Method and system for speed synchronization control of dual-motor driving system for electromechanical actuator

Abstract

This application relates to the field of synchronous motor technology, specifically providing a method and system for speed synchronization control of a dual-motor drive system for electromechanical actuators. The method includes: establishing an extended state-space model with unified cross-coupling of the two motors, determining the corresponding extended state observer, and generating disturbance estimates in real time; adaptively tuning the gain parameters of the extended state observer based on the real-time observation error; designing a dual-motor active disturbance rejection speed synchronization controller after feedforward compensation based on the disturbance estimates, and adaptively tuning the control parameters to obtain an active disturbance rejection control law adapted to the real-time operating conditions; designing an adaptive law for the cross-coupling coefficient, updating the cross-coupling coefficient in real time, and synchronously updating the extended state-space model and the active disturbance rejection control law, and adjusting the dual-motor control input in real time. Through the collaborative adaptive mechanism of the cross-coupling coefficient, observer bandwidth, and controller bandwidth, the synchronization accuracy, disturbance rejection capability, and dynamic response capability under complex and variable aerospace operating conditions are significantly improved.

Description

Technical Field

[0001] This application relates to the field of synchronous motor technology, and in particular to a method and system for synchronous speed control of a dual-motor drive system for electromechanical actuators. Background Technology

[0002] As aircraft evolve towards greater electrification and full electrification, higher demands are placed on the output power, dynamic response, and reliability of electromechanical actuators. Employing a dual-motor parallel drive electromechanical actuator design, through power sharing and redundancy, has become a novel technical approach to meet these stringent requirements.

[0003] However, while improving performance, dual-motor drive systems also introduce complex synchronization control problems. Traditional methods for dual-motor synchronization control mainly employ master-slave control, parallel control, or cross-coupling control based on deviation compensation. Master-slave control has a simple structure, but the slave motor always lags behind the master motor, resulting in poor dynamic synchronization performance and an inability to handle disturbances from sudden load changes to the master motor. Parallel control involves designing independent controllers for the two motors, but it is extremely sensitive to parameter differences and disturbances; while steady-state accuracy can be guaranteed, dynamic synchronization performance is insufficient. Classical cross-coupling control compensates for synchronization errors by introducing speed difference feedback, improving dynamic synchronization performance to some extent, but it cannot fundamentally describe and utilize the coupled dynamic characteristics inherent in the dual-motor system.

[0004] Meanwhile, in practical aviation applications, actuators face complex nonlinear loads, wide range of parameter perturbations, and uncertain external disturbances. Existing control strategies rely on accurate motor models, and their disturbance rejection capability is essentially limited by control bandwidth and model accuracy. When faced with the above-mentioned combined disturbances, it is difficult to simultaneously guarantee high-precision speed tracking and high-dynamic synchronization performance. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a method and system for speed synchronization control of a dual-motor drive system for electromechanical actuators. Through a collaborative adaptive mechanism of observer bandwidth, controller bandwidth, and cross-coupling coefficient, it significantly improves synchronization accuracy, disturbance rejection capability, and dynamic response capability under complex and ever-changing aerospace conditions.

[0006] To achieve the objectives of this application, the following technical solution is provided:

[0007] In a first aspect, this application provides a method for synchronous speed control of a dual-motor drive system for an electromechanical actuator, comprising:

[0008] A basic dual-motor unified state-space model considering internal and external disturbances is established, and the basic dual-motor unified state-space model is extended to form an extended state-space model containing lumped disturbance terms.

[0009] Based on the extended state space model, a cross-coupling term is introduced to establish the coupling relationship between the two-axis states, forming an extended state space model with unified modeling of cross-coupling between the two motors. Real-time compensation for the synchronization error of the two-axis motion is achieved through the cross-coupling effect.

[0010] The extended state space model based on the unified modeling of the dual-motor cross-coupling determines the corresponding extended state observer and generates disturbance estimates in real time; wherein, the gain parameter of the extended state observer is adaptively tuned according to the real-time observation error.

[0011] After feedforward compensation based on the disturbance estimate, a dual-motor active disturbance rejection speed synchronization controller is designed, and the control parameters are adaptively tuned to obtain an active disturbance rejection control law that adapts to the real-time operating conditions.

[0012] Using the real-time speed synchronization error as the driving quantity, an adaptive law for the cross-coupling coefficient is designed to update the cross-coupling coefficient in real time. Based on the updated cross-coupling coefficient, the extended state space model of the unified model of the cross-coupling of the two motors and the active disturbance rejection control law are updated synchronously to complete the real-time adjustment of the control input of the two motors.

[0013] A further improvement of this invention is that the step of expanding the basic dual-motor unified state-space model to form an extended state-space model including lumped disturbance terms includes: taking the dual permanent magnet synchronous motors as the controlled object, and considering the lumped disturbance of the first motor channel... Lumped disturbance of the second motor channel As newly added state variables, they are extended to the states of the dual-motor drive system, forming an extended state-space model that includes both motion and disturbance states; specifically:

[0014] Formula 1;

[0015] In the formula, Let be the electrical angular acceleration of the first motor. The electric angular acceleration of the second motor. Let be the time-varying rate of the lumped disturbance of the first motor. Let be the time-varying rate of the lumped disturbance of the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. For the first motor shaft current, For the second motor shaft current, This is the lumped disturbance of the first motor channel. This is the lumped disturbance of the second motor channel. This is the nominal torque-current mapping coefficient for the dual motors;

[0016] Based on the extended state-space model, a cross-coupling term is introduced to establish the coupling relationship between the two-axis states, forming an extended state-space model for unified modeling of cross-coupling between the two motors, including:

[0017] A coupling relationship is established between the states of the two motors by introducing a cross-coupling coefficient, specifically as follows:

[0018] Formula 2;

[0019] In the formula, The cross-coupling coefficient;

[0020] Furthermore, rearranging Equation 2 into matrix form, we obtain Equation 3 as follows:

[0021] Formula 3;

[0022] In the formula, Let the system's extended state vector be... , Transpose the mathematical format; The derivative of the system's extended state vector; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, For the input current matrix, The perturbation input matrix is... For the system output vector, This is the output matrix.

[0023] A further improvement of this invention lies in that the step of determining the corresponding extended state observer based on the extended state space model of the unified modeling of the dual-motor cross-coupling, and generating disturbance estimates in real time, includes: designing the corresponding extended state observer based on the extended state space equations of the unified modeling of the dual-motor cross-coupling, specifically:

[0024] Formula 4;

[0025] in, The time derivative of the observation vector of the extended state observer; This is the observation vector of the extended state observer. , This is a mathematical transpose. The estimated value of the electric angular velocity of the first motor. This is the estimated lumped disturbance value for the first motor speed loop. The estimated value of the electric angular velocity of the second motor. This is the estimated lumped disturbance value for the second motor speed loop; The observer gain matrix of the extended state observer. , , , For the gain parameters of the extended state observer, Transpose the mathematical format; The true state vector of the extended state-space model for unified modeling of cross-coupling between two motors; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, This is the output matrix of the extended state-space model; For the input matrix With the control input vector of the dual motors The matrix multiplication terms characterize the driving effect of the control input on the observer; The observer gain matrix With output matrix Matrix multiplication terms; The system matrix for the extended state-space model and The difference matrix;

[0026] Expanding equation four above, we get equation five as follows:

[0027] Formula 5;

[0028] After adaptively tuning the gain parameters of the extended state observer, the speed state and lumped disturbance state of the two motors are estimated in real time, and the speed estimate and disturbance estimate are output.

[0029] Specifically, the initial gain parameters of the extended state observer are determined using the pole placement method, and the bandwidth of the extended state observer is dynamically adjusted based on the real-time observation error using an adaptive law of bandwidth.

[0030] Formula Six;

[0031] In the formula, To expand the bandwidth of the state observer while satisfying boundary constraints , The time derivative of the bandwidth of the extended state observer. This is the minimum limit for the bandwidth of the extended state observer. This is the maximum limit for the bandwidth of the extended state observer; The adaptive gain coefficients for expanding the bandwidth of the state observer. This is the damping coefficient for bandwidth regression, used to prevent parameter drift; for The nominal value, Let $\begin{bmatrix} \ ... , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. The estimated value of the electric angular velocity of the first motor. This is an estimated value for the electric angular velocity of the second motor; A projection operator for expanding the bandwidth of the state observer;

[0032] The gain of the extended state observer is updated in real time according to Equation 6 above, specifically as follows:

[0033] .

