A self-disturbance position servo control method of a permanent magnet synchronous motor

Abstract

The application relates to the technical field of motor control and servo driving, and discloses a permanent magnet synchronous motor active disturbance rejection position servo control method, which comprises the following steps: obtaining a reference position signal and a motor feedback signal of a permanent magnet synchronous motor, performing smooth processing on the reference position signal through a double-compensation tracking differentiator to obtain a smooth position signal and a smooth speed signal; wherein, on the basis of a linear tracking differentiator framework, a finite-time convergence compensation term based on a position tracking error is introduced into an error forward channel, and an adaptive damping compensation term based on the smooth speed signal is introduced into a speed feedback channel; the position tracking error is determined based on the smooth position signal and the reference position signal; and based on the smooth position signal, the smooth speed signal and the motor feedback signal, a control instruction is generated through an active disturbance rejection controller to drive the permanent magnet synchronous motor to operate; the application provides the permanent magnet synchronous motor active disturbance rejection position servo control method, and the overshoot phenomenon can be effectively inhibited.

Description

Technical Field

[0001] This invention relates to the field of motor control and servo drive technology, and in particular to a method for self-disturbance rejection position servo control of a permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors, with their advantages of high power density, strong overload capacity, fast response speed, and high operating efficiency, have been widely used in servo applications such as industrial robots and new energy vehicles, which have high requirements for motor performance and control precision.

[0003] High-precision, fast-response position control technology is the core key to realizing high-performance industrial servo systems. Currently, the industry has put forward higher requirements for the tracking accuracy, response speed and other performance of permanent magnet synchronous motor position servo systems.

[0004] Linear Active Disturbance Rejection Control (LADRC) has become the mainstream high-performance control scheme in engineering practice due to its independence from accurate models, simple structure, small number of parameters, ease of engineering implementation, clear noise suppression capability, and sufficient robustness. Traditional LADRC typically uses a linear tracking differentiator (LTD) to smooth the transition reference signal, preventing the rate of change of the input signal from exceeding the system's tracking capability, and accurately tracking the reference signal while extracting the derivative. Then, a linear extended state observer (LESO) is used to estimate the total disturbance of the system (including unmodeled dynamics, parameter perturbations, external load torque changes, etc.) in real time, and compensation is performed through a linear state feedback control law.

[0005] Existing linear control methods employ a linear feedback structure in the LTD control structure, designing the convergence law of the tracking error as a fixed linear relationship. While simple to implement, it is weaker than nonlinear methods in finite-time convergence and overshoot suppression. There is always an inherent trade-off between response speed and signal smoothness, limiting further improvements in the transient performance of linear active disturbance rejection control systems. Nonlinear methods, on the other hand, replace the entire LTD control structure. However, these schemes often suffer from poor engineering feasibility due to high computational complexity, a large number of parameters, and difficult tuning. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for self-disruption-resistant position servo control of a permanent magnet synchronous motor, which can effectively suppress overshoot.

[0007] This invention provides a method for self-disturbance rejection position servo control of a permanent magnet synchronous motor, comprising the following steps: Acquire the reference position signal and the motor feedback signal of the permanent magnet synchronous motor; The reference position signal is smoothed by a dual-compensation tracking differentiator to obtain a smoothed position signal and a smoothed velocity signal. The dual-compensation tracking differentiator is based on the linear tracking differentiator framework. It introduces a finite-time convergence compensation term based on the position tracking error in the error forward channel and an adaptive damping compensation term based on the smoothed velocity signal in the velocity feedback channel. The position tracking error is determined based on the smoothed position signal and the reference position signal. Based on the smooth position signal, smooth speed signal and motor feedback signal, control commands are generated by the active disturbance rejection controller to drive the permanent magnet synchronous motor.

[0008] Specifically, the finite-time convergence compensation term is configured as follows: as the position tracking error approaches zero, its gain decays more slowly than that of the linear term, maintaining high gain to accelerate error convergence; The adaptive damping compensation term is configured to increase the damping coefficient as the smooth speed signal increases, so as to adaptively enhance damping and suppress overshoot in the high-speed stage.

[0009] Specifically, the expression for the finite-time convergence compensation term includes a fractional power function based on the position tracking error; The expression for the adaptive damping compensation term includes a velocity squared saturation function based on the smoothed velocity signal; The expression for the finite-time convergence compensation term includes... The expression for the adaptive damping compensation term includes ,in, This refers to the position tracking error; and For compensation coefficient, After smoothing , For reference position signal, for The derivative of Let Sgn(e) be the tracking factor, and Sgn(e) be the sign function.

[0010] Specifically, the state equation of the dual-compensation tracking differentiator is: , in and They represent and The first derivative with respect to time.

