Adaptive model prediction control method for aviation electromechanical actuator

Abstract

The invention discloses an adaptive model prediction control method for an aviation electromechanical actuator, relates to the technical field of aviation electromechanical actuators, and designs a corresponding gear clearance torque and friction torque current compensation method by adopting a simplified dead zone model and a LuGre friction model. By organically combining gear backlash compensation and friction compensation and redesigning a control law, the invention provides a control strategy combining feed-forward compensation and model prediction control, and the q-axis current of the system is accurately compensated and controlled; furthermore, an extended Kalman filter is introduced to carry out on-line identification of multiple parameters of the permanent magnet synchronous motor, a high-precision parameter identification result is obtained, and it is ensured that the model parameters of the system can be updated in real time in the control process, so that accurate control over the system is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of aviation electromechanical actuators, and particularly to an adaptive model predictive control method for aviation electromechanical actuators. Background Art

[0002] With the continuous progress of power electronics technology, semiconductor technology, new electrical engineering materials, and motor control technology, the electromechanical actuation system (EMA), as one of the key core technologies of more-electric aircraft, has been widely used in this field. The electromechanical actuator is used to drive the movement and positioning of components such as the aircraft's control surfaces, landing gear, and flaps, and its actuation performance directly affects the safety of the aircraft during takeoff and landing. The electromechanical actuation system directly or indirectly controls the load by controlling the movement of the motor, thereby achieving position or pressure servo control. To meet the aircraft design requirements, the airborne electromechanical actuator must have high control accuracy, fast response speed, and strong anti-interference ability. However, as a highly nonlinear, multivariable, and strongly coupled system, the gear clearance in the mechanical transmission mechanism and the nonlinear friction generated during operation result in problems such as low control accuracy and large torque ripple of electromechanical actuators such as flaps, seriously affecting the stability and safety of the aircraft.

[0003] Currently, the compensation methods for gear clearance can be optimized from two aspects: mechanical and control algorithms. Mechanical backlash elimination techniques, such as dual-motor drive and spring devices, although they can solve the problem to a certain extent, have low efficiency and increase the cost and weight of the equipment. In contrast, compensation through control algorithms can effectively avoid the deficiencies of mechanical methods. Common clearance compensation methods include inverse backlash compensation and observer compensation, etc. The inverse backlash compensation method constructs an inverse backlash model based on the backlash model and converts it into a control quantity to be added to the system control signal to eliminate the backlash nonlinearity. However, the inverse backlash compensation is discontinuous and easily leads to chattering phenomena in the system. The observer compensation method highly depends on the initial conditions of the system during design and is sensitive to interference. If there are deviations in the initial conditions or the model is inaccurate, the observer may not be able to correctly estimate the system disturbance, thereby affecting the compensation effect.

[0004] In terms of control methods, traditional linear control algorithms are difficult to achieve ideal control performance. To balance dynamic response and anti-interference ability, non-linear control methods such as adaptive control, sliding mode control, robust control, and active disturbance rejection control have been proposed and used in the research of gear backlash. However, these methods usually have problems such as strong model dependence, complex parameter debugging processes, high computational burden, and implementation difficulties, which limit their application in practical engineering. For the influence of non-linear friction in mechanical transmission systems on servo systems, scholars at home and abroad have adopted various control compensation methods to compensate for the friction torque. Currently, common classical friction models include Coulomb-viscous friction model, Stribeck model, Dahl model, and LuGre model, etc. Among them, the LuGre friction model is widely used in servo systems because it can comprehensively reflect the motion mechanism of friction and accurately describe the non-linear characteristics of various frictions.

[0005] With the further increase in the demand for safety and high-precision servo systems in the aviation field, applying corresponding compensation methods can effectively reduce the adverse effects of gear backlash and non-linear friction on system performance, thereby ensuring the static and dynamic performance of the system. In addition, compensating through control algorithms instead of using mechanical methods to improve clearance and friction characteristics can not only reduce economic costs, reduce the mechanical complexity of the servo system, but also improve the service life and reliability of the system.