[0034] A further improvement of this invention lies in the design of a dual-motor active disturbance rejection speed synchronization controller, and the adaptive tuning of control parameters to obtain an active disturbance rejection control law adapted to real-time operating conditions, including: constructing a time-domain control law to adjust the speed error, wherein the time-domain control law is specifically:

[0035] Formula 7;

[0036] In the formula, This is the input matrix for the dual motors. For reference rotational speed matrix, This is the speed command for the first motor. This is the speed command for the second motor, and , This is the observation vector of the extended state observer; The gain matrix is ​​the reference rotational speed. The state feedback gain matrix is... , ,in, To control the gain, The nominal torque-current mapping coefficient;

[0037] By combining the time-domain dynamic equations of the extended state observer with the time-domain control law, a Laplace transform is performed to derive the frequency-domain expression of the observed state estimate. Substituting the frequency-domain expression of the observed state estimate into the time-domain control law, the frequency-domain control input expression is obtained. Using the real-time control error as the driving variable, a controller bandwidth adaptive law is designed, and the control gain is tuned based on the real-time adaptively updated controller bandwidth to obtain an active disturbance rejection control law adapted to the real-time operating conditions.

[0038] A further improvement of this invention lies in the fact that the derivation of the frequency domain expression of the observed state estimate, and the substitution of the frequency domain expression of the observed state estimate into the time domain control law, yields the frequency domain control input expression, including:

[0039] Combining Equations 7 and 4 above, a Laplace transform is performed to obtain the frequency domain expression of the observed state estimate, specifically:

[0040] Formula 8;

[0041] In the formula, The Laplace transform of the observation vector For the complex frequency variable of the Laplace transform, It is the identity matrix; The observer gain matrix With output matrix Matrix multiplication terms, The system matrix for the extended state-space model and The difference matrix; The input matrix for the extended state-space model With state feedback gain matrix The product; The input matrix for the extended state-space model With state feedback gain matrix The product; Laplace transform of the reference rotational speed matrix The Laplace transform of the true state vector;

[0042] Substituting Equation 8 into Equation 7, we obtain the frequency domain control input expression for Equation 9, which is as follows:

[0043] Formula Nine;

[0044] In the formula, To control the Laplace transform of the input vector.

[0045] A further improvement of this invention is that the step of designing a controller bandwidth adaptive law using real-time speed control error as the driving variable, and tuning the control gain based on the real-time adaptively updated controller bandwidth to obtain an active disturbance rejection control law adapted to real-time operating conditions, includes:

[0046] The controller bandwidth adaptive law is:

[0047] Formula 10;

[0048] In the formula, The controller bandwidth must satisfy the boundary constraints. , For controller bandwidth Time derivative, For controller bandwidth Minimum limit, For controller bandwidth Maximum limit; For controller bandwidth The adaptive gain coefficient, The damping coefficient for bandwidth regression; for The nominal value, The speed control error of the controller. , This is the speed command for the first motor. This is the speed command for the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; For controller bandwidth The projection operator;

[0049] The control gain is set according to formula eleven:

[0050] Formula 11.

[0051] A further improvement of this invention is that the step of designing an adaptive law for the cross-coupling coefficient using the real-time speed synchronization error as the driving quantity, and updating the cross-coupling coefficient in real time, includes: using the real-time speed synchronization error... To drive the variable, an adaptive law for the cross-coupling coefficient is designed, specifically as follows:

[0052] Formula 12;

[0053] In the formula, The cross-coupling coefficients satisfy the boundary constraints. , This represents the minimum limit for the cross-coupling coefficient. This represents the maximum limit of the cross-coupling coefficient; Cross-coupling coefficient The rate of change; The adaptive gain coefficient is the cross-coupling coefficient. This refers to the speed synchronization error; The damping coefficient; Cross-coupling coefficient The nominal value, The projection operator is the cross-coupling coefficient.

[0054] A further improvement of this invention is that, before adaptively tuning the cross-coupling coefficient, it further includes: deriving the load disturbance to the speed synchronization error based on the extended state-space model of the unified modeling of the dual-motor cross-coupling and the frequency domain control input expression. The transfer function is determined, and the correlation between the pole distribution of the transfer function and the cross-coupling coefficient is analyzed to determine the quantitative result of the effect of the cross-coupling coefficient on the synchronization accuracy.

[0055] Specifically, the transfer function is:

[0056] Formula Thirteen;

[0057] In the formula, For speed synchronization error Laplace transform, This represents the lumped disturbance deviation between the first motor and the second motor. ,in, Lumped disturbance for the first motor channel Laplace transform, Lumped disturbance for the second motor channel Laplace transform, For cross-coupling coefficients, For controller bandwidth, , For the gain parameters of the extended state observer, For the Laplace complex frequency operator.

[0058] A further improvement of this invention lies in analyzing the stability of the dual-motor drive system after real-time adjustment of the dual-motor control input. Specifically, the comprehensive error vector of the dual-motor system is defined as:

[0059] Formula Fourteen;

[0060] In the formula, This represents the overall error vector of the dual-motor system. For speed synchronization error, , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; Let be the observation error vector of the extended state observer. , The estimated value of the electric angular velocity of the first motor. This is an estimated value for the electric angular velocity of the second motor; For speed control error, , This is the speed command for the first motor. This is the speed command for the second motor; Transpose the mathematical format;

[0061] By designing Lyapunov functions, a positive definite function is constructed, specifically as follows:

[0062] Formula 15;

[0063] In the formula, It is a Lyapunov function. This represents the overall error vector of the dual-motor system. For the cross-coupling coefficient error, , The ideal cross-coupling coefficient; For the bandwidth error of the extended state observer, , For the bandwidth of the ideal extended state observer; For controller bandwidth error, , Ideal controller bandwidth; This is the transpose of the comprehensive error vector of the dual-motor system; It is a positive definite weight matrix. ; The adaptive gain coefficients for expanding the bandwidth of the state observer. For controller bandwidth The adaptive gain coefficient, The adaptive gain coefficient is the cross-coupling coefficient.

[0064] because , and Since all are constants, the derivative is 0. Therefore, the derivative of the Lyapunov function can be calculated:

[0065] Formula 16;

[0066] In the formula, The derivative of the Lyapunov function. Let be the derivative of the comprehensive error vector of the dual-motor system. The derivative of the bandwidth of the extended state observer, For controller bandwidth The derivative of The derivative of the cross-coupling coefficient;

[0067] Substituting the adaptive laws of equations 6, 10, and 12 into equation 16, we obtain equation 17:

[0068] Formula 17;

[0069] In the formula, It is a symmetric positive definite weight matrix. This confirms the stability of the dual-motor drive system.

[0070] Secondly, this application provides a speed synchronization control system for a dual-motor drive system for electromechanical actuators, used to implement the above-mentioned speed synchronization control method for a dual-motor drive system for electromechanical actuators, comprising:

[0071] The model building module is used to establish a basic dual-motor unified state space model that considers internal and external disturbances, and to augment the basic dual-motor unified state space model to form an extended state space model that includes lumped disturbance terms.

[0072] The coupling and association module is used to introduce cross-coupling terms based on the extended state space model, establish coupling associations between the states of the two axes, form an extended state space model with unified modeling of cross-coupling of the two motors, and realize real-time compensation for the synchronization error of the two-axis motion through cross-coupling.

[0073] The disturbance generation module is used to determine the corresponding extended state observer based on the extended state space model of the unified modeling of the dual-motor cross-coupling, and generate disturbance estimates in real time; wherein, the gain parameter of the extended state observer is adaptively tuned according to the real-time observation error.

[0074] The active disturbance rejection control module is used to design a dual-motor active disturbance rejection speed synchronization controller after feedforward compensation based on the disturbance estimate, and adaptively tune the control parameters to obtain an active disturbance rejection control law that adapts to the real-time operating conditions.