[0011] Specifically, when the compensation coefficient and When both are zero, the double-compensated tracking differentiator degenerates into a linear tracking differentiator.

[0012] Specifically, the active disturbance rejection controller includes a linear extended state observer and a linear state error feedback control law; The method also includes: estimating the mechanical angle of the permanent magnet synchronous motor in real time based on the position signal contained in the control command and motor feedback signal using a linearly extended state observer. Mechanical angular velocity and aggregate disturbance The state estimate is obtained; The control commands are generated by the active disturbance rejection controller, including: generating control commands based on smooth position signals and state estimates using a linear state error feedback control law.

[0013] Specifically, the state equation of the linearly extended state observer is: , in, , , They are mechanical angles Mechanical angular velocity and aggregate disturbance The estimated value, To control the amount, i.e. For q-axis current, , , Let represent the first derivatives of the three estimates with respect to time, and let represent the rate of change of the state estimate over time. For position estimation error, , , For observer gain, This is the inherent coefficient of the velocity loop.

[0014] A permanent magnet synchronous motor position servo active disturbance rejection control system includes: The signal acquisition unit acquires the reference position signal and the motor feedback signal of the permanent magnet synchronous motor; The dual-compensation tracking differentiator smooths the reference position signal to obtain a smoothed position signal and a smoothed velocity signal. Based on the linear tracking differentiator framework, the dual-compensation tracking differentiator introduces a finite-time convergence compensation term based on the position tracking error in the error forward channel and an adaptive damping compensation term based on the smoothed velocity signal in the velocity feedback channel. The position tracking error is determined based on the smoothed position signal and the reference position signal. The active disturbance rejection controller generates control commands based on smooth position signals, smooth speed signals, and motor feedback signals to drive the permanent magnet synchronous motor.

[0015] The technical solution provided by this invention has the following advantages compared with the prior art: This invention makes a structural improvement to the tracking differentiator stage in linear active disturbance rejection control (ADRC), solving the inherent contradiction between the speed and smoothness of traditional linear tracking differentiators, enabling independent adjustment of response speed and overshoot suppression, and overcoming the bottleneck of limited transient performance in linear ADRC. Compared with traditional nonlinear ADRC schemes, this invention achieves the performance advantages unique to nonlinear ADRC within the concise framework of linear ADRC. Specifically: On the one hand, this invention retains the engineering advantages of linear ADRC, such as simple structure, few parameters, and low computational cost; on the other hand, by introducing a double-compensation nonlinear term, the system possesses the finite-time convergence characteristics and strong robustness unique to nonlinear ADRC, achieving a breakthrough in nonlinear performance within the linear framework. By introducing a finite-time convergence term, the system is endowed with finite-time convergence characteristics, resulting in faster error convergence and fundamentally improving the dynamic response capability of the system; by introducing an adaptive damping term, automatic damping enhancement is achieved in the high-speed stage, effectively suppressing overshoot. This invention does not rely on a precise mathematical model, has strong anti-interference capabilities, and compared with existing nonlinear active disturbance rejection control algorithms, it does not suffer from output chattering problems, making it more suitable for high-precision position servo control. The compensation coefficient is adjustable, and when the compensation coefficient is zero, it strictly degenerates into a traditional linear tracking differentiator, resulting in good engineering compatibility. Furthermore, its core concept is highly versatile and can be easily extended to other motion control strategies and AC servo systems. Attached Figure Description

[0016] Figure 1 A block diagram of a three-phase PMSM active disturbance rejection position tracking control structure provided in an embodiment of the present invention; Figure 2 A structural diagram of a dual-compensation tracking differentiator DC-TD is provided in an embodiment of the present invention; Figure 3 The tracking waveform of a step signal provided by an embodiment of the present invention is an LADRC algorithm and an ADRC algorithm based on a dual-compensation tracking differentiator. Figure 4 This invention provides an embodiment of LADRC and an ADRC algorithm based on a dual-compensation tracking differentiator for tracking waveforms of sinusoidal signals. Figure 4 The top image shows the position tracking signal, and the bottom image shows the position error waveform. Detailed Implementation

[0017] The following detailed description of a specific embodiment of the present invention is provided in conjunction with the accompanying drawings. However, it should be understood that the scope of protection of the present invention is not limited to the specific embodiment.

[0018] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the technical solution of this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0019] The present invention will be described below through several specific embodiments. To keep the following description of the embodiments clear and concise, detailed descriptions of known functions and components may be omitted. When any component of an embodiment of the present invention appears in more than one drawing, the component may be represented by the same reference numerals in each drawing.

