Adaptive robust control method for electric actuator based on improved LuGre friction model

Abstract

This invention discloses an adaptive robust control method for electric actuators based on an improved LuGre friction model, comprising: establishing an electric actuator model architecture; compensating for nonlinear friction in the system using an improved LuGre friction model; designing a dual observer to estimate the unmeasurable average deformation of the bristles in the improved LuGre friction model; identifying the parameters of the improved LuGre friction model using a particle swarm optimization algorithm to obtain a mathematical model of the electric actuator; and, based on the electric actuator model, employing an adaptive sliding mode control strategy, using a nonlinear sliding surface switching function, and designing an adaptive robust controller for the electric actuator based on the improved LuGre friction model using a backstepping method. This invention reduces the impact of nonlinear friction on the electric actuator control system, enhances the system's robustness, and improves the control performance of the electric actuator.

Description

Technical Field

[0001] This invention relates to the field of electric valve technology, and in particular to an adaptive robust control method for electric actuators based on an improved LuGre friction model. Background Technology

[0002] With the development of industrial automation, electric actuators are being used more and more widely, and various control fields are placing increasingly higher demands on electric actuator control systems in terms of response speed, control accuracy, and anti-interference performance. Researching and optimizing electric actuator control systems has significant theoretical and practical value for improving system control accuracy and stability.

[0003] As a crucial component of intelligent valve electric actuators, the control system aims to precisely control the valve position. Existing control methods for intelligent valve electric actuators consider the impact of temperature variations on the control system. This is achieved by establishing a three-loop control system based on current, speed, and position loops. A variable gain coefficient MRAS is used to identify the system's moment of inertia online, and the moment of inertia is used as the input to the observer to monitor the system's load torque online. The system controller parameters are then tuned based on the observation results. Furthermore, a temperature detection circuit monitors changes in the rotor time constant, and temperature compensation is performed based on the relationship between the rotor time constant and electromagnetic torque to address errors caused by temperature in the observation of the control system's load torque.

[0004] While existing electric actuator technologies offer temperature compensation to address errors in the observation of load torque in the control system caused by temperature, nonlinear friction remains a major source of disturbance in the control system. Its time-varying nature often leads to problems such as steady-state errors, limit cycles, and low-speed creep. Failure to control friction will significantly degrade the control performance of the electric actuator. Existing control algorithms for electric actuators do not adequately consider the impact of nonlinear friction on control performance.

[0005] Therefore, how to provide an adaptive robust control method for electric actuators that reduces the impact of nonlinear friction on the control system of electric actuators is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In response to the aforementioned research status and existing problems, this invention employs a compensation method based on an improved LuGre friction model to reduce the impact of nonlinear friction on the control system of electric actuators, thereby improving the control performance of electric actuators.

[0007] This invention first provides an adaptive robust control method for electric actuators based on an improved LuGre friction model, comprising the following steps:

[0008] S1: Establish an electric actuator model architecture, including an electric actuator execution model and an improved LuGre friction model; the electric actuator execution model receives the target input of the electric actuator system and obtains the dynamic response of the electric actuator, and the improved LuGre friction model changes the dynamic response through friction.

[0009] S2: Construct a system state observer and a bristle deformation observer to estimate the system state and bristle deformation of the electric actuator in real time, respectively; Based on the particle swarm optimization algorithm, use the real-time estimation results to identify the model parameters of the improved LuGre friction model to obtain the mathematical model of the electric actuator.

[0010] S3: Based on the mathematical model of the electric actuator, an adaptive sliding mode control strategy is adopted, combined with a nonlinear sliding surface switching function, and an adaptive robust controller for the electric actuator based on the improved LuGre friction model is designed through the backstepping method.

[0011] Preferably, the electric actuator model architecture is as follows:

[0012]

[0013] The output shaft model of the permanent magnet synchronous motor is as follows:

[0014] T f LuGre friction torque; J1 is the equivalent moment of inertia on the motor output shaft; B is the viscous damping coefficient; T e denoted as , where is the driving torque, i.e., the electromagnetic torque of the motor; is the reduction ratio of the gear transmission mechanism; is the output torque of the gear reduction mechanism; is the resistance torque, i.e., the output torque of the motor shaft; and is the output angle of the gear transmission mechanism. θ1 is the speed of the output shaft of the gear transmission reduction mechanism; θ2 is the mechanical angle of the motor output shaft. T is the speed of the motor output shaft. e This refers to the driving torque, which is the electromagnetic torque of the motor.