[0075] The adaptive update module is used to design an adaptive law for the cross-coupling coefficient with the real-time speed synchronization error as the driving quantity, update the cross-coupling coefficient in real time, and synchronously update the extended state space model of the unified model of the cross-coupling of the two motors and the active disturbance rejection control law according to the updated cross-coupling coefficient, so as to complete the real-time adjustment of the control input of the two motors.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] This application provides a speed synchronization control method and system for a dual-motor drive system for electromechanical actuators. Addressing load disturbances, parameter perturbations, and unknown external disturbances in harsh operating environments of aerospace electromechanical actuators, it utilizes an extended state observer to treat external load abrupt changes, model uncertainties, parameter perturbations, and dual-motor coupling effects as a unified lumped disturbance for real-time observation and feedforward compensation. A collaborative adaptive mechanism based on three key parameters—observer bandwidth, controller bandwidth, and cross-coupling coefficient—is introduced: the observer bandwidth is adaptively adjusted online based on disturbance observation errors, achieving an optimal trade-off between rapid acquisition of lumped disturbances and suppression of high-frequency noise; the controller bandwidth is adaptively adjusted based on closed-loop control errors, dynamically matching the system's closed-loop pole characteristics after disturbance compensation to prevent excessively large parameters from causing resonance and excessively small parameters from reducing tracking speed; the cross-coupling coefficient is adaptively adjusted based on real-time speed synchronization errors, balancing synchronization suppression strength and system stability. Through the real-time linkage of these three parameters, high-precision speed tracking and high dynamic synchronization performance of the dual-motor drive system are achieved. Attached Figure Description

[0078] The accompanying drawings are provided to further understand this application and form part of the specification. They are used together with the embodiments of this application to explain this application and do not constitute a limitation thereof.

[0079] Figure 1 A schematic flowchart of an optional speed synchronization control method for a dual-motor drive system for electromechanical actuators provided in an embodiment of this application;

[0080] Figure 2 A schematic flowchart of an optional speed synchronization control method for a dual-motor drive system for aircraft electromechanical actuators provided in an embodiment of this application;

[0081] Figure 3 A control block diagram of a speed synchronization control method for a dual-motor drive system for aircraft electromechanical actuators provided in an embodiment of this application;

[0082] Figure 4 This is a schematic diagram illustrating the impact of total disturbance on speed synchronization error under different cross-coupling coefficients, provided in an embodiment of this application.

[0083] Figure 5 The simulation results of dual motors under steady-state loading when using independent active disturbance rejection control for motors provided in the embodiments of this application;

[0084] Figure 6 The simulation results of steady-state loading of dual motors using fixed-parameter cross-coupling active disturbance rejection control provided in the embodiments of this application;

[0085] Figure 7 The simulation results of dual motors under steady-state loading using adaptive cross-coupling active disturbance rejection control provided in the embodiments of this application are shown. Detailed Implementation

[0086] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0087] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature; in the description of this application, unless otherwise stated, "multiple" means two or more.

[0088] An electromechanical actuator (EMA) is a two-stage actuation device that directly converts electrical energy into controlled mechanical force or mechanical displacement (linear or rotational). It drives an electric motor via a power electronic controller, and through a high-reduction-ratio mechanical transmission mechanism, converts the motor's high-speed, low-torque output into a low-speed, high-torque / high-thrust output to drive aircraft control surfaces, landing gear, or other loads. As aircraft evolve towards greater electrification and full electrification, higher demands are placed on the output power, dynamic response, and reliability of EMAs. Employing a dual-motor parallel-drive EMA design, through power sharing and redundancy design, has become a new technological approach to meet these high requirements.

[0089] However, while dual-motor drive systems improve performance, they also introduce complex synchronization control problems. Mechanical connections between the two motors, load disturbances, and differences in the parameters of the driver hardware components can all lead to asynchronous speed outputs, resulting in torque conflicts, uneven mechanical stress, and even system oscillations, severely damaging the actuator's dynamic performance, efficiency, and lifespan. Currently, traditional methods for dual-motor synchronization control mainly employ master-slave control, parallel control, or cross-coupling control based on deviation compensation: Master-slave control has a simple structure, but the slave motor always lags behind the master motor, resulting in poor dynamic synchronization performance and an inability to handle sudden load disturbances to the master motor; parallel control involves designing independent controllers for the two motors (such as PID, Proportional-Integral-Derivative Controller), but it is extremely sensitive to parameter differences and disturbances, and while steady-state accuracy can be guaranteed, dynamic synchronization performance is insufficient; classic cross-coupling control compensates for synchronization errors by introducing speed difference feedback, improving dynamic synchronization performance to some extent, but it cannot fundamentally describe and utilize the coupled dynamic characteristics inherent in the dual-motor system.

[0090] Meanwhile, although traditional cross-coupling control performs well under ideal conditions, its coupling coefficient is usually a fixed value. In practical aviation applications, actuators face complex nonlinear loads, large-range parameter perturbations, and uncertain external disturbances. Fixed-parameter cross-coupling control struggles to maintain optimal synchronization performance across the entire flight envelope. Furthermore, traditional control strategies rely on accurate motor models, and their disturbance rejection capability is inherently limited by control bandwidth and model accuracy. When faced with the aforementioned combined disturbances, it is difficult to simultaneously guarantee high-precision speed tracking and high-dynamic synchronization performance.

[0091] To address the aforementioned technical problems, the present invention proposes the following technical solutions and corresponding embodiments.

[0092] The following is combined Figures 1 to 7 The illustrated embodiments describe the technical solution of the present invention:

[0093] Example 1

[0094] This application provides an embodiment of a speed synchronization control method for a dual-motor drive system for an electromechanical actuator, referring to... Figure 1 As shown, the content includes the following steps S101 to S105:

[0095] Step S101: Establish a basic dual-motor unified state space model that considers internal and external disturbances, and augment the basic dual-motor unified state space model to form an extended state space model that includes lumped disturbance terms.

[0096] In this embodiment, internal and external disturbances are integrated into a lumped disturbance term. Based on state-space theory, the rotational speed and disturbance of the dual motors are treated as state variables to construct a unified mathematical model (basic dual-motor unified state-space model). First, an ideal single-motor model is established; starting from the dynamic model of a single permanent magnet synchronous motor, its mechanical motion equations are considered:

[0097] ;

[0098] In the formula, The electromagnetic torque of the motor. This represents the load torque of the motor. This represents the number of pole pairs of the motor. The electric angular velocity of the motor rotor. For rotational inertia, The viscous friction coefficient of the motor. This is the angular acceleration of the motor rotor.

[0099] Among them, for surface-mounted permanent magnet synchronous motors used in aircraft electromechanical actuators, their electromagnetic torque ,in, This represents the number of pole pairs of the motor. It is a permanent magnet flux linkage. For motor shaft current, This refers to the electromagnetic torque coefficient of a surface-mounted permanent magnet synchronous motor.

[0100] In this embodiment, considering internal and external disturbances, a basic dual-motor unified state-space model incorporating uncertain disturbances is established:

[0101]

[0102] ;

[0103] In the formula, The electric angular acceleration of the first motor represents the dynamic change in the rotational speed of the first motor. The electric angular acceleration of the second motor characterizes the dynamic change in the rotational speed of the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. For the first motor shaft current, For the second motor shaft current, External disturbances This represents the number of pole pairs of the motor. This represents the load torque of the first motor. This is the load torque of the second motor. For rotational inertia, For internal disturbances, Nominal parameters The disturbance caused by the perturbation; considering that the nominal parameters of the first motor and the second motor are the same, i.e., nominal parameters This reflects the natural decay characteristics of the system, among which, It is the coefficient of viscous friction; The nominal torque-current mapping coefficient (nominal parameter), nominal parameter This characterizes the mapping relationship between input current and torque, where... The electromagnetic torque coefficient of a surface-mounted permanent magnet synchronous motor; These are the actual parameters of the first motor. These are the actual parameters of the second motor. This is the lumped disturbance of the first motor channel. This is the lumped disturbance for the second motor channel.

[0104] In this embodiment, a dual permanent magnet synchronous motor is used as the controlled object, and the lumped disturbance of the first motor channel is... Lumped disturbance of the second motor channel As newly added state variables, they are extended to the states of the dual-motor drive system, forming an expanded state-space model that includes both motion and disturbance states (extended state-space model); specifically:

[0105] Formula 1;

[0106] In the formula, Let be the electrical angular acceleration of the first motor. The electric angular acceleration of the second motor. Let be the time-varying rate of the lumped disturbance of the first motor. Let be the time-varying rate of the lumped disturbance of the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. For the first motor shaft current, For the second motor shaft current, This is the lumped disturbance of the first motor channel. This is the lumped disturbance of the second motor channel. This is the nominal torque-current mapping coefficient for the dual motors.