[0006] The present invention adopts a simplified dead zone model and LuGre friction model, and designs corresponding compensation methods for gear backlash torque and friction torque current. By organically combining gear backlash compensation and friction compensation, and redesigning the control law, the present invention proposes a control strategy combining feedforward compensation and model predictive control (MPC) to accurately compensate and control the q-axis current of the system. Further, the present invention introduces an extended Kalman filter (EKF) for online identification of multiple parameters of a permanent magnet synchronous motor (PMSM), obtains high-precision parameter identification results, and ensures that the model parameters of the system can be updated in real time during the control process, thereby achieving precise control of the system. Summary of the Invention

[0007] The object of the present invention is to provide an adaptive model predictive control method for an aviation electromechanical actuator to solve the above problems.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows: The present invention provides an adaptive model predictive control method for an aviation electromechanical actuator, including the following steps: S1: Based on the simplified dead-zone model and LuGre friction model, a new comprehensive compensation strategy for gear clearance and friction is proposed, which organically combines the gear clearance compensation and nonlinear friction compensation in the mechanical transmission mechanism of the aircraft electro-mechanical actuator. The corresponding compensation methods for gear clearance torque and friction torque current are designed, and the feedforward compensation strategy is adopted to accurately compensate the q-axis current of the system, so as to improve the control accuracy and reduce the torque ripple. S2: A multi-parameter online identification method for permanent magnet synchronous motor (PMSM) based on the extended Kalman filter (EKF) is proposed. By real-time online estimating the key parameters such as the stator resistance Rs and stator inductance Ls of the PMSM, high-precision parameter identification results are obtained, so as to ensure that the model parameters of the system can be dynamically updated during the control process, and the adaptability and robustness of the system are improved. S3: A combined compensation mechanism for gear clearance and nonlinear friction is introduced into the mechanical transmission mechanism, and combined with the adaptive model predictive control (MPC) method, which can not only effectively compensate the gear clearance and friction interference, but also dynamically optimize the control input through model predictive control, ensuring the high-precision control and stability of the aircraft electro-mechanical actuator during actual flight.

[0009] Furthermore, the simplified clearance dead-zone model can be written in the form of equations (1-2): (1) (2) Aiming at the non-differentiable part in the mathematical expression of the above simplified dead-zone model, the Sigmoid function can be introduced for correction, and the corrected dead-zone model is shown in equation (3): (3).

[0010] Furthermore, the LuGre friction model can comprehensively reflect various static and dynamic phenomena of friction, and the specific mathematical model is as follows: (4) (5) (6) In the formula, z is the deflection of the bristles; ω is the relative velocity between the contact surfaces; F c is the Coulomb friction force; F s is the maximum static friction force; F f is the total friction torque of the mechanical transmission system; σ 0 is the stiffness coefficient; σ 1 is the damping coefficient; σ2 is the viscous friction coefficient; ω s is the Stribeck speed.

[0011] When the system runs stably , substituting it into Equation (4) gives: (7) That is: (8) Substituting Equation (8) into Equation (5) gives: (9) Substituting Equation (7) and Equation (9) into Equation (6) gives: (10).

[0012] Further, the rotor flux-oriented synchronous rotating coordinate system is adopted to analyze the performance of the permanent magnet synchronous motor. The voltage equations of the permanent magnet synchronous motor in the d, q rotating coordinate system are: (11) (12) Where: R s is the stator resistance; i d , i q are the d, q axis currents; u q , u d are the d, q axis voltages; L d , L q are the d, q axis inductances; ψ q , ψ d are the stator flux link components; ω e is the electrical angular velocity of the rotor; ψ f is the flux of the permanent magnet rotor; The surface-mounted permanent magnet synchronous motor is adopted, so L d = L q = L s ; Equation (11) becomes: (13) For the state equation (13), the identification of the intermediate variables of the resistance and inductance simplifies the steps of designing the identification equation. Let a = R s / L s , b = 1 / L s , Equation (13) becomes: (14) (15) where: w is the model disturbance of the system; v is the measurement disturbance of the system; x = [i d i q a b] T , x is the state variable matrix of the system; y(x) = [i d i q T , y is the output variable matrix of the system; For equations (14) and (15), discretize them with a sampling period T s , and the difference equations are as follows: (16) (17) where: the coefficient matrices A , B , H are respectively: , B is the zero matrix, ; Select the initial matrix P 0, variance matrix Q and R as follows under the principle of ensuring steady-state tracking and non-divergence of filtering: , , ; (6) State prediction Predict the state and the covariance matrix of the error at time k based on the optimal state estimate at time k - 1.

