodeled dynamics and disturbance are inhibited. According to the method, Lyapunov stability analysis proves that the fixed time stability is met, and comparison experiment verification is carried out on an aero-engine hardware-in-the-loop experiment platform. The method solves the problems that in traditional synchronous control, convergence time depends on initial conditions and is sensitive to uncertainty, and a nonlinear HJB equation is difficult to solve, high-precision synchronous motion control within fixed time is achieved, and the method is suitable for an aero-engine electro-hydraulic execution system with the high reliability requirement.

Description

A fixed-time optimal synchronization control method for electro-hydraulic actuators in aero engines Technical Field

[0001] This invention relates to the field of electro-hydraulic system motion control technology, and in particular to a fixed-time optimal synchronization control method for electro-hydraulic actuators in aero engines. Background Technology

[0002] The dual-cylinder hydraulic synchronous control system of a turbofan engine belongs to the complex power system of aero-engines. Adjustable geometry mechanisms in the air path (such as adjustable guide vanes, bleed valves, and nozzle adjustment mechanisms) are key components ensuring stable engine operation and precise adjustment. They are often driven collaboratively by a dual-cylinder electro-hydraulic system to achieve precise control of aerodynamic parameters such as flow rate and pressure. In recent years, compared with independent control methods, the synchronous control method based on cross-coupling has shown advantages in practical engineering, such as improved tracking accuracy, coordinated movement of multiple actuators, and suppression of load disturbances. Reinforcement learning, as a data-driven optimization method, can adaptively adjust control strategies through online learning and is suitable for hydraulic systems with strong nonlinearity and uncertainty.

[0003] However, due to unmodeled dynamics such as model uncertainties, changes in external aerodynamic loads, friction, and leakage in hydraulic actuators during operation, traditional synchronization control methods often struggle to achieve high-precision synchronization within a finite time. Furthermore, the convergence time frequently depends on the system's initial state, impacting the reliability and response speed of the control system. Therefore, optimizing the synchronous tracking accuracy of dual-cylinder systems under conditions of model uncertainty and dynamic nonlinearity, while balancing speed and robustness, has become a key issue in improving the performance of aero-engine hydraulic actuation systems. Summary of the Invention

[0004] The purpose of this invention is to provide a fixed-time optimal synchronization control method for electro-hydraulic actuators in aero-engines. This method is based on the actor-critic architecture in reinforcement learning, and combines a fixed-time stabilization mechanism with neural network adaptive compensation to achieve high-precision synchronous tracking of dual hydraulic cylinders within a fixed time under uncertain dynamics and external disturbances.

[0005] The technical solution of this invention: A fixed-time optimal synchronization control method for electro-hydraulic actuators in aero engines, the specific steps of which are as follows:

[0006] S1: Establish a dynamic model of the dual-cylinder hydraulic system and define the tracking error and coupling synchronization error;

[0007] S2: Using tracking error and coupling synchronization error as control inputs, the optimal virtual control law is generated based on the reinforcement learning actor-critic architecture, and a fixed-time convergence mechanism is introduced;

[0008] S3: Introduce robust compensation control terms into the actor network to suppress unmodeled dynamics and disturbances in the dual-cylinder hydraulic system;

[0009] S4: The optimal virtual control law based on reinforcement learning generated in S2 is superimposed with the robust compensation control term introduced in S3 to synthesize the final control signal applied to the servo valves of each hydraulic cylinder.

[0010] Step S1 specifically involves:

[0011] S1.1: Considering a dual-cylinder hydraulic system consisting of two single-lever hydraulic actuators, establish a dynamic model for each inertial load:

[0012]

[0013] in, Indicates the first Actuator For the mass load of the dual-cylinder hydraulic system, and These are the piston rod motion displacement and velocity feedback measurements, respectively. These represent the Coulomb friction force and damping force coefficients of the system, respectively. This represents the total external force uncertainty, including modeling errors and aerodynamic load disturbances from aero-engines. This represents the resultant force acting on the piston rod; These are pressure feedback measurements of the rodless chamber of the actuator and pressure feedback measurements of the rod chamber of the actuator, respectively. These represent the piston area in the rodless chamber and the piston ring area in the rod chamber, respectively.