[0107] Step S102: Based on the extended state space model, introduce cross-coupling terms to establish the coupling relationship between the two-axis states, forming an extended state space model for unified modeling of cross-coupling between the two motors.

[0108] In this embodiment, when a dual-motor speed cross-coupling control mechanism is introduced, a coupling relationship is established between the states of the two motors by introducing a cross-coupling coefficient. This allows the state change (speed / disturbance) of one motor to feed back and affect the control input of the other motor, thereby achieving synchronous error compensation for dual-axis motion. Based on Equation 1 above, the state equation is shown in Equation 2:

[0109] Formula 2;

[0110] In the formula, This represents the cross-coupling coefficient.

[0111] Rearranging Equation 2 into matrix form, we get:

[0112] Formula 3;

[0113] In the formula, Let the system's extended state vector be... , Transpose the mathematical format; The derivative of the system's extended state vector; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, For the input current matrix, The perturbation input matrix is... For the system output vector, This is the output matrix.

[0114] In this way, by embedding synchronization error compensation into the essence of the model, the control objective is upgraded from single-motor tracking of the reference speed to dual-motor synchronous tracking and error cancellation, providing model-level coupling support for subsequent synchronous control.

[0115] Step S103: Determine the corresponding extended state observer based on the extended state space model of the unified modeling of the dual-motor cross-coupling, and generate disturbance estimates in real time; wherein, the gain parameter of the extended state observer is adaptively tuned according to the real-time observation error.

[0116] In this embodiment, based on the constructed extended state space equation of the unified modeling of cross-coupling of two motors, a corresponding extended state observer is designed. After adaptively tuning the gain parameters of the extended state observer, the speed state and lumped disturbance state of the two motors are estimated in real time, and the speed estimate and disturbance estimate are output in real time.

[0117] The expression for the generated extended state observer is:

[0118] Formula 4;

[0119] in, The time derivative of the observation vector of the extended state observer; This is the observation vector (time domain) of the extended state observer. , This is a mathematical transpose. The estimated value of the electric angular velocity of the first motor. This is the estimated lumped disturbance value for the first motor speed loop. The estimated value of the electric angular velocity of the second motor. This is the estimated lumped disturbance value for the second motor speed loop; The observer gain matrix of the extended state observer. , , , For the gain parameters of the extended state observer, Transpose the mathematical format; The true state vector of the extended state-space model for unified modeling of cross-coupling between two motors; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, This is the output matrix of the extended state-space model; For the input matrix With the control input vector of the dual motors The matrix multiplication terms characterize the driving effect of the control input on the observer; The observer gain matrix With output matrix Matrix multiplication terms; The system matrix for the extended state-space model and The difference matrix.

[0120] Expanding equation four above, we get:

[0121] Formula 5;

[0122] For the extended state observer shown in Equation 5 above, the convergence characteristic of its observation error dynamic equation is determined by the pole positions of the characteristic equation. Through pole placement design and the introduction of an adaptive mechanism, the adaptive law of the bandwidth of the extended state observer is as follows:

[0123] Formula Six;

[0124] In the formula, To expand the bandwidth of the state observer while satisfying boundary constraints , The time derivative of the bandwidth of the extended state observer. This is the minimum limit for the bandwidth of the extended state observer. This is the maximum limit for the bandwidth of the extended state observer; The adaptive gain coefficients for expanding the bandwidth of the state observer. This is the damping coefficient for bandwidth regression, used to prevent parameter drift; for The nominal value, Let $\begin{bmatrix} \ ... , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. The estimated value of the electric angular velocity of the first motor. Here is the estimated electrical angular velocity of the second motor; where, The projection operator is used to extend the bandwidth of the state observer. Defined as:

[0125] ;

[0126] Using the pole placement method, based on the observer error dynamic equation Convergence requirements, tuning the observer gain matrix The gain of the extended state observer is updated in real time.

[0127] .

[0128] In this way, the extended state observer can simultaneously observe rotational speed and disturbances, and the adaptive gain can dynamically adjust the observer bandwidth according to the operating conditions, balancing response speed and noise immunity. This can solve the problems of complex disturbances and variable operating conditions in the aviation electromechanical actuator scenario and improve the disturbance suppression capability.

[0129] Step S104: After performing feedforward compensation based on the disturbance estimate, design a dual-motor active disturbance rejection speed synchronization controller and adaptively tune the control gain to obtain an active disturbance rejection control law that adapts to the real-time operating conditions.

[0130] In this embodiment, after completing the disturbance feedforward compensation based on the disturbance estimate output in step S103, according to the active disturbance rejection control principle, the observation state vector containing the speed observation value and the disturbance estimate value is... A closed loop is introduced to construct a time-domain control law for speed error regulation. Specifically, the disturbance estimate is encapsulated into the observed state vector and integrated into the time-domain control law. The observed disturbance component is used to complete the disturbance feedforward compensation within the time-domain control law.

[0131] Furthermore, by combining the time-domain dynamic equations and time-domain control law of the extended state observer, a Laplace transform is performed to derive the frequency-domain expression of the observed state estimate. Substituting the frequency-domain expression of the observed state estimate into the time-domain control law, the frequency-domain control input expression is obtained. Using the real-time speed control error as the driving variable, a controller bandwidth adaptive law is designed, and the control gain is tuned based on the real-time adaptively updated controller bandwidth to obtain an active disturbance rejection control law adapted to the real-time operating conditions.

[0132] In this embodiment of the application, based on the principle of active disturbance rejection, after implementing disturbance compensation, the following time-domain control law is constructed to adjust the speed error, specifically:

[0133] Formula 7;

[0134] In the formula, This is the input matrix for the dual motors. For reference rotational speed matrix, This is the speed command (reference speed) for the first motor. This is the speed command (reference speed) for the second motor, and , This is the observation vector of the extended state observer; The gain matrix is ​​the reference rotational speed. The state feedback gain matrix is... , ,in, To control the gain (scalar). This is the nominal torque-current mapping coefficient.

[0135] Combining Equation 7 above and Equation 4 in step S103, a Laplace transform is performed to obtain the frequency domain expression of the observed state estimate, specifically:

[0136] Formula 8;

[0137] In the formula, The Laplace transform of the observation vector For the complex frequency variable of the Laplace transform, It is the identity matrix; The observer gain matrix With output matrix Matrix multiplication terms, The system matrix for the extended state-space model and The difference matrix; The input matrix for the extended state-space model With state feedback gain matrix The product; The input matrix for the extended state-space model With state feedback gain matrix The product; Laplace transform of the reference rotational speed matrix This is the Laplace transform of the true state vector.

[0138] Substituting Equation 8 into Equation 7, we obtain the frequency domain control input expression:

[0139] Formula Nine;

[0140] In the formula, To control the Laplace transform of the input vector.

[0141] According to Equation 9 above, configuring the controller poles can ensure rapid convergence of control errors and controller bandwidth. The adaptive law is designed as follows:

[0142] Formula 10;

[0143] In the formula, The controller bandwidth must satisfy the boundary constraints. , For controller bandwidth Time derivative, For controller bandwidth Minimum limit, For controller bandwidth Maximum limit; For controller bandwidth The adaptive gain coefficient, This is the damping coefficient for bandwidth regression, used to prevent parameter drift; for The nominal value, The speed control error of the controller. , This is the speed command for the first motor. This is the speed command for the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; For controller bandwidth The projection operator.

[0144] In the embodiments of this application, the control gain Set according to the following formula:

[0145] Formula 11;

[0146] In the formula, This is the controller bandwidth. Thus, by adjusting the control gain through an adaptive mechanism, the control bandwidth is adapted to the system's dynamic characteristics; the adaptive control parameters enable the controller to cope with parameter perturbations and changes in operating conditions, further ensuring synchronization accuracy and dynamic response speed.

[0147] Step S105: Using the real-time speed synchronization error as the driving quantity, design an adaptive law for the cross-coupling coefficient, update the cross-coupling coefficient in real time, and synchronously update the extended state space model of the unified modeling of the cross-coupling of the two motors and the active disturbance rejection control law according to the updated cross-coupling coefficient, so as to complete the real-time adjustment of the control input of the two motors.