[0013] (18)

[0014] (7) Covariance matrix prediction (19) (8) Update the Kalman filter gain matrix (20) (9) Update the state estimate (21) (10) Update the covariance matrix (22).

[0015] Furthermore, the adaptive MPC principle of the gear clearance and friction compensation is as follows: The system speed loop controller and the current loop d-axis controller are PI controllers, and the current loop q-axis controller is a model predictive controller,​ m is the position of the driving wheel, d is the position of the driven wheel. The backlash dead zone model is represented by Equation (3), and the LuGre friction model is represented by Equation (10). The influence brought by the gear backlash torque and the friction torque disturbance is compensated in the form of current. The compensation equation is i q =i PI +i Tf +i τc . The control law is divided into three parts. i PI is the PI control output, and i c is the current compensation amount based on the backlash model, and i Tf is the current compensation amount based on the friction model. Then, the q-axis current reference value i q obtained from the speed loop is input into the q-axis controller; The control process of the q-axis model predictive current is as follows: Apply the k optimal voltage vector u opt (k) determined by the -1 control moment to obtain the current i q (k), the DC bus voltage, and the speed at time k. The q-axis current reference value i q can be obtained from the speed loop and the current compensation amounts of the backlash model and the friction model; Calculate u opt ( k ) acting on the k +1 moment predicted current ; In the actual system, there is an error between the q-axis current predicted value and the actual value. The difference between the q-axis current predicted value and the actual value at the k +1 moment is used to obtain the prediction error through Equation (17), and then the prediction error of the q-axis current predicted value at the next moment is corrected by using error weighting through Equation (23); Finally, the value function is used to judge the error of the current predicted value through Equation (24), and the current predicted value that minimizes the total prediction error of the q-axis current is selected, and its corresponding switching state is output in the next cycle. At the same time, according to the established PMSM multi-parameter identification model based on the extended Kalman filter, the online parameter identification of the permanent magnet synchronous motor stator resistance R s and the stator inductance L s is completed to obtain high-precision parameter identification results; The state equation of the updated surface-mounted PMSM in the synchronous rotating coordinate system is: (23) (24) Since id ≡ 0, and the d-axis current controller is a PI controller, so only the q-axis current equation is studied. Define T s as the sampling period, and discretize the q-axis current state equation in Eq. (24) at two adjacent sampling points k and k 1 using the first-order Euler method as follows: (25) (26) Since i d ≡ 0, the coupling term related to i d in the above equation is not considered. Subtracting Eq. (26) from (25) gives k The predicted value of the q-axis current at the +1 moment is: (27) In the formula, Δ u q ( k ) = u q ( k ) - u q ( k - 1) is the voltage increment at the k moment; let , , then Eq. (27) can be simplified to: (28) k The predicted value of the q-axis current at the +2 moment can be obtained by recursive call of Eq. (14): (29) At the N moment, the general formula for the predicted value of the q-axis current is: (30) In the actual system, there is an error between the predicted value and the actual value of the q-axis current. Subtracting the predicted value of the q-axis current at the k moment from the actual value gives the prediction error, that is: (31) The predicted values of the q-axis current at other moments are corrected by error weighting, that is: (32) The three-phase two-level inverter has eight different switching states, and each state corresponds to a voltage vector. A cost function is used to judge the error of the current prediction value, and the current prediction value that minimizes the total error of the q-axis current prediction is selected, and the corresponding switching state is output in the next cycle. The value function is expressed as: (33) (34) (35) (36) In the formula, N y and N u ( N y ≥ N u ≥1) represent the prediction time domain and the control time domain; i PI is the output current of the speed loop PI controller; i τc is the gear backlash torque compensation current; i Tf is the LuGre friction torque compensation current; i q is the q-axis current reference value.