[0020] Figure 1 This invention provides a block diagram of a three-phase PMSM active disturbance rejection position tracking control structure. Figure 2 This is a structural diagram of a dual-compensation tracking differentiator DC-TD provided in an embodiment of the present invention. Figure 3 This invention provides an embodiment of LADRC and an ADRC algorithm based on a dual-compensation tracking differentiator for tracking step signals. Figure 4 This invention provides an embodiment of LADRC and an ADRC algorithm based on a dual-compensation tracking differentiator for tracking waveforms of sinusoidal signals. Figure 4 The top image shows the position tracking signal, and the bottom image shows the position error waveform.

[0021] like Figure 1 and Figure 2 As shown, this embodiment provides a method for active disturbance rejection (ADRROC) position servo control of a permanent magnet synchronous motor. This method improves the tracking differentiator stage in a traditional linear ADRROC control architecture, achieving decoupled adjustment of the dynamic response speed and signal smoothness of the position servo system.

[0022] Before introducing the control method of this embodiment, a mathematical model of the controlled object is first established. Taking a surface-mounted permanent magnet synchronous motor (…) as an example… Taking a permanent magnet synchronous motor rotor position servo system as an example, considering the total disturbance, the dynamic equation is shown in equation (1):

[0023] (1) In the formula, and These are the motor's mechanical angle and mechanical angular velocity, respectively. For extreme logarithms, It is a permanent magnet flux linkage. For rotational inertia, For load torque, This is the motor damping coefficient. For q-axis current, This represents an unknown disturbance. For the inherent coefficient of the velocity loop, As a lumped disturbance, it treats load torque, damping friction, and parameter perturbations as a unified total disturbance, expressed as: The modeling method described above normalizes various uncertainties into a single disturbance, laying the foundation for the subsequent design of active disturbance rejection controllers.

[0024] In a traditional second-order linear active disturbance rejection controller, the equation of the linear tracking differentiator (LTD) is shown in equation (2): (2) In the formula, For reference position signal, After smoothing , for The derivative of and They represent and The first derivative with respect to time, This is a tracking factor used to adjust the speed of the transition process. When When the value is large, the response is fast but it is prone to overshoot. The inherent contradiction between smooth performance at smaller values ​​and slow response limits further improvement in the transient performance of linear active disturbance rejection control systems. To address this, this embodiment proposes an improved dual-compensation tracking differentiator (DC-TD), with the specific steps as follows.

[0025] A dual-compensation tracking differentiator model is established. Based on the linear framework of the traditional linear tracking differentiator, the dual-compensation tracking differentiator simultaneously introduces a finite-time convergence compensation term and an adaptive damping compensation term. Specifically, as follows... Figure 2As shown, the dual-compensation tracking differentiator retains the linear feedback path determined by the tracking factor r as the baseline framework to ensure that the system possesses the engineering characteristics of a traditional linear tracking differentiator, such as simple structure and easy parameter tuning. Based on this, this embodiment introduces two nonlinear compensation branches in parallel. The finite-time convergence compensation term is constructed based on the product of the square of the position tracking error and the sign function. This construction method aims to utilize the gain characteristics of the nonlinear function near zero to accelerate the error to zero. It should be understood that the construction based on the product of the square of the position tracking error and the sign function is a functional generalization of the nonlinear convergence law. In specific implementations, it can be expressed as a fractional power of the absolute value of the error (such as a first power of 2) or other nonlinear function forms with similar finite-time convergence characteristics, as long as it can provide strong recovery when the error is large and maintain high gain when the error approaches zero. The adaptive damping compensation term is constructed based on the ratio of the square of the velocity to the square plus one of the velocity, which constitutes a saturation function that varies with velocity. This construction method allows the equivalent damping coefficient to change smoothly with speed: at higher speeds, damping automatically increases to suppress overshoot; at lower speeds, damping decreases to ensure sensitivity. These two compensation mechanisms work together to fundamentally resolve the inherent contradiction between speed and smoothness in traditional linear tracking differentiators.

[0026] The position reference signal is smoothed and its differential signal is extracted using a dual-compensation tracking differentiator. Specifically, after the position reference signal is input into the dual-compensation tracking differentiator, it is processed by the linear framework and dual nonlinear compensation terms to output a high-quality smoothed position signal and its corresponding differential signal (i.e., velocity reference signal). Compared to traditional methods, the reference trajectory generated in this step avoids system shocks caused by signal abrupt changes and overcomes phase lag caused by over-smoothing, laying a signal foundation for subsequent high-precision tracking.

[0027] In some embodiments, the state equation of the dual-compensation tracking differentiator is expressed as follows: (3) in, This refers to the position tracking error; and For compensation coefficient, After smoothing , for The derivative of For tracking factors.