[0148] In this embodiment, based on the extended state-space model of the unified modeling of the dual-motor cross-coupling and the frequency domain control input expression, the transfer function from load disturbance to speed synchronization error is derived, and the correlation between the pole distribution of the transfer function and the cross-coupling coefficient is analyzed to determine the quantitative result of the effect of the cross-coupling coefficient on synchronization accuracy. Using the real-time speed synchronization error as the driving quantity, an adaptive law for the cross-coupling coefficient is designed to update the cross-coupling coefficient in real time. The extended state-space model and the active disturbance rejection control law are updated synchronously based on the updated cross-coupling coefficient. Finally, the dual-motor control input is adjusted in real time based on the updated extended state-space model and the active disturbance rejection control law.

[0149] In this embodiment, the rotational speed synchronization error is used as a feedback signal, and the cross-coupling coefficient is adaptively designed. Combining Equation 2 of step S102 and Equation 9 of step S104 above, the lumped disturbance deviation of the first motor and the second motor can be obtained. To speed synchronization error The specific expression for the transfer function is as follows:

[0150] Formula Thirteen;

[0151] In the formula, For speed synchronization error Laplace transform, For cross-coupling coefficients, For controller bandwidth, , Here are the gain parameters for the extended state observer. Based on the transfer function expression of the speed synchronization error with respect to the load disturbance, the cross-coupling coefficient can be seen. As a characterization of dual-axis synchronization compensation error, increasing its value can shift the system poles towards the left half of the complex plane, reducing the speed synchronization error caused by disturbances and making error convergence more stable. Excessive error can make the system sensitive to high-frequency noise. Therefore, in this embodiment, the real-time rotational speed synchronization error is used as a reference. To drive the variable, an adaptive law for the cross-coupling coefficient is designed:

[0152] Formula 12;

[0153] In the formula, The cross-coupling coefficients satisfy the boundary constraints. , This represents the minimum limit for the cross-coupling coefficient. This represents the maximum limit of the cross-coupling coefficient; Cross-coupling coefficient The rate of change; The adaptive gain coefficient is the cross-coupling coefficient. This refers to the speed synchronization error; The damping coefficient is... To prevent parameter drift; Cross-coupling coefficient The nominal value, The projection operator is the cross-coupling coefficient.

[0154] Therefore, the cross-coupling coefficient is updated by implementing the adaptive law of cross-coupling coefficient, and the cross-coupling coefficient in step S102 above is updated synchronously. With the aforementioned control law, dynamic coupling compensation of the dual-axis state is achieved; then, based on the updated extended state space model and control law, the control input of the dual motors is adjusted in real time.

[0155] In this way, the convergence speed of synchronization error is accelerated, the steady-state synchronization error is reduced, and system instability caused by excessive coupling coefficient is avoided, thus balancing synchronization accuracy and system stability. Therefore, in this embodiment, the control parameters are adaptively adjusted according to the dynamic characteristics of the system, and the coupling coefficient is dynamically matched with the synchronization error, forming a dual adaptive mechanism. This enables the system to maintain high synchronization accuracy and rapid response under complex operating conditions such as parameter perturbations, sudden disturbances, and speed changes, avoiding performance degradation caused by fixed parameters and meeting the stringent robustness requirements of the aerospace field.

[0156] As a feasible implementation method, after completing the above-described adaptive active disturbance rejection speed cross-coupling synchronization control, the stability of the speed synchronization control system is analyzed. Specifically, the comprehensive error vector of the dual-motor system is defined as:

[0157] Formula Fourteen;

[0158] In the formula, This represents the overall error vector of the dual-motor system. For speed synchronization error, , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; Let be the observation error vector of the extended state observer. , The estimated value of the electric angular velocity of the first motor. This is an estimated value for the electric angular velocity of the second motor; For speed control error, , This is the speed command for the first motor. This is the speed command for the second motor; Transpose the mathematical format;

[0159] Then, through the design of Lyapunov functions, a positive definite function is constructed, specifically:

[0160] Formula 15;

[0161] In the formula, It is a Lyapunov function. This represents the overall error vector of the dual-motor system. For the cross-coupling coefficient error, , The ideal cross-coupling coefficient; For the bandwidth error of the extended state observer, , For the bandwidth of the ideal extended state observer; For controller bandwidth error, , Ideal controller bandwidth; This is the transpose of the comprehensive error vector of the dual-motor system; It is a positive definite weight matrix. ; The adaptive gain coefficients for expanding the bandwidth of the state observer. For controller bandwidth The adaptive gain coefficient, The adaptive gain coefficient is the cross-coupling coefficient.

[0162] because , and Since all are constants, the derivative is 0. Therefore, the derivative of the Lyapunov function can be calculated:

[0163] Formula 16;

[0164] In the formula, The derivative of the Lyapunov function. Let be the derivative of the comprehensive error vector of the dual-motor system. The derivative of the bandwidth of the extended state observer, For controller bandwidth The derivative of This is the derivative of the cross-coupling coefficient. If the ideal cross-coupling coefficient... The truth value is in the interval Ideal observer parameters The truth value is in the interval Ideal control parameters The truth value is in the interval Within, according to the properties of the projection operator, we have , , Substituting the adaptive laws from equations 6, 10, and 12 into equation 16, we obtain:

[0165] Formula 17;

[0166] In the formula, It is a symmetric positive definite weight matrix. .

[0167] Therefore, the designed adaptive law can guarantee the global stability of the closed-loop system, and all errors are bounded consistent with the parameter errors. In this embodiment, the cross-coupling coefficient, observer bandwidth, and controller bandwidth are designed collaboratively based on Lyapunov stability theory, and the boundedness of the parameters is guaranteed by the projection operator, ensuring the global stability of the closed-loop system. As a result, synchronization accuracy, disturbance rejection capability, and dynamic response are significantly improved under complex and variable aerospace conditions.

[0168] This embodiment provides a speed synchronization control method and system for a dual-motor drive system for electromechanical actuators. Addressing load disturbances, parameter perturbations, and unknown external disturbances in harsh operating environments of aerospace electromechanical actuators, it utilizes an extended state observer to treat external load abrupt changes, model uncertainties, parameter perturbations, and dual-motor coupling effects as a unified lumped disturbance for real-time observation and feedforward compensation. A collaborative adaptive mechanism based on three key parameters—observer bandwidth, controller bandwidth, and cross-coupling coefficient—is introduced: the observer bandwidth is adaptively adjusted online based on disturbance observation errors, achieving an optimal trade-off between rapid acquisition of lumped disturbances and high-frequency noise suppression; the controller bandwidth is adaptively adjusted based on closed-loop control errors, dynamically matching the system's closed-loop pole characteristics after disturbance compensation to prevent excessively large parameters from causing resonance and excessively small parameters from reducing tracking speed; the cross-coupling coefficient is adaptively adjusted based on real-time speed synchronization errors, balancing synchronization suppression strength and system stability. Through real-time linkage of these three parameters, high-precision speed tracking and high dynamic synchronization performance of the dual-motor drive system are achieved.

[0169] Example 2

[0170] Based on the above embodiments, the specific parameters of the permanent magnet synchronous motor used in this embodiment are shown in Table 1. To verify the effectiveness of the proposed speed synchronization control method, the speed synchronization control method of the dual-motor drive system for aircraft electromechanical actuators was simulated and verified using Matlab / Simulink software.

[0171] Table 1

[0172]

[0173] This embodiment provides a method for speed synchronization control of a dual-motor drive system for aircraft electromechanical actuators, referring to... Figure 2 and Figure 3 As shown, the specific steps include S201 to S208:

[0174] Step S201: Establish a unified dynamic mathematical model of the two motors considering disturbances.

[0175] Starting from the dynamic model of a single permanent magnet synchronous motor, consider its mechanical motion equations:

[0176] Formula D1;

[0177] In the formula, The electromagnetic torque of the motor. This represents the load torque of the motor. This represents the number of pole pairs of the motor. The electric angular velocity of the motor rotor. For rotational inertia, The viscous friction coefficient of the motor. This refers to the angular acceleration of the motor rotor. For surface-mounted permanent magnet synchronous motors used in aircraft electromechanical actuators, its electromagnetic torque... ,in, This represents the number of pole pairs of the motor. It is a permanent magnet flux linkage. For motor shaft current, The electromagnetic torque coefficient of a surface-mounted permanent magnet synchronous motor. .