[0014] S1.2: The flow dynamics model of each hydraulic cylinder in a dual-cylinder hydraulic system is expressed as follows:

[0015]

[0016]

[0017] in, ; These represent the hydraulic oil volumes in the rodless chamber, This indicates the volume of hydraulic oil in the rod chamber. and These represent the rodless cavity in... The initial volume of hydraulic oil and the rod chamber at that time The initial volume of hydraulic oil at that time; Indicates the effective bulk modulus of a fluid; These represent the concentrated flow uncertainty of the rodless cavity and the concentrated flow uncertainty of the rod cavity, respectively, including modeling error, internal leakage and hose elastic deformation disturbance; These represent the forward flow rate through the servo valve port and the return flow rate through the servo valve port, respectively, as follows:

[0018]

[0019]

[0020] in, and These are the flow gain coefficients for the forward loop and the reverse loop, respectively. This indicates the pump's oil supply pressure. This refers to the displacement of the slide valve. For a proportional valve model, where To control the voltage, This refers to the gain coefficient of the servo valve.

[0021] S1.3: For a dual-cylinder hydraulic system under nominal operating conditions, based on the load dynamics model, flow dynamics model, and proportional valve model, the following state-space model is derived:

[0022]

[0023] in, These are the three state variables of a dual-cylinder hydraulic system. They are defined as follows:

[0024]

[0025] Let each represent an unknown nonlinear term of the lumped set, defined as follows: S1.4: Define the tracking error of a two-cylinder hydraulic system and synchronization error :

[0026]

[0027] in , Indicates the first Tracking error of a hydraulic cylinder;

[0028] System coupling error Defined as:

[0029]

[0030] in It is the identity matrix. It is the gain used to adjust the synchronization control weights.

[0031] Step S2 specifically involves:

[0032] S2.1: Design the following fixed-time sliding surface:

[0033]

[0034] in, ; Design a virtual control law with fixed time parameters. ;

[0035] S2.2: For each step Define the performance metric function:

[0036]

[0037] in, It is a positive definite weight matrix. This is a virtual control variable;

[0038] S2.3: This is the optimal virtual control quantity for this step. Based on optimal control theory, the following Hamilton-Jacobi-Bellman equation is obtained:

[0039]

[0040] make ,get:

[0041]

[0042] S2.4: Based on the fixed-time stability theorem, actor networks and critic networks are used respectively to solve the Hamilton-Jacobi-Bellman equation to approximate the gradient of the optimal performance index. With optimal virtual control ;

[0043]

[0044]

[0045] in, ; These are the weight estimates for the critic network and the actor network, respectively. It is a radial basis function vector;

[0046] S2.5: Introduce a fixed-time convergence mechanism and design a double-power adaptive law to update network weights:

[0047]

[0048]

[0049] in, The learning rate satisfies .

[0050] Step S3 specifically involves:

[0051] S3.1: For unmodeled dynamics Design robust compensation control terms:

[0052]

[0053] in, , For approximation The radial basis function vector of the neural network; Network weights;

[0054] S3.2: Order Design parameter update law:

[0055]

[0056] By iterating continuously according to the aforementioned weight update law, the robust compensation control term is obtained. This is used to synthesize the final control quantity.

[0057] Specifically, step S4 involves superimposing the optimal virtual control law based on reinforcement learning generated in S2 with the robust compensation control term introduced in S3. ):

[0058]

[0059] in, This is the virtual control quantity in the first step. It is the virtual control quantity of the second step, and has ;

[0060] Based on the system state-space equations in S1.3, the final control signal is obtained:

[0061] .