[0015] Preferably, the improved LuGre friction model is as follows:

[0016]

[0017] In the formula, T f σ is the LuGre friction torque; σ0 is the friction stiffness coefficient; σ1 is the friction damping coefficient; B0 is the viscous friction coefficient; θ is the output angle of the gear transmission reduction mechanism; z is the average displacement change between the bristle contact surfaces; θ represents the parameters of the Stribeck effect.s For stribeck speed; T s The maximum static friction force; T c For Coulomb friction.

[0018] Preferably, the steps for constructing a system state observer include:

[0019] A Kalman filter or Luenberger observer is constructed using the target input and the measured output of the electric actuator system. The state of the electric actuator system, including the motion speed and / or displacement of the electric actuator, is estimated in real time by the error between the target input and the measured output.

[0020] Preferably, the steps for constructing a bristle deformation observer include:

[0021] A method for constructing a sliding mode observer or dynamic observer using the target input and measured output of the electric actuator system, thereby estimating the deformation of the bristles in real time through the error between the target input and the measured output.

[0022] Preferably, the step of identifying the model parameters of the improved LuGre friction model includes:

[0023] Initialization: Randomly generate a specified number of particles, each particle representing a set of parameters of the improved LuGre friction model;

[0024] Fitness assessment: The fitness of the particles is assessed based on the error between the state estimate output by the model and the measured output of the electric actuator system.

[0025] Update particle position: Update the particle's position and velocity based on its own historical best position and global best position;

[0026] Iteration: Repeat the fitness evaluation and position update process until the stopping condition is met, then stop the iteration and output the parameters of the improved LuGre friction model.

[0027] Preferably, the adaptive sliding mode control strategy includes the following steps:

[0028] S31: Select a sliding surface S that is compatible with the electric actuator system.

[0029] S=e+λ∫edt;

[0030] Where e is the tracking error and λ is a positive gain;

[0031] S32: Designing sliding surfaces using nonlinear switching functions:

[0032]

[0033] Where η is a design parameter, and α and β are parameters related to system characteristics;

[0034] S33: Design of control laws based on sliding mode control principle:

[0035]

[0036] Where K is the control gain. It is an estimate of the control input.

[0037] Preferably, the steps for obtaining an adaptive robust controller for an electric actuator based on an improved LuGre friction model through backstepping design include:

[0038] S34: Introduce virtual control input u1 for controlling the state of the system.

[0039] u1=-K1·SF friction ;

[0040] Where K1 is the control gain corresponding to the virtual control input;

[0041] S35: Design an adaptive parameter update law based on the system state:

[0042]

[0043] Here, γ is the adaptive gain, used to guide the convergence of the parameters.

[0044] Compared with existing technologies, it has the following advantages:

[0045] This invention proposes a novel adaptive robust control method for electric actuators based on an improved LuGre friction model. By using an adaptive sliding mode control strategy and backstepping method, combined with the improved LuGre friction model, a robust electric actuator controller capable of adapting to uncertainties can be designed. This control algorithm effectively compensates for nonlinear friction in the electric actuator, improving the system's convergence speed and tracking accuracy, and enhancing its robustness. This method can effectively improve the control accuracy and stability of electric actuators under complex operating conditions. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without creative effort.

[0047] Figure 1 This is a control block diagram of an electric actuator provided in an embodiment of the present invention;

[0048] Figure 2 A flowchart of an adaptive robust control method for an electric actuator provided in an embodiment of the present invention;

[0049] Figure 3 This is a dual closed-loop control diagram for the position current of an electric actuator provided in an embodiment of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] like Figure 1-2 As shown in the embodiments of the present invention, the adaptive robust control method for electric actuators based on the improved LuGre friction model includes the following steps:

[0052] S1: Establish the model architecture of the electric actuator, including the electric actuator execution model and the improved LuGre friction model. The electric actuator execution model receives the target input of the electric actuator system and obtains the dynamic response of the electric actuator. The improved LuGre friction model changes the dynamic response through friction. The improved LuGre friction model is used to compensate for the nonlinear friction in the system. S2: Construct a system state observer and a bristle deformation observer to estimate the system state and bristle deformation of the electric actuator in real time, respectively. Based on the particle swarm optimization algorithm, the model parameters of the improved LuGre friction model are identified using the real-time estimation results to obtain the mathematical model of the electric actuator. S3: Based on the mathematical model of the electric actuator, an adaptive sliding mode control strategy is adopted, combined with a nonlinear sliding surface switching function, and an adaptive robust controller for the electric actuator based on the improved LuGre friction model is designed through backstepping.