[0016] Compared with the prior art, the present invention has the following beneficial effects: By carrying out mechanism modeling on the gear backlash of the mechanical transmission mechanism of the electro-mechanical actuator and combining with a simplified dead zone model, a corresponding gear backlash torque-current compensation strategy is designed; secondly, a LuGre friction model is introduced, and a friction torque-current compensation method is designed to effectively compensate the non-linear friction torque generated during the operation of the system. By organically combining the gear backlash compensation and the friction compensation method, the control law is redesigned to optimize the system performance.

[0017] On this basis, a strategy combining feedforward compensation and model predictive control is adopted to achieve precise compensation and control of the q-axis current of the system. To further improve the control accuracy, an extended Kalman filter is introduced to optimize the online identification of multiple parameters of the permanent magnet synchronous motor. By optimizing the gain matrix in the observer through the extended Kalman filter algorithm, the measurement noise error is effectively eliminated, and a high-precision parameter identification result is obtained, ensuring that the model parameters can be updated in real time during the control process, thereby achieving precise control of the system. Brief Description of the Drawings

[0018] Figure 1Structural diagram of the adaptive MPC control considering gear clearance and friction compensation according to the present invention; Figure 2 Flow chart of the adaptive MPC control considering gear clearance and friction compensation according to the present invention; Figure 3 Bristle structure of the LuGre model according to the present invention; Figure 4 LuGre friction model curve according to the present invention; Figure 5 Principle diagram of the adaptive MPC for gear clearance and friction compensation according to the present invention. Detailed implementation manners

[0019] To make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the present invention will be further described below in conjunction with the detailed implementation manners.

[0020] The present invention provides an adaptive model predictive control method for an aviation electromechanical actuator. As Figures 1 - 5 shown, to solve the problems of gear clearance interference and non-linear friction torque interference in the high-precision servo system of the aviation electromechanical actuator, and further overcome the challenges such as low control accuracy and large torque ripple of the electromechanical actuator. This method designs corresponding compensation strategies for gear clearance torque and friction torque current by adopting a simplified dead zone model and a LuGre friction model; organically combines gear clearance compensation and friction compensation, and redesigns the control law. Combining the feedforward compensation strategy with the model predictive control (MPC) method, precise compensation and control of the q-axis current of the system are realized.

[0021] Traditional model predictive control methods usually highly rely on the accurate mathematical model of the controlled object. However, in practical applications, due to the influence of factors such as temperature change and magnetic flux saturation on parameters such as inductance and resistance, the system parameters will be perturbed. Therefore, on this basis, this solution introduces an extended Kalman filter (EKF) to realize the online identification of multiple parameters of the permanent magnet synchronous motor (PMSM), so as to obtain high-precision parameter identification results. This method ensures that the model parameters of the system can be updated in real time during the control process for precise control. The system control structure diagram and control flow chart are respectively as Figure 1 and Figure 2 shown.

[0022] Establishment of the clearance compensation model

[0023] In an aviation electromechanical actuator, the gear operation process mainly consists of two parts: the instantaneous impact caused by the different speeds of the master and slave gears during movement and the mutual extrusion caused by the different positions between the master and slave gears. The mutual gear torque between the gear sets is also related to these two items. In the dead zone model, the input signals are the speed difference Δ ω (t) between the master and slave gears and the position difference Δ θ between the master and slave gears, and the output value is the torque between the gear sets. In this model, we assume that the transmission is purely rigid, so the damping part is ignored during the modeling process. Then, the simplified clearance dead zone model can be written in the form of equations (1 - 2): (1) (2) For the non - differentiable part in the above - mentioned simplified dead zone model mathematical expression, the Sigmoid function can be introduced for correction. The corrected dead zone model is shown in equation (3): (3) LuGre friction compensation model The non - linear friction disturbance part is described by the LuGre friction model. The LuGre friction model represents the friction behavior through the contact, deformation, and relative displacement of elastic bristles. The bristle structure of the model is as Figure 3 shown.