[0062] The beneficial effects of this invention are as follows:

[0063] This invention addresses the challenges of model uncertainty, large load disturbances, and high synchronization accuracy requirements in dual-cylinder hydraulic systems for aero-engines. It proposes a fixed-time optimal synchronization control method for electro-hydraulic actuators in aero-engines. This method introduces an actor-critic architecture for online optimization control strategies, combines a fixed-time convergence mechanism to ensure system state convergence within a preset time, and incorporates an enhanced neural network robust compensation term to effectively suppress unmodeled dynamics and external disturbances. Compared to traditional synchronization control methods, this invention significantly improves synchronization accuracy, response speed, and anti-interference capability, making it suitable for high-reliability hydraulic synchronization control systems such as those used in aero-engines. Attached Figure Description

[0064] Figure 1 is a flowchart of the control method of the present invention;

[0065] Figure 2 is a schematic diagram of the experimental platform structure of the dual-cylinder hydraulic system;

[0066] Figure 3 shows the comparison curves of piston trajectory tracking under different control methods;

[0067] Figure 4 shows the comparison curves of synchronization error under different control methods;

[0068] Figure 5 shows the tracking error comparison curves under different control methods;

[0069] Figure 6 shows the convergence curves of the actor network and the critic network weights; (a), (b), (c), and (d) represent the actor network weights at the first step (…). , ) and the second step ( , The convergence curve of (e), (f), (g), and (h) are respectively the convergence curves of the commentator network weights in the first step ( , ) and the second step ( , The convergence curve of );

[0070] Figure 7 shows the convergence curve of the robust adaptive network weights; (a) and (b) show the convergence curve of the robust adaptive network weights in the first step of hydraulic cylinder 1 ( ) and hydraulic cylinder 2 ( (c) and (d) are the convergence curves of the robust adaptive network weights in the second step of the hydraulic cylinder 1. ) and hydraulic cylinder 2 ( The convergence curve of ). Detailed Implementation

[0071] The present invention will be further described in detail below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only a part of the embodiments of the invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0072] As shown in Figure 1, this invention provides a specific flowchart of a fixed-time optimal synchronization control method for a dual-cylinder hydraulic system of an aero-engine, which mainly includes the following steps:

[0073] S1: System Modeling and Error Definition

[0074] S1.1: As shown in Figure 2, this embodiment is implemented on a hardware-in-the-loop experimental platform for a certain type of aero-engine. The platform includes a servo valve 1, two single-rod hydraulic cylinders 2, two mass loads 3, a displacement sensor 4, a data acquisition unit 5, an engine electronic controller 6, and a host computer 7. The two single-rod hydraulic cylinders 2 have rod diameters of 25 mm and piston diameters of 40 mm, and are equipped with two ATOSDLHZO-level servo valves for flow control. The position and speed of the hydraulic cylinders are measured by NADO-TPM displacement sensors. The data acquisition unit is composed of an STM32H7 series microcontroller and is responsible for acquiring analog signals from the sensors and servo valves. All status parameters and control voltages are measured and generated by a PXIe-8840 industrial computer, and the data is converted through a PXI-8431 communication card. Subsequently, it is processed by the engine electronic controller 6. The control algorithm is implemented through LabVIEW on the host computer 7. Control commands are transmitted via an RS-422 communication interface at a cycle of 0.002 seconds, and the computer displays the measurement data and signals in real time.

[0075] S1.2: The system calculates the trajectory tracking error of each actuator in real time. And the synchronization error between the two actuators Through a coupling transformation matrix These two types of errors are then fused into a single coupled synthetic error:

[0076]

[0077] Among them, setting synchronization weights The desired trajectory is defined as a smooth trapezoidal trajectory widely used in electromechanical industrial systems, with a maximum displacement of 0.15 m, a velocity of 0.2 m / s, and an acceleration of 0.25 m / s².

[0078] S2: Fixed-time optimal synchronous controller parameter configuration;

[0079] S2.1: Design the following fixed-time sliding surface:

[0080]

[0081] Among them, the selection of fixed time parameters Sliding surface gain .

[0082] S2.2: For each step Define the performance metric function:

[0083]

[0084] Among them, the positive definite weight matrix Set as The unit array.