[0053] In one embodiment, the electric actuator execution model includes a drive motor model and an electric actuator transmission system model. The drive motor is a permanent magnet synchronous motor, and its mathematical model in a two-phase rotating dq coordinate system is as follows:

[0054]

[0055] In the formula, u d ,u q These are the voltages along the d and q axes;

[0056] i d i q For d-axis and q-axis currents;

[0057] ψ d , ψ q For the d and q axis flux linkages;

[0058] L d ,L q For d-axis and q-axis inductance;

[0059] R s Phase resistance;

[0060] ω r This refers to the rotor angular velocity;

[0061] ψ f It is a permanent magnet chain;

[0062] T e Electromagnetic torque;

[0063] p represents the number of pole pairs of the motor.

[0064] The output shaft model of the permanent magnet synchronous motor is as follows:

[0065]

[0066] In the formula, J1 is the equivalent moment of inertia on the motor output shaft, kg·m 2 ;

[0067] B is the viscous damping coefficient;

[0068] M1 is the resistance torque, which is the output torque of the motor shaft, in N·m;

[0069] T e The driving torque is the electromagnetic torque of the motor, expressed in N·m.

[0070] K is the torsional stiffness of the motor shaft, N·m / rad;

[0071] θ1 is the mechanical angle of the motor output shaft.

[0072] In this embodiment, the transmission system model of the electric actuator adopts a gear transmission reduction mechanism model. Since the gear reduction mechanism has high stiffness, it is generally regarded as a first-order linear transmission system.

[0073]

[0074] In the formula, θ is the output angle of the gear transmission reduction mechanism, °:

[0075] i represents the reduction ratio of the gear transmission reduction mechanism;

[0076] M is the output torque of the gear reduction mechanism, N·m.

[0077] In one embodiment, the electric actuator model architecture is as follows:

[0078]

[0079] The output shaft model of the permanent magnet synchronous motor is as follows:

[0080] T f LuGre friction torque; J1 is the equivalent moment of inertia on the motor output shaft; B is the viscous damping coefficient; T e M is the driving torque, i.e., the electromagnetic torque of the motor; i is the reduction ratio of the gear transmission mechanism; M is the output torque of the gear reduction mechanism; M1 is the resistance torque, i.e., the output torque of the motor shaft; θ is the output angle of the gear transmission mechanism; θ1 is the mechanical angle of the motor output shaft; T e This refers to the driving torque, which is the electromagnetic torque of the motor.

[0081] In one embodiment, the improved LuGre friction model is as follows:

[0082]

[0083] In the formula, T f σ is the LuGre friction torque; σ0 is the friction stiffness coefficient; σ1 is the friction damping coefficient; B0 is the viscous friction coefficient; θ is the output angle of the gear transmission reduction mechanism; z is the average displacement change between the bristle contact surfaces. θ represents the parameters of the Stribeck effect. s For stribeck speed; T s The maximum static friction force; T c For Coulomb friction.

[0084] It should be noted that in the electric actuator model architecture constructed in this embodiment, the relationship between the drive motor model, the electric actuator transmission system model, and the improved LuGre friction model is as follows:

[0085] The input voltage (u) of the drive motor affects the current (i) and torque (T) transmitted to the actuator. The actuator then adjusts the current (i) and torque (T) according to the input torque (T) and load torque (T). e The change in angle or position caused by ω affects the angular velocity (ω).

[0086] The friction model uses frictional force (T) f This affects the dynamic response of the actuator, and consequently affects the position and speed output of the actuator.

[0087] By coupling the above models, the input-output relationship of the entire system can be established. Numerical simulation is usually required to analyze the dynamic behavior and stability of the system.

[0088] like Figure 1 As shown, the entire system is a closed-loop control system, achieving precise control of the mechanical position through sensor feedback and controller commands. Specifically:

[0089] Position input is the target input of the control system, usually referring to the input signal that tells the system where to move or what state to reach.