[0024] Compared with the traditional friction model, the LuGre friction model can comprehensively reflect various static and dynamic phenomena of friction. The specific mathematical model is as follows: (4) (5) (6) In the formula, z is the deformation of the bristles; ω is the relative velocity between the contact surfaces; F c is the Coulomb friction force; F s is the maximum static friction force; F f is the total friction torque of the mechanical transmission system; σ 0 is the stiffness coefficient; σ 1 is the damping coefficient; σ 2 is the viscous friction coefficient; ω s is the Stribeck speed.

[0025] From the above formula, the friction model curve is as Figure 4 shown.

[0026] In Figure 4 , ω th is the speed threshold of the linear region; ω min is the minimum speed required to convert static friction into viscous friction; F brk represents the static friction force; F ω is the viscous friction force; F c is the Coulomb friction force; F s is the maximum static friction force.

[0027] When the system runs stably , substituting it into Equation (4) gives: (7) That is: (8) Substituting Equation (8) into Equation (5) gives: (9) Substituting Equation (7) and Equation (9) into Equation (6) gives: (10) Establishment of a PMSM multi-parameter identification model based on the extended Kalman filter Permanent magnet synchronous motors have the properties of multi-variable, strong coupling, and non-linearity. To obtain good speed regulation performance, approximate decoupling of the object needs to be achieved during control. Therefore, the rotor flux-oriented synchronous rotating coordinate system (i.e., the d, q rotating coordinate system) is often used to analyze and study the performance of permanent magnet synchronous motors. The voltage equations of permanent magnet synchronous motors in the d, q rotating coordinate system are: (11) (12) Where: R s is the stator resistance; i d , i q are the d, q axis currents; u q , u d are the d, q axis voltages; L d , L q are the d, q axis inductances; ψ q , ψ d are the stator flux link components; ω e is the electrical angular velocity of the rotor; ψ f is the flux of the permanent magnet rotor (a constant value).

[0028] For the space vector control system of permanent magnet synchronous motors, the resistance and inductance are unknown quantities. Therefore, the stator resistance R s , inductance L d and L qis considered as a state variable. This scheme adopts a surface-mounted permanent magnet synchronous motor, so L d =L q =L s . Equation (11) is transformed into: (13) For the state equation (13), if R s and L s are directly used as state variable identification, there are coupling terms in the coefficient matrix, and it is troublesome to use the Jacobian matrix to separate parameters. This scheme proposes to identify the intermediate variables of resistance and inductance, simplifies the steps of designing the identification equation, and let a = R s / L s , b = 1 / L s . Equation (13) is transformed into: (14) (15) Where: w is the model disturbance of the system; v is the measurement disturbance of the system; x = [i d i q a b] T , x is the state variable matrix of the system; y(x) = [i d i q T , y is the output variable matrix of the system. Assume that the model disturbance w and the measurement disturbance v are both white noise sequences with zero mean, and the two are independent of each other. Their covariance matrices are Q = cov(ww T ) and R = cov(vv T ). For simplicity of calculation, constant matrices Q and R are generally directly used to replace them in the Kalman recursion formula. For equations (14) and (15), discretization is performed with the sampling period T s , and the following difference equations can be obtained: (16) (17) Where: the coefficient matrices A , B , H are respectively: , B is a zero matrix, .

[0029] Select the initial matrix P 0, variance matrices Q and R as follows under the principle of ensuring steady-state tracking and non-divergence of filtering: ​ , , .

[0030] (11) State prediction

[0031] Predict the state and the covariance matrix of the error at time k based on the optimal state estimate at time k-1.