[0178] Considering internal and external disturbances, a unified state-space model of a basic dual-motor system incorporating uncertain disturbances is established:

[0179]

[0180] Formula D2

[0181] In the formula, Let be the electrical angular acceleration of motor 1; Let be the electrical angular acceleration of motor 2; Let be the electrical angular velocity of motor 1. Let be the electrical angular velocity of motor 2. For motor 1 shaft current, For motor 2 shaft current, External disturbances This represents the number of pole pairs of the motor. This represents the load torque of motor 1. This is the load torque of motor 2. For rotational inertia, For internal disturbances, Nominal parameters Disturbance caused by perturbation; These are the actual parameters of motor 1. These are the actual parameters of motor 2. This is the lumped disturbance for motor channel 1. This refers to the lumped disturbance of motor channel 2; considering that motors 1 and 2 have the same nominal parameters, there are nominal parameters. nominal parameters .

[0182] Step S202: Extend the system model to an extended state equation form that includes lumped disturbance terms.

[0183] Disturbance and disturbance Extending this to the state of a dual-motor drive system, we obtain the expanded state-space model:

[0184] Formula D3.

[0185] Step S203: Establish the state-space equations for unified modeling of cross-coupling of dual motors.

[0186] A dual-motor speed cross-coupling control is introduced to establish a coupling relationship between the states of the two axes, which is used to compensate for the synchronization error of the two-axis motion. The state equation is as follows:

[0187] Formula D4;

[0188] In the formula, This represents the cross-coupling coefficient.

[0189] Rearranging Equation D4 into matrix form, we obtain the state equation:

[0190] Formula D5;

[0191] In the formula, Let the system's extended state vector be... ; The derivative of the system's extended state vector; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, For the input current matrix, The perturbation input matrix is... For the system output vector, This is the output matrix.

[0192] Step S204: Design an extended state observer for the established state-space equations of the dual-motor cross-coupling unified model.

[0193] Formula D6;

[0194] in, The time derivative of the observation vector of the extended state observer; This is the observation vector (time domain) of the extended state observer. For state variables, Here is the estimated electrical angular velocity of motor 1. This is the estimated value of the lumped disturbance in the speed loop of motor 1. The estimated value of the electric angular velocity of motor 2. This is the estimated value of the lumped disturbance in the second speed loop of the motor; The observer gain matrix of the extended state observer. , , , For the gain parameters of the extended state observer; The true state vector of the extended state-space model for unified modeling of cross-coupling between two motors;

[0195] Expanding equation D6 above, we get:

[0196] Formula D7

[0197] Step S205: Adaptively tune the gain parameters of the extended state observer.

[0198] Formula D8;

[0199] In the formula, To expand the bandwidth of the state observer while satisfying boundary constraints , The time derivative of the bandwidth of the extended state observer. , Adaptive gain coefficient of extended state observer bandwidth Damping coefficient , nominal value Among them, the projection operator Defined as:

[0200] Formula D9;

[0201] The parameters of the extended state observer are updated based on the results of equation D8 as follows:

[0202] Formula D10;

[0203] in, The poles configured for the extended state observer.

[0204] Step S206: Design a dual-motor self-disruption speed synchronization controller and adaptively tune the control parameters.

[0205] The following control law is constructed to adjust the speed error:

[0206] Formula D11;

[0207] In the formula, This is the input matrix for the dual motors. For reference rotational speed matrix, This is the reference speed for motor 1. This is the reference speed of motor 2, and , This is the observation vector of the extended state observer; The gain matrix is ​​the reference rotational speed. The state feedback gain matrix is... , ,in, To control the gain. Controller bandwidth. ω c The adaptive law is designed as follows:

[0208] Formula D12;

[0209] In the formula, The controller bandwidth must satisfy the boundary constraints. , The time derivative of the controller bandwidth. This is the minimum limit for the controller bandwidth. , This is the maximum limit of the controller bandwidth. ; The adaptive gain coefficient for the controller bandwidth. , is the damping coefficient for bandwidth regression. To prevent parameter drift; for The nominal value, ; The speed control error of the controller. , This is the speed command for motor 1. This is the speed command for motor 2. Let be the electrical angular velocity of motor 1. Let be the electric angular velocity of motor 2; The projection operator is the controller bandwidth.

[0210] In this embodiment, the control gain is set by the following formula:

[0211] Formula D13;

[0212] Step S207: Adaptively design the cross-coupling coefficient based on the speed synchronization error.

[0213] Lumped disturbance deviation of motor 1 and motor 2 To speed synchronization error The transfer function expression is:

[0214] Formula D14;

[0215] In the formula, For speed synchronization error Laplace transform, For cross-coupling coefficients, For controller bandwidth, , This refers to the gain coefficient of the observer. (The text abruptly ends here, seemingly mid-sentence.) k c The effect of disturbance on synchronization error under the following conditions is as follows: Figure 4 It can be seen that as the coupling coefficient increases, the system's disturbance suppression capability decreases in the low and medium frequency range (approximately 1). The cross-coupling coefficient (100 rad / s) is significantly enhanced. Its amplitude-frequency curve shifts downwards overall, indicating that the impact of external disturbances on speed synchronization error is further attenuated, especially in the critical low-frequency range of speed synchronization control. However, an excessively high cross-coupling coefficient can introduce excessive noise, thus affecting system performance. Therefore, a reasonable selection of the cross-coupling coefficient is necessary. k c .

[0216] In this embodiment, the real-time rotational speed synchronization error is used. To drive the variable, an adaptive law for the cross-coupling coefficient is designed:

[0217] Formula D15;

[0218] In the formula, The cross-coupling coefficients satisfy the boundary constraints. ; Cross-coupling coefficient The rate of change; The adaptive gain coefficient is the cross-coupling coefficient. ; The damping coefficient is... ; Cross-coupling coefficient The nominal value, , The projection operator is the cross-coupling coefficient.

[0219] Therefore, by implementing the adaptive law of cross-coupling coefficients, the cross-coupling coefficients are updated, and the equation D6 in step S204 above is updated synchronously. With the aforementioned control law, dynamic coupling compensation of the dual-axis state is achieved; then, based on the updated extended state space model and control law, the control input of the dual motors is adjusted in real time.

[0220] Step S208: Analyze the stability of the speed synchronization control system.

[0221] Define the comprehensive error vector of the dual-motor system as:

[0222] Formula D16;

[0223] In the formula, This represents the overall error vector of the dual-motor system. This refers to the speed synchronization error; Let be the observation error vector of the extended state observer. , Here is the estimated electrical angular velocity of motor 1. This is the estimated value of the electric angular velocity of motor 2; For speed control error, , This is the speed command for motor 1. This is the speed command for motor 2; Transpose the mathematical format;

[0224] Then, through the design of Lyapunov functions, a positive definite function is constructed, specifically:

[0225] Formula D17;

[0226] In the formula, It is a Lyapunov function. For the deviation of the cross-coupling coefficient, , The ideal cross-coupling coefficient; For the bandwidth error of the extended state observer, , For the bandwidth of the ideal extended state observer; For controller bandwidth error, , Ideal controller bandwidth; It is a positive definite weight matrix. In this embodiment, it is taken as ; , , ;

[0227] Then calculate the derivative of the Lyapunov function:

[0228] Formula D18;

[0229] In the formula, The derivative of the Lyapunov function. Let be the derivative of the comprehensive error vector of the dual-motor system. The derivative of the bandwidth of the extended state observer, The derivative of the controller bandwidth. This is the derivative of the controller bandwidth. If the ideal cross-coupling coefficient... The truth value is in the interval Ideal extended state observer bandwidth The truth value is in the interval Ideal control The truth value is in the interval Within, according to the properties of the projection operator, we have , , Substituting the adaptive laws of equations D8, D12, and D15 into equation D18, we obtain:

[0230] ;

[0231] In the formula, It is a symmetric positive definite weight matrix. In this embodiment, it is taken as Therefore, the designed adaptive law can guarantee the global stability of the closed-loop system, and all errors are consistent with the bounded parameter errors.