[0090] Position output is the actual output of the control system, representing the system's response to the input signal, such as moving to a specified position.

[0091] The controller system's brain is responsible for receiving position input signals, processing these signals, and issuing instructions to control the motor.

[0092] An electric motor is an actuator that drives a mechanical device according to the instructions of a controller, thereby moving or adjusting its position.

[0093] Mechanical transmission devices are devices that convert the rotational motion of an electric motor into the required linear motion or other forms of motion, such as gears and belts.

[0094] The power drive provides the necessary power to ensure that the electric motor can work properly and drive the mechanical transmission device.

[0095] Position sensors are used to detect the actual position or state of the system and feed this information back to the controller so that the controller can make adjustments to ensure precise control of the system.

[0096] like Figure 3 As shown, the entire system is a highly integrated motor control system that achieves precise and efficient control of the motor through various control algorithms and sensor feedback.

[0097] Figure 3In motor control, an adaptive robust controller is a control algorithm that can adapt to changes in system parameters and resist external disturbances. A PI current controller, or proportional-integral controller, is used for current control, maintaining stable motor operation by adjusting the current magnitude. "Space" refers to the coordinate transformation space in motor control. The PARK transformation is used to transform the motor's current and voltage from a synchronous rotating coordinate system to a stationary coordinate system, simplifying the control algorithm. PARK and CLARK transformations are used to transform the expression of current and voltage in motor control, simplifying the control strategy. Vector control is a motor control strategy that achieves efficient and precise control by controlling the motor's flux and torque. An inverter is a key component in a motor control system, converting direct current (DC) to alternating current (AC) to drive the motor.

[0098] The electric motor is the power source of the entire system, while the mechanical transmission system converts the motor's rotational motion into other forms of mechanical motion. qref and u q These are variables in the control algorithm, where i qref This represents a reference value for the current, while u q This represents the voltage associated with that current. d and u b It is a voltage variable related to motor control.

[0099] In motor control, modulation typically refers to PWM (Pulse Width Modulation) technology, used to control the voltage waveform output by the inverter. Speed ​​and angle are crucial parameters of motor operation, usually measured by an encoder. The encoder provides information on the motor's actual speed and angle, which is essential for the closed-loop control system to ensure the motor operates according to predetermined parameters.

[0100] In this embodiment, the control method is a dual closed-loop control of current and position, and the motor adopts an i... d The vector control strategy with =0 has an inner loop of current and an outer loop of adaptive robust control proposed in this embodiment.

[0101] In one embodiment, the steps of constructing a system state observer include:

[0102] A Kalman filter or Luenberger observer is constructed using the target input and measured output of the electric actuator system. The state of the electric actuator system is estimated in real time by the error between the target input and the measured output. The state includes the motion speed and / or displacement of the electric actuator, i.e., the output of the electric actuator system.

[0103] In practice, the state observer performs two steps: a prediction step and a correction step.

[0104] Prediction Steps: Based on the electric actuator execution model and the target input of the electric actuator system, obtain the state estimate of the predicted system dynamic response.

[0105] Correction steps: Use the actual output data of the electric actuator system measured by the sensor to correct the predicted state estimate in order to reduce the estimation error.

[0106] In one embodiment, the steps of constructing a bristle deformation observer include:

[0107] A method for constructing a sliding mode observer or dynamic observer using the target input and measured output of an electric actuator system, thereby estimating the deformation of the bristles in real time by using the error between the target input and the measured output.

[0108] In one embodiment, the step of identifying the model parameters of the improved LuGre friction model includes:

[0109] S21: Initialization: Randomly generate a specified number of particles, each particle representing a set of parameters of the improved LuGre friction model, such as friction stiffness coefficient, friction damping coefficient, viscous friction coefficient, etc.

[0110] S22: Fitness assessment: The fitness of particles is assessed based on the error, such as mean square error, between the state estimate output by the model and the measured output of the electric actuator system.

[0111] S23 Update Particle Position: Updates the particle's position and velocity based on its own historical best position and global best position;

[0112] S24: Iteration: Repeat the fitness evaluation and position update process until the stopping condition is met, then stop iterating. If the maximum number of iterations is reached or the error converges, output the parameters of the improved LuGre friction model.