[0085] S2.3: Based on optimal control theory, the optimal virtual control quantity for this step can be obtained. :

[0086]

[0087] S2.4: Based on the fixed-time stability theorem, the gradient of the optimal performance index is approximated using both the actor network and the critic network. With optimal virtual control ;

[0088]

[0089]

[0090] Among them, control gain , The critic network and actor network each have 6 nodes, with weights... The initial values ​​are set as follows:

[0091]

[0092]

[0093] S2.5: Introduce a fixed-time convergence mechanism and design a double-power adaptive update law:

[0094]

[0095]

[0096] The learning rate is set to .

[0097] S3: Enhanced Neural Network Robust Compensation Parameter Settings;

[0098] S3.1: For robust compensation control items The neural network has 4 nodes and weights. Initial value set to .

[0099] S3.2: Design Parameter Update Law:

[0100]

[0101] in, .

[0102] S4: Synthesize the final control signal;

[0103] The optimal virtual control law based on reinforcement learning generated in S2 is superimposed with the robust compensation control term introduced in S3:

[0104]

[0105] in, This is the virtual control quantity in the first step. It is the virtual control quantity of the second step, and has Therefore, the final control signal is obtained: .

[0106] Stability analysis and verification of this method are performed as follows:

[0107] Constructing Lyapunov functions:

[0108]

[0109] Prove that the system satisfies the fixed-time stability condition:

[0110]

[0111] in, Each satisfies

[0112]

[0113] Convergence time satisfy:

[0114]

[0115] Therefore, the fixed-time stability of the system is proven.

[0116] The control method described in this invention (denoted as C1) is implemented and compared with traditional adaptive quasi-synchronous control (C2) and cross-coupled PID control (C3).

[0117] As shown in Figure 4, the synchronization error of C1 is significantly lower than that of C2 and C3, quickly converging to near 0 without overshoot. Throughout the entire operation time, the maximum periodic synchronization error also gradually converges, eventually stabilizing within the range of ±0.6 mm. Figure 5 shows that the dual-cylinder position tracking error under the C1 method is significantly lower than that of C2 and C3, with a tracking accuracy improvement of approximately 40%. Calculations show that within the stable range of [20,30] s, the root mean square (RMS) of the synchronization error under the C1 method [mm]... 2 The integral of absolute error, IAE [mm·s], is 0.2753, which is 34% higher than C2 and 85% higher than C3. The integral of absolute error, IAE [mm·s], is 1.83, which is 36% higher than C2 and 78% higher than C3.

[0118] Figures 6 and 7 show the convergence of the actor, critic network weights, and robust adaptive network weights, respectively, indicating that the learning process is fast and stable.

[0119] In summary, the fixed-time optimal synchronization control method proposed in this invention achieves high-precision, fast-convergence, and robust synchronous motion control in a dual-cylinder hydraulic system of an aero-engine. It effectively overcomes the influence of model uncertainties and external disturbances, demonstrating significant engineering application value. This method achieves precise synchronous motion control of a dual-cylinder system under complex aerodynamic loads and unmodeled dynamic conditions. Furthermore, it optimizes coupling errors through a reinforcement learning architecture, ensuring that all closed-loop error signals converge within a fixed time, thereby improving the system's synchronization accuracy, anti-interference capability, and control reliability.

Claims

1. A fixed-time optimal synchronization control method for electro-hydraulic actuators in aero engines, characterized in that, The specific steps are as follows: S1: Establish a dynamic model of the dual-cylinder hydraulic system, define the tracking error and coupling synchronization error, and obtain the coupled synthesis; S2: Using the tracking error and coupling synchronization error as control inputs, generate the optimal virtual control law based on the reinforcement learning actor-critic architecture, and introduce a fixed-time convergence mechanism; S3: Introduce a robust compensation control term in the actor network to suppress unmodeled dynamics and disturbances in the dual-cylinder hydraulic system; S4: Superimpose the optimal virtual control law generated in S2 based on reinforcement learning with the robust compensation control term introduced in S3 to synthesize the final control signal applied to the servo valves of each hydraulic cylinder.