[0032] (18)

[0033] (12) Covariance matrix prediction (19) (13) Update the Kalman filter gain matrix (20) (14) Update the state estimate (21) (15) Update the covariance matrix (22) Adaptive MPC control considering gear backlash and friction compensation Gear backlash torque and friction torque, as an external disturbance, will not only cause steady-state fluctuations in the system speed, reduce the steady-state accuracy of the system, but also cause system torque pulsation, resulting in a decrease in the EMA position control accuracy and limiting the application of the electromechanical actuator in high-precision control occasions. To improve the control performance of the electromechanical actuator, this scheme designs corresponding current compensation methods for gear backlash torque and friction torque existing in the mechanical transmission mechanism of the system. Compensate the influence brought by gear backlash torque and friction torque disturbance in the form of current. At the same time, an extended Kalman filter is introduced to realize online identification of multiple parameters of the permanent magnet synchronous motor and obtain high-precision parameter identification results. Ensure that the model parameters can be updated in real time during the control process, so as to complete the precise control of the system. The principle of adaptive MPC with gear backlash and friction compensation is as Figure 5 shown.

[0034] Figure 5 In it, the system speed loop controller and the current loop d-axis controller are PI controllers, and the current loop q-axis controller is a model predictive controller. m is the position of the driving wheel, d is the position of the driven wheel, the backlash dead zone model is represented by Equation (3), and the LuGre friction model is represented by Equation (10). Compensate the influence brought by gear backlash torque and friction torque disturbance in the form of current, and the compensation equation is i q =i PI +i Tf +i τc , the control law is divided into three parts, i PI is the PI control output, i c is the current compensation amount based on the backlash model, i Tf is the current compensation amount based on the friction model, and then the q-axis current reference value i q obtained by the speed loop is input into the q-axis controller. The control process of the q-axis model predictive current is as follows: Apply k the optimal voltage vector u opt (k) determined at the -1 control moment, then the current i q (k), the DC bus voltage, and the speed can be obtained; the q-axis current reference value i q can be obtained from the speed loop and the current compensation amounts of the backlash model and the friction model; calculate u opt ( k ) and the predicted current at the k +1 moment; in the actual system, there is an error between the predicted value and the actual value of the q-axis current. The difference between the predicted value and the actual value of the q-axis current at the +1 moment is used to obtain the prediction error through Equation (17), and then the predicted value of the q-axis current at the next moment is corrected by error weighting through Equation (23); finally, the error of the current predicted value is judged by the cost function through Equation (24), and the current predicted value that minimizes the total prediction error of the q-axis current is selected, and its corresponding switching state is output in the next cycle. At the same time, according to the established PMSM multi-parameter identification model based on the extended Kalman filter, the online parameter identification of the stator resistance R k and the stator inductance L s and s is completed, and high-precision parameter identification results are obtained. Ensure that the model parameters can be updated in real time during the control process, so as to complete the precise control of the system.

[0035] The state equation of the updated surface-mounted PMSM in the synchronous rotating coordinate system is: (23) (24) Since i d ≡0, and the d-axis current controller is PI control, so only the q-axis current equation is studied. Define T s as the sampling period, and the q-axis current state equation in Equation (24) at two adjacent sampling points k andk 1. The first-order Euler method is used for the following discretization: (25) (26) Since i d ≡0, the coupling terms related to i d in the above formula are not considered. Subtracting formula (26) from (25) gives k The predicted value of the q-axis current at the +1 moment is: (27) In the formula, Δ u q ( k )= u q ( k ) - u q ( k - 1) is the voltage increment at the k moment; Let , , then formula (27) can be simplified to: (28) k The predicted value of the q-axis current at the +2 moment can be obtained by recursive call of formula (14): (29) At the N moment, the general formula for the predicted value of the q-axis current is: (30) In the actual system, there is an error between the predicted value and the actual value of the q-axis current. Subtracting the predicted value of the q-axis current at the k moment from the actual value gives the prediction error. For the convenience of research, it is assumed that the prediction error at any moment is a fixed value, that is: (31) The predicted values of the q-axis current at other moments are corrected by error weighting, that is: (32) The three-phase two-level inverter has 8 different switching states, and each state corresponds to a voltage vector. According to the idea of finite set model predictive control, the predicted current values under all switching states of the inverter are traversed. To ensure accurate current tracking, a cost function is required to judge the error of the predicted current values, select the predicted current value that minimizes the total error of the q-axis current prediction, and output the corresponding switching state in the next cycle. The value function is expressed as: (33) (34) (35) (36) In the formula, N y and N u ( N y ≥ N u ≥1) represent the prediction time domain and the control time domain; i PI is the output current of the speed loop PI controller; i τc is the backlash torque compensation current; i Tf is the LuGre friction torque compensation current; i q is the q-axis current reference value.