[0113] This embodiment also includes the following steps:

[0114] S25: Simulation experiments were conducted on the designed dual observer and parameter identification algorithm.

[0115] The accuracy of the observer and the effectiveness of parameter identification were verified by testing with real system data.

[0116] Analyze the impact of different parameters on the model's predictive performance.

[0117] S26: Results Analysis:

[0118] Compare the observer's estimated results with the actual values ​​to assess the accuracy of the estimation.

[0119] The convergence speed and effectiveness of the particle swarm optimization algorithm in parameter identification are analyzed.

[0120] The effects of dual-observer design and particle swarm optimization on the improvement of the LuGre friction model were directly obtained.

[0121] This method can effectively estimate the unmeasurable average deformation of the bristles and achieve accurate identification of model parameters through optimization algorithms.

[0122] In one embodiment, the adaptive sliding mode control strategy includes the following steps:

[0123] S31: Select a sliding surface S that is compatible with the electric actuator system.

[0124] S=e+λ∫edt;

[0125] Where e is the tracking error and λ is a positive gain;

[0126] S32: Designing sliding surfaces using nonlinear switching functions:

[0127]

[0128] Where η is a design parameter, and α and β are parameters related to system characteristics;

[0129] S33: Design of control laws based on sliding mode control principle:

[0130]

[0131] Where K is the control gain. It is an estimate of the control input, F friction It is frictional torque.

[0132] It should be noted that F friction It is described by an improved LuGre friction model. This frictional torque is a significant disturbance factor in the control system of electric actuators, exhibiting nonlinear characteristics and affecting the system's dynamic response and control performance.

[0133] Control input This includes the control inputs for the motor. The estimation of the control input for the control rate is related to the following parameters:

[0134] The electromagnetic torque of a motor: that is, the driving torque generated by the motor, which is usually determined by the input signal of the control system and affects the output of the motor.

[0135] Improving the frictional torque in the LuGre friction model: The LuGre friction model is used to compensate for the effects of friction, and the frictional torque affects the dynamic response of the system. This frictional torque is closely related to the nonlinear friction phenomena in the system and is a key area for compensation in adaptive sliding mode control strategies.

[0136] System state estimation: The control input is also related to the state of the electric actuator, such as the motor's position and speed. These states are estimated in real time by observers to help determine the current behavior of the system. Specifically, the system state observer and the bristle deformation observer provide real-time estimates of the system state, which in turn affect the calculation of the control input.

[0137] Disturbances and disturbances: Control inputs not only depend on known models, but also need to consider disturbances and uncertainties, which may come from system friction, load changes, etc. In particular, when the friction model is complex, the output of the disturbance observer will affect the control input.

[0138] In this embodiment, the steps for obtaining an adaptive robust controller for an electric actuator based on an improved LuGre friction model through backstepping design include:

[0139] S34: Introduce virtual control input u1 for controlling the state of the system.

[0140] u1=-K1·SF friction ;

[0141] Where K1 is the control gain corresponding to the virtual control input;

[0142] S35: Design an adaptive parameter update law based on the system state:

[0143]

[0144] Here, γ is the adaptive gain, used to guide the convergence of the parameters.

[0145] In this embodiment, the following steps are included after S35:

[0146] S36: Stability Analysis:

[0147] By constructing the Lyapunov function (V), the stability of the system is analyzed to ensure that the system error converges to zero under the action of the control law and the adaptive law.

[0148]

[0149] By analyzing the derivative of (V), the asymptotic stability of the system can be proven.

[0150] In this embodiment, after the controller design is completed, simulation tools (such as MATLAB / Simulink) are used to perform system simulation to verify the controller's performance.

[0151] Test the control effect under different operating conditions, including disturbances and model uncertainties.

[0152] Comparing the performance of the adaptive robust control method for electric actuators with that of traditional controllers, the adaptive robust control method for electric actuators proposed in this embodiment of the invention can effectively compensate for nonlinear friction in electric actuators, thereby enhancing the robustness of the system.

[0153] The above provides a detailed description of an adaptive robust control method for electric actuators based on an improved LuGre friction model. Specific examples have been used to illustrate the principles and implementation methods of the invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the invention. Therefore, the content of this specification should not be construed as a limitation of the invention.