[0232] The speed synchronization control method of the dual-motor drive system for aircraft electromechanical actuators in this embodiment is simulated and verified. Figures 5 to 7 The simulation results are for applying load torque disturbance to two motors under steady-state speed conditions. i d1 , i d2The d-axis currents and speed synchronization errors of motors 1 and 2 are respectively. When the dual motors reach steady-state speed, a load disturbance of 0.4 N·m is applied to motor 1 at 0.4 s. The performance of three control strategies—motor independent active disturbance rejection control, fixed parameter cross-coupled active disturbance rejection control, and adaptive cross-coupled active disturbance rejection control—is compared. Figure 5 In the case of independent active disturbance rejection control of the motor, a cross-coupling coefficient is set. k c =0, controller bandwidth ω c =150, observer bandwidth ω o =600, Motor 1 speed drops significantly, speed synchronization error Peak value 40.2 rad / s, and the rotational speed recovery is slow; Figure 6 In this context, fixed-parameter cross-coupled active disturbance rejection control combines the advantages of active disturbance compensation and synchronization deviation correction, with a cross-coupling coefficient... k c =50, controller bandwidth ω c =150, observer bandwidth ω o =600, which reduces the speed drop of motor 1 and the speed synchronization error. Peak value reduced to The speed recovery is faster at 28 rad / s, the peak value of the synchronization error and the convergence time are significantly optimized, and the disturbance rejection performance is improved compared with the independent active disturbance rejection control of the motor; the simulation results of adaptive cross-coupling active disturbance rejection control are as follows: Figure 7 As shown, after applying a load for 0.4 s, when the sudden change in load causes an increase in observation and synchronization errors, the cross-coupling coefficient... k c Controller bandwidth ω c and extended state observer bandwidth ω o All three parameters are automatically increased to accelerate the convergence of the dual motor speed synchronization error, thus reducing the speed synchronization error. ω err Peak value only With a gain of 17.8 rad / s, the recovery speed is faster, the synchronization performance between the two motors is stronger, and the three parameters automatically return to their nominal values ​​in steady state, avoiding excessive gain that could cause system instability.

[0233] Based on the above frequency domain theoretical analysis and time domain simulation results, the proposed speed synchronization control method for dual-motor drive systems of aircraft electromechanical actuators demonstrates significant advantages in multiple dimensions. In the frequency domain, the cross-coupling coefficient was clarified through parametric Bode plot analysis. k c The impact on the system's anti-disturbance performance provides a theoretical basis for the selection of adaptive boundary limits for parameters. In time-domain simulation, the method exhibits characteristics of fast response, small synchronization error, strong recovery capability, and high robustness under sudden load disturbance conditions, providing an excellent solution for achieving high-precision dual-motor speed synchronization control of electromechanical actuators.

[0234] This application also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the method in any of the embodiments of this application. Specifically, a system or apparatus equipped with a storage medium may be provided, on which software program code implementing the functions of any of the above embodiments is stored, and the computer (or CPU (Central Processing Unit) or MPU (Microprocessor Unit) of the system or apparatus may read and execute the program code stored in the storage medium.

[0235] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable storage medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication component, and / or installed from a removable medium. When the computer program is executed by a central processing unit (CPU), it performs the functions defined in the system of this application.

[0236] It should be noted that the computer-readable storage medium shown in this invention can be a computer-readable signal medium, a computer-readable storage medium, or any combination thereof. For example, a computer-readable storage medium can be an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM) or flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. The transmitted data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium can also be any computer-readable storage medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF (Radio Frequency), etc., or any suitable combination thereof.

[0237] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0238] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0239] It should be noted that although several modules or units of the device for performing actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of the present invention, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0240] In the several embodiments provided in this application, it should be understood that the disclosed systems, modules, and methods can be implemented in other ways. For example, the module embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between modules or units, and may be electrical, mechanical, or other forms.

[0241] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. This application is not limited to the exact structures described above and illustrated in the accompanying drawings, and it should not be considered that the specific implementation of this application is limited to these descriptions. For those skilled in the art, various changes and modifications made without departing from the concept of this application should be considered to fall within the protection scope of this application.

Claims

1. A method of controlling the rotation speed of a dual-motor drive system for an electromechanical actuator, characterized by, include: A basic dual-motor unified state-space model considering internal and external disturbances is established, and the basic dual-motor unified state-space model is extended to form an extended state-space model containing lumped disturbance terms. Based on the extended state space model, a cross-coupling term is introduced to establish the coupling relationship between the two-axis states, forming an extended state space model with unified modeling of cross-coupling between the two motors. Real-time compensation for the synchronization error of the two-axis motion is achieved through the cross-coupling effect. The extended state space model based on the unified modeling of the dual-motor cross-coupling determines the corresponding extended state observer and generates disturbance estimates in real time; wherein, the gain parameter of the extended state observer is adaptively tuned according to the real-time observation error. After feedforward compensation based on the disturbance estimate, a dual-motor active disturbance rejection speed synchronization controller is designed, and the control parameters are adaptively tuned to obtain an active disturbance rejection control law that adapts to the real-time operating conditions. Using the real-time speed synchronization error as the driving quantity, an adaptive law for the cross-coupling coefficient is designed to update the cross-coupling coefficient in real time. Based on the updated cross-coupling coefficient, the extended state space model of the unified model of the cross-coupling of the two motors and the active disturbance rejection control law are updated synchronously to complete the real-time adjustment of the control input of the two motors.

2. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 1, characterized by, The process of augmenting the basic dual-motor unified state-space model to form an extended state-space model containing lumped disturbance terms includes: Taking double permanent magnet synchronous motor as control object, the lumped disturbance of the first motor channel and the lumped disturbance of the second motor channel are augmented into the state of the double motor drive system as new state variables, to form an extended state space model containing motion state and disturbance state; specifically: Formula 1; In the formula, Let be the electrical angular acceleration of the first motor. The electric angular acceleration of the second motor. Let be the time-varying rate of the lumped disturbance of the first motor. Let be the time-varying rate of the lumped disturbance of the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. For the first motor shaft current, For the second motor shaft current, This is the lumped disturbance of the first motor channel. This is the lumped disturbance of the second motor channel. This is the nominal torque-current mapping coefficient for the dual motors; Based on the extended state-space model, a cross-coupling term is introduced to establish the coupling relationship between the two-axis states, forming an extended state-space model for unified modeling of cross-coupling between the two motors, including: A coupling relationship is established between the states of the two motors by introducing a cross-coupling coefficient, specifically as follows: Formula 2; wherein is the cross-coupling coefficient; Then, rearranging Equation 2 into matrix form, we obtain Equation 3 as follows: Formula 3; In the formula, Let the system's extended state vector be... , Transpose the mathematical format; The derivative of the system's extended state vector; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, For the input current matrix, The perturbation input matrix, For the system output vector, This is the output matrix.

3. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 2, characterized by, The extended state space model based on the unified modeling of the dual-motor cross-coupling determines the corresponding extended state observer and generates disturbance estimates in real time, including: Based on the extended state-space equations of the unified modeling of the dual-motor cross-coupling, a corresponding extended state observer is designed, specifically as follows: Formula 4; in, This is the observation vector of the extended state observer. , For mathematical format transpose, The estimated value of the electric angular velocity of the first motor. This is the estimated lumped disturbance value for the first motor speed loop. The estimated value of the electric angular velocity of the second motor. This is the estimated lumped disturbance value for the second motor speed loop; The observer gain matrix is... , , , For the gain parameters of the extended state observer, Transpose the mathematical format; The true state vector of the extended state-space model for unified modeling of cross-coupling between two motors; The time derivative of the observation vector of the extended state observer; For the system matrix of the extended state-space model, The input matrix for the extended state-space model, This is the output matrix of the extended state-space model; For the input matrix With the control input vector of the dual motors The matrix multiplication terms characterize the driving effect of the control input on the observer; The observer gain matrix With output matrix Matrix multiplication terms; The system matrix for the extended state-space model and The difference matrix; Expanding equation four above, we get equation five as follows: Formula 5; After adaptively tuning the gain parameters of the extended state observer, the speed state and lumped disturbance state of the two motors are estimated in real time, and the speed estimate and disturbance estimate are output. Specifically, the initial gain parameters of the extended state observer are determined using the pole placement method, and the bandwidth of the extended state observer is dynamically adjusted based on the real-time observation error using an adaptive law of bandwidth. Formula Six; In the formula, To expand the bandwidth of the state observer while satisfying boundary constraints , This is the minimum limit for the bandwidth of the extended state observer. This is the maximum limit for the bandwidth of the extended state observer; The adaptive gain coefficients for expanding the bandwidth of the state observer. The damping coefficient for bandwidth regression; for The nominal value, Let $\begin{bmatrix} \ ... , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor. The estimated value of the electric angular velocity of the first motor. This is an estimated value for the electric angular velocity of the second motor; For the projection operator that expands the bandwidth of the state observer, The time derivative of the bandwidth of the extended state observer; The gain of the extended state observer is updated in real time according to Equation 6 above, specifically as follows: 。 4. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 3, characterized by The design of the dual-motor active disturbance rejection speed synchronization controller, and the adaptive tuning of the control parameters, yields an active disturbance rejection control law adapted to real-time operating conditions, including: A time-domain control law is constructed to adjust the speed error. Specifically, the time-domain control law is as follows: Formula 7; In the formula, This is the input matrix for the dual motors. For reference rotational speed matrix, This is the speed command for the first motor. This is the speed command for the second motor, and , This is the observation vector of the extended state observer; The gain matrix is ​​the reference rotational speed. The state feedback gain matrix, , ,in, To control the gain, The nominal torque-current mapping coefficient; By combining the time-domain dynamic equations of the extended state observer with the time-domain control law, a Laplace transform is performed to derive the frequency-domain expression of the observed state estimate. The frequency-domain expression of the observed state estimate is then substituted into the time-domain control law to obtain the frequency-domain control input expression. Using the real-time speed control error as the driving variable, an adaptive controller bandwidth law is designed, and the control gain is tuned based on the real-time adaptively updated controller bandwidth to obtain an active disturbance rejection control law that adapts to the real-time operating conditions.