2. The fixed-time optimal synchronization control method for electro-hydraulic actuators of aero engines according to claim 1, characterized in that, Step S1 specifically involves: S1.1: Considering a dual-cylinder hydraulic system composed of two single-rod hydraulic actuators, establish a dynamic model for each inertial load: ;in, Indicates the first Actuator For the mass load of the dual-cylinder hydraulic system, and These are the piston rod motion displacement and velocity feedback measurements, respectively. These represent the Coulomb friction force and damping force coefficients of the system, respectively. This represents the total external force uncertainty, including modeling errors and aerodynamic load disturbances from aero-engines. This represents the resultant force acting on the piston rod; These are pressure feedback measurements of the rodless chamber of the actuator and pressure feedback measurements of the rod chamber of the actuator, respectively. S1.2: The flow dynamics model of each hydraulic cylinder in the dual-cylinder hydraulic system is expressed as follows: ； ;in, ； These represent the hydraulic oil volumes in the rodless chamber, This indicates the volume of hydraulic oil in the rod chamber. and These represent the rodless cavity in... The initial volume of hydraulic oil and the rod chamber at that time Initial volume of hydraulic oil at that time; Indicates the effective bulk modulus of a fluid; These represent the concentrated flow uncertainty of the rodless cavity and the concentrated flow uncertainty of the rod cavity, respectively, including modeling error, internal leakage and hose elastic deformation disturbance; These represent the forward flow rate through the servo valve port and the return flow rate through the servo valve port, respectively, as follows: ； ;in, and These are the flow gain coefficients for the forward loop and the reverse loop, respectively. This indicates the pump's oil supply pressure. This refers to the displacement of the slide valve. For a proportional valve model, where To control the voltage, S1.3: For a dual-cylinder hydraulic system under nominal operating conditions, based on the load dynamics model, flow dynamics model, and proportional valve model, the following state-space model is derived: ;in, These are the three state variables of a dual-cylinder hydraulic system. They are defined as follows: ； Let each represent an unknown nonlinear term of the lumped set, defined as follows: S1.4: Define the tracking error of a dual-cylinder hydraulic system. and synchronization error ： ;in ， Indicates the first Tracking error of individual hydraulic cylinders; system coupling error Defined as: ;in It is the identity matrix. It is the gain used to adjust the synchronization control weights.

3. The fixed-time optimal synchronization control method for electro-hydraulic actuators of aero engines according to claim 1, characterized in that, Step S2 specifically includes: S2.1: Designing the following fixed-time sliding surface: ;in, ； Design parameters for fixed time; design virtual control law. S2.2: For each step Define the performance metric function: ;in, It is a positive definite weight matrix. For virtual control variables; S2.3: This is the optimal virtual control quantity for this step. Based on optimal control theory, the following Hamilton-Jacobi-Bellman equation is obtained: ;make ,get: S2.4: Based on the fixed-time stability theorem, actor networks and critic networks are used respectively to solve the Hamilton-Jacobi-Bellman equation to approximate the gradient of the optimal performance index. With optimal virtual control ； ； ;in, ； These are the weight estimates for the critic network and the actor network, respectively. It is a radial basis function vector; S2.5: Introduce a fixed-time convergence mechanism and design a double power adaptive law to update network weights: ； ;in, The learning rate satisfies 。 4. The fixed-time optimal synchronization control method for electro-hydraulic actuators of aero engines according to claim 1, characterized in that, Step S3 specifically includes: S3.1: For unmodeled dynamics Design robust compensation control terms: ;in, ， For approximation The radial basis function vector of the neural network; For network weights; S3.2: Let Design parameter update law: By iteratively updating the weights according to the aforementioned weight update law, the robust compensation control term is obtained. This is used to synthesize the final control quantity.

5. The fixed-time optimal synchronization control method for electro-hydraulic actuators of aero engines according to claim 1, characterized in that, Specifically, step S4 involves superimposing the optimal virtual control law based on reinforcement learning generated in S2 with the robust compensation control term introduced in S3. ）： ;in, This is the virtual control quantity in the first step. It is the virtual control quantity of the second step, and has Based on the system state-space equations in S1.3, the final control signal is obtained: 。

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