[0154] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. An adaptive robust control method for an electric actuator based on an improved LuGre friction model, characterized in that, Includes the following steps: S1: Establish an electric actuator model architecture, including an electric actuator execution model and an improved LuGre friction model; the electric actuator execution model receives the target input of the electric actuator system and obtains the dynamic response of the electric actuator, and the improved LuGre friction model changes the dynamic response through friction. S2: Construct a system state observer and a bristle deformation observer to estimate the system state and bristle deformation of the electric actuator in real time, respectively; Based on the particle swarm optimization algorithm, use the real-time estimation results to identify the model parameters of the improved LuGre friction model to obtain the mathematical model of the electric actuator. S3: Based on the mathematical model of the electric actuator, an adaptive sliding mode control strategy is adopted, combined with a nonlinear sliding surface switching function, and an adaptive robust controller for the electric actuator based on the improved LuGre friction model is designed through the backstepping method; the adaptive sliding mode control strategy includes the following steps: S31: Select a sliding surface S that is compatible with the electric actuator system. ； Where e is the tracking error, It is a positive gain; S32: Designing sliding surfaces using nonlinear switching functions: ； in, It is a design parameter. and These are parameters related to system characteristics; S33: Design of control laws based on sliding mode control principle: ； Where K is the control gain. It is frictional torque. It is an estimate of the control input; The steps for obtaining an adaptive robust controller for an electric actuator based on an improved LuGre friction model through backstepping design include: S34: Introducing virtual control input Used to control the state of the system: ； in, It is the control gain corresponding to the virtual control input; S35: Design an adaptive parameter update law based on the system state: ； in, It is an adaptive gain used to guide the convergence of parameters.

2. The adaptive robust control method for an electric actuator based on an improved LuGre friction model according to claim 1, characterized in that, The electric actuator model architecture is as follows: The output shaft model of the permanent magnet synchronous motor is as follows: LuGre friction torque; J 1 represents the equivalent moment of inertia on the motor output shaft; B represents the viscous damping coefficient. This refers to the driving torque, i.e., the electromagnetic torque of the motor; The reduction ratio of the gear transmission reduction mechanism; Output torque of the gear reduction mechanism; This is the resistance torque, which is the output torque of the motor shaft; The output angle of the gear reduction mechanism. The speed of the output shaft of the gear transmission reduction mechanism; Mechanical angle of motor output shaft The speed of the motor output shaft; This refers to the driving torque, which is the electromagnetic torque of the motor.

3. The adaptive robust control method for an electric actuator based on an improved LuGre friction model according to claim 1, characterized in that, The improved LuGre friction model is as follows: ； In the formula, LuGre friction torque; The frictional stiffness coefficient; The friction damping coefficient; It is the coefficient of viscous friction; The output angle of the gear transmission reduction mechanism; This represents the average displacement change between the contact surfaces of the bristles; These are the parameters of the Stribeck effect; For Stribeck speed; This represents the maximum static friction force. This is the Coulomb friction force.

4. The adaptive robust control method for an electric actuator based on an improved LuGre friction model according to claim 1, characterized in that, The steps to construct a system state observer include: A Kalman filter or Luenberger observer is constructed using the target input and the measured output of the electric actuator system. The state of the electric actuator system, including the motion speed and / or displacement of the electric actuator, is estimated in real time by the error between the target input and the measured output.

5. The adaptive robust control method for an electric actuator based on an improved LuGre friction model according to claim 1, characterized in that, The steps to construct a bristle deformation observer include: A method for constructing a sliding mode observer or dynamic observer using the target input and measured output of the electric actuator system, thereby estimating the deformation of the bristles in real time through the error between the target input and the measured output.

6. The adaptive robust control method for an electric actuator based on an improved LuGre friction model according to claim 1, characterized in that, The steps for identifying the model parameters of the improved LuGre friction model include: Initialization: Randomly generate a specified number of particles, each particle representing a set of parameters of the improved LuGre friction model; Fitness assessment: The fitness of the particles is assessed based on the error between the state estimate output by the model and the measured output of the electric actuator system. Update particle position: Update the particle's position and velocity based on its own historical best position and global best position; Iteration: Repeat the fitness evaluation and position update process until the stopping condition is met, then stop the iteration and output the parameters of the improved LuGre friction model.

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