5. The method for synchronous speed control of a dual-motor drive system for an electromechanical actuator according to claim 4, characterized in that, The process involves deriving the frequency domain expression of the observed state estimate and substituting this expression into the time domain control law to obtain the frequency domain control input expression, including: Combining Equations 7 and 4 above, a Laplace transform is performed to obtain the frequency domain expression of the observed state estimate, specifically: Formula 8; In the formula, The Laplace transform of the observation vector For the complex frequency variable of the Laplace transform, It is the identity matrix; The observer gain matrix With output matrix Matrix multiplication terms, The system matrix for the extended state-space model and The difference matrix; The input matrix for the extended state-space model With state feedback gain matrix The product; The input matrix for the extended state-space model With state feedback gain matrix The product; Laplace transform of the reference rotational speed matrix The Laplace transform of the true state vector; The frequency domain control input expression is determined as follows: Formula Nine; wherein is the Laplacian transform of the control input vector.

6. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 5, characterized by The method of designing an adaptive controller bandwidth law using real-time speed control error as the driving variable, and tuning the control gain based on the real-time adaptively updated controller bandwidth to obtain an active disturbance rejection control law adapted to real-time operating conditions, includes: The controller bandwidth adaptive law is: Formula 10; In the formula, The controller bandwidth must satisfy the boundary constraints. , The time derivative of the controller bandwidth. This is the minimum limit for the controller bandwidth. This is the maximum limit of the controller bandwidth; The adaptive gain coefficient for the controller bandwidth. The damping coefficient for bandwidth regression; for The nominal value, The speed control error of the controller. , This is the speed command for the first motor. This is the speed command for the second motor. Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; The projection operator for the controller bandwidth; The control gain is set according to formula eleven: Formula 11; In the formula, is the nominal torque current mapping coefficient for the dual motor.

7. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 6, characterized by The method of designing an adaptive law for the cross-coupling coefficient, using real-time speed synchronization error as the driving variable, and updating the cross-coupling coefficient in real time, includes: Based on real-time speed synchronization error To drive the variable, an adaptive law for the cross-coupling coefficient is designed, specifically as follows: Formula 12; In the formula, The cross-coupling coefficients satisfy the boundary constraints. , This represents the minimum limit for the cross-coupling coefficient. This represents the maximum limit of the cross-coupling coefficient; The adaptive gain coefficient is the cross-coupling coefficient. This refers to the speed synchronization error; The damping coefficient is... ; Cross-coupling coefficient The nominal value, The projection operator for the cross-coupling coefficients; Cross-coupling coefficient The rate of change.

8. The method according to any one of claims 4 to 7, wherein the method is characterized by: Before adaptively tuning the cross-coupling coefficients, the following is also included: Based on the extended state-space model of the unified modeling of the dual-motor cross-coupling and the frequency domain control input expression, the load disturbance to speed synchronization error is derived. The transfer function is determined, and the correlation between the pole distribution of the transfer function and the cross-coupling coefficient is analyzed to determine the quantitative result of the effect of the cross-coupling coefficient on the synchronization accuracy. Specifically, the transfer function is: Formula Thirteen; In the formula, For speed synchronization error Laplace transform, This represents the lumped disturbance deviation between the first motor and the second motor. ,in, Lumped disturbance for the first motor channel Laplace transform, Lumped disturbance for the second motor channel Laplace transform, For cross-coupling coefficients, For controller bandwidth, , For the gain parameters of the extended state observer, For the Laplace complex frequency operator.

9. The dual-motor drive system rotational speed synchronization control method for an electromechanical actuator according to claim 8, characterized by, After completing the real-time adjustment of the dual-motor control input, the stability of the dual-motor drive system is analyzed, specifically as follows: Define the comprehensive error vector of the dual-motor system as: Formula Fourteen; In the formula, This represents the overall error vector of the dual-motor system. For speed synchronization error, , Let be the electrical angular velocity of the first motor. The electric angular velocity of the second motor; Let be the observation error vector of the extended state observer. , The estimated value of the electric angular velocity of the first motor. This is an estimated value for the electric angular velocity of the second motor; For speed control error, , This is the speed command for the first motor. This is the speed command for the second motor; Transpose the mathematical format; By designing Lyapunov functions, a positive definite function is constructed, specifically as follows: Formula 15; In the formula, It is a Lyapunov function. This represents the overall error vector of the dual-motor system. For the deviation of the cross-coupling coefficient, , The ideal cross-coupling coefficient; For the bandwidth error of the extended state observer, , For the bandwidth of the ideal extended state observer; For controller bandwidth error, , Ideal controller bandwidth; This is the transpose of the comprehensive error vector of the dual-motor system; It is a positive definite weight matrix. ; The adaptive gain coefficients for expanding the bandwidth of the state observer. The adaptive gain coefficient for the controller bandwidth. The adaptive gain coefficient is the cross-coupling coefficient. Since , and are constants, the derivative is zero, and the Lyapunov function derivative is calculated as: Formula 16; In the formula, The derivative of the Lyapunov function. Let be the derivative of the comprehensive error vector of the dual-motor system. The derivative of the bandwidth of the extended state observer, The derivative of the controller bandwidth. The derivative of the cross-coupling coefficient; Substituting the adaptive laws of equations 6, 10, and 12 into equation 16, we obtain equation 17: Formula 17; In the formula, is a symmetric positive definite weight matrix, ; the stability of the dual-motor drive system is verified.

10. A dual-motor drive system rotational speed synchronization control system for an electromechanical actuator, for implementing the dual-motor drive system rotational speed synchronization control method according to any one of claims 1 to 9, characterized by include: The model building module is used to establish a basic dual-motor unified state space model that considers internal and external disturbances, and to augment the basic dual-motor unified state space model to form an extended state space model that includes lumped disturbance terms. The coupling and association module is used to introduce cross-coupling terms based on the extended state space model, establish coupling associations between the states of the two axes, form an extended state space model with unified modeling of cross-coupling of the two motors, and realize real-time compensation for the synchronization error of the two-axis motion through cross-coupling. The disturbance generation module is used to determine the corresponding extended state observer based on the extended state space model of the unified modeling of the dual-motor cross-coupling, and generate disturbance estimates in real time; wherein, the gain parameter of the extended state observer is adaptively tuned according to the real-time observation error. The active disturbance rejection control module is used to design a dual-motor active disturbance rejection speed synchronization controller after feedforward compensation based on the disturbance estimate, and adaptively tune the control parameters to obtain an active disturbance rejection control law that adapts to the real-time operating conditions. The adaptive update module is used to design an adaptive law for the cross-coupling coefficient with the real-time speed synchronization error as the driving quantity, update the cross-coupling coefficient in real time, and synchronously update the extended state space model of the unified model of the cross-coupling of the two motors and the active disturbance rejection control law according to the updated cross-coupling coefficient, so as to complete the real-time adjustment of the control input of the two motors.

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