[0036] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claimed rights.

[0037] In addition, it should be understood that although this specification is described according to embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An adaptive model predictive control method for an aircraft electromechanical actuator, characterized in that, It includes the following steps: S1: Based on the simplified dead-zone model and the LuGre friction model, a new comprehensive compensation strategy for gear clearance and friction is proposed. The gear clearance compensation and non-linear friction compensation in the mechanical transmission mechanism of the aircraft electro-mechanical actuator are organically combined. The corresponding compensation methods for gear clearance torque and friction torque current are designed, and the feed-forward compensation strategy is adopted to accurately compensate the q-axis current of the system, so as to improve the control accuracy and reduce torque ripple. S2: A multi-parameter online identification method for permanent magnet synchronous motor (PMSM) based on the extended Kalman filter (EKF) is proposed. By real-time online estimating key parameters such as the stator resistance Rs and stator inductance Ls of the PMSM, high-precision parameter identification results are obtained, so as to ensure that the model parameters of the system can be dynamically updated during the control process, and the adaptability and robustness of the system are improved. S3: A combined compensation mechanism for gear clearance and non-linear friction is introduced into the mechanical transmission mechanism, and combined with the adaptive model predictive control (MPC) method, which can not only effectively compensate for gear clearance and friction disturbances, but also dynamically optimize the control input through model predictive control, ensuring high-precision control and stability of the aircraft electro-mechanical actuator during actual flight.

2. The adaptive model predictive control method for an aircraft electromechanical actuator according to claim 1, wherein: The simplified clearance dead-zone model can be written in the form of Eqs. (1~2): (1) (2) For the non-differentiable part in the mathematical expression of the above simplified dead-zone model, the Sigmoid function can be introduced for correction, and the corrected dead-zone model is shown in Eq. (3): (3)。 3. The adaptive model predictive control method for an aviation electromechanical actuator according to claim 1, wherein: The LuGre friction model can comprehensively reflect various static and dynamic phenomena of friction, and the specific mathematical model is as follows: (4) (5) (6) In the formula, z is the deformation of the bristles; ω is the relative velocity between the contact surfaces; F c is the Coulomb friction force; F s is the maximum static friction force; F f is the total friction torque of the mechanical transmission system; σ 0 is the stiffness coefficient; σ 1 is the damping coefficient; σ 2 is the viscous friction coefficient; ω s is the Stribeck velocity; When the system runs stably , substituting it into Equation (4) gives: (7) That is: (8) Substituting Eq. (8) into Eq. (5) gives: (9) Substituting Eqs. (7) and (9) into Eq. (6) gives: (10)。 4. The adaptive model predictive control method for an aviation electromechanical actuator according to claim 1, wherein: The performance of the permanent magnet synchronous motor is analyzed by using the rotor flux-oriented synchronous rotating coordinate system. The voltage equations of the permanent magnet synchronous motor in the d, q rotating coordinate systems are: (11) (12) Where: R s is the stator resistance; i d , i q are the currents on the d- and q-axes; u q , u d are the voltages on the d- and q-axes; L d , L q are the inductances on the d- and q-axes; ψ q , ψ d are the stator flux linkages; ω e is the electrical angular velocity of the rotor; ψ f is the magnetic flux of the permanent magnet rotor; Adopt a surface-mounted permanent magnet synchronous motor, so L d = L q = L s ; Equation (11) is changed to: (13) For the state equation (13), the identification of the intermediate variables of the resistance and inductance simplifies the steps of designing the identification equation. Let a = R s / L s , b = 1 / L s , Equation (13) becomes: (14) (15) Where: w is the model disturbance of the system; v is the measurement disturbance of the system; x = [i d i q a b] T , x is the state variable matrix of the system; y(x) = [i d i q T , y is the output variable matrix of the system;​ For equations (14) and (15), with a sampling period of T s Discretization is performed, and the difference equations are as follows: (16) (17) In the formula: coefficient matrix A , B , H are respectively , B is a zero matrix, ； Select the initial matrix under the principle of ensuring steady-state tracking and non-divergence of filtering P 0, variance matrix Q and R are as follows: ， ， ； (1) State prediction Predict the state and the covariance matrix of the error at time k based on the optimal state estimate at time k-1; (18) (2) Covariance matrix prediction (19) (3) Update the Kalman filter gain matrix (20) (4) Update the state estimate (21) (5) Update the covariance matrix (22)。 5. The adaptive model predictive control method for an aviation electromechanical actuator according to claim 1, wherein: The adaptive MPC principle of the gear clearance and friction compensation is as follows: The system speed loop controller and the current loop d-axis controller are PI controllers, and the current loop q-axis controller is a model predictive controller. m is the position of the driving wheel. d is the position of the driven wheel. The backlash dead zone model is represented by Equation (3), and the LuGre friction model is represented by Equation (10). The influence brought by the gear backlash torque and the friction torque disturbance is compensated in the form of current, and the compensation equation is i q =i PI +i Tf +i τc . The control law is divided into three parts. i PI is the PI control output, and i c is the current compensation amount based on the backlash model, and i Tf is the current compensation amount based on the friction model. Then, the q-axis current reference value i q obtained by the speed loop is input into the q-axis controller. The control process of the q-axis model predictive current is as follows: Apply k the optimal voltage vector u opt (k) determined by the -1 control moment to obtain the current i q (k), the DC bus voltage, and the rotational speed at time k; The q-axis current reference value i can be obtained from the speed loop and the current compensation amounts of the backlash model and the friction model q ; Calculate u through Equation (13) opt ( k ) Under the action of k The predicted current at time +1 ; In the actual system, there is an error between the predicted value and the actual value of the q-axis current. Through Equation (17), k The difference between the predicted value and the actual value of the q-axis current at time +1 is used to obtain the prediction error, and then Equation (23) is used to correct the predicted value of the q-axis current at the next time by error weighting; Finally, the value function is used to judge the error of the current predicted value through Equation (24), and the current predicted value that minimizes the total prediction error of the q-axis current is selected, and its corresponding switching state is output in the next cycle. At the same time, according to the established PMSM multi-parameter identification model based on the extended Kalman filter, the online parameter identification of the stator resistance R s and the stator inductance L s is completed to obtain high-precision parameter identification results; The state equation of the updated surface-mounted PMSM in the synchronous rotating coordinate system is: (23) (24) Since i d ≡ 0, and the d-axis current controller is PI control, only the q-axis current equation is studied; define T s as the sampling period, and discretize the q-axis current state equation in Eq. (24) at two adjacent sampling points k and k 1 using the first-order Euler method as follows: (25) (26) Since i d ≡0, the coupling terms related to i d in the above equation are not considered. Subtracting Equation (26) from (25) gives k The predicted value of the q-axis current at time +1 is:[[]] (27) where Δ u q ( k ) = u q ( k ) - u q ( k - 1) is the voltage increment at time k ; let , , then Equation (27) can be simplified to: (28) k The predicted value of the q-axis current at the +2 instant can be obtained by recursive call of Equation (14) as follows: (29) At N The general formula for predicting the q-axis current value at time is: (30) In an actual system, there is an error between the predicted value and the actual value of the q-axis current. Subtract k the predicted value of the q-axis current from the actual value at time (31) The predicted value of the q-axis current at other times is corrected by error weighting, that is: (32) The three-phase two-level inverter has 8 different switching states, and each state corresponds to a voltage vector. The cost function is used to judge the error of the current prediction value, and the current prediction value that minimizes the total error of the q-axis current prediction is selected, and its corresponding switching state is output in the next cycle. The value function is expressed as: (33) (34) (35) (36) In the formula, N y and N u ( N y ≥ N u ≥ 1) represent the prediction horizon and the control horizon; i PI is the output current of the speed loop PI controller; i τc is the backlash torque compensation current; i Tf is the LuGre friction torque compensation current; i q is the q-axis current reference value.

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