[0028] Specifically, the above state equation mathematically precisely constructs the dual compensation mechanism described in Example 1. The first term in the equation... The linear part in the second term Together, these form the baseline framework of a traditional linear tracking differentiator, ensuring the system possesses basic signal tracking capabilities and the inheritability of engineering parameters. Building upon this, the equations introduce two nonlinear compensation terms to achieve a performance breakthrough. The first nonlinear term is a finite-time convergent compensation term, whose specific algebraic expression is as follows: This term utilizes the unique property of fractional power functions: when the position tracking error... When the error is large, the restoring torque provided by this compensation term is significantly greater than that of the linear term, driving the system state to move rapidly towards the equilibrium point; while when the error is large... As it approaches zero, due to the exponent , The decay rate is much slower than that of the linear term. This allows the term to maintain extremely high gain near the zero point, thereby overcoming the slow convergence problem caused by insufficient gain in linear feedback near the steady state, forcing the error to return to zero precisely within a finite time. It should be understood that the construction of the product of the squared term of the position tracking error and the sign function mentioned in Example 1 is a functional overarching generalization of this type of nonlinear convergence law, while the method used in this embodiment... The form represents a preferred specific implementation of finite-time convergence. The second nonlinear term is the adaptive damping compensation term, whose specific algebraic expression is as follows: This term essentially constitutes a variable with velocity. The changing saturation function. From a physical perspective, the system's equivalent damping coefficient becomes... When the system is in the high-speed motion phase (i.e. When the value is relatively large, the equivalent damping coefficient automatically approaches its maximum value. By enhancing damping, overshoot and oscillation caused by rapid response are effectively suppressed; when the system is in a low-speed or steady-state phase (i.e., When the value is relatively small, the coefficient smoothly returns to the baseline value. This avoids the negative impact of fixed high damping on system sensitivity and response speed. This adaptive adjustment mechanism based on the speed square ratio ensures a dynamic balance between smoothness and speed of the transient process across the entire speed domain. Furthermore, by constructing a suitable Lyapunov function, it can be proven that under the above dual compensation mechanism, regardless of the compensation coefficient... and Regardless of the non-negative values ​​chosen, the closed-loop system is globally asymptotically stable, which provides solid theoretical support for the flexible tuning of parameters in engineering applications.

[0029] A linear extended state observer is used to estimate the total system disturbance in real time. Specifically, such as... Figure 1As shown, the linear extended state observer treats all internal and external disturbances during the operation of the permanent magnet synchronous motor, such as load torque changes, friction torque, parameter perturbations, and unmodeled dynamics, as a total disturbance, and observes and estimates them in real time through extended state variables. The equation of the linear extended state observer is shown in equation (4):

[0030] (4) In the formula, , , They are mechanical angles Mechanical angular velocity and aggregate disturbance The estimated value, For control quantity (i.e. ), , , Let represent the first derivatives of the three estimates with respect to time, and let represent the rate of change of the state estimate over time. For position estimation error, , , Let be the observer gain. To make equation (4) converge, according to the bandwidth parameterization method, all eigenvalues ​​of the observer are set to . place, thereby obtaining , , ,in This represents the bandwidth of the observer. This approach eliminates the need for the controller to rely on a precise mathematical model of the motor, significantly improving the system's robustness and anti-interference capability.

[0031] Using the smoothed signal and its derivative from the output of a dual-compensated tracking differentiator as reference inputs, combined with the state estimate from a linearly extended state observer, a control quantity is generated through a linear state error feedback control law to drive the permanent magnet synchronous motor. Specifically, when the observer achieves accurate observation, the system is equivalent to a second-order integral element; therefore, a proportional-derivative (PD) controller can be applied to achieve stable control of the system. To avoid... The oscillation problem caused by rapid changes is addressed by using a derivative term in the PD controller. replace The expression for the linear state error feedback control law is shown in equation (5):

[0032] (5) In the formula, and For controller gain, It is the smoothed reference signal output by the dual-compensation tracking differentiator. After disturbance compensation, the system adopts PD control to form a dual-integral system. Based on the pole placement theory of second-order closed-loop systems, we can obtain... , The parameter settings, among which This refers to the controller's bandwidth. The final generated control quantity (i.e., the q-axis current reference value) The signal is sent to the drive unit, and after passing through the current loop PI controller and coordinate transformation, it drives the permanent magnet synchronous motor to run. Combining equations (3) to (5), the overall structure of the second-order position tracking active disturbance rejection control strategy is as follows: Figure 1 As shown. Through the above closed-loop control process, this embodiment effectively improves the transient performance and steady-state accuracy of the servo system while ensuring the simplicity of the linear active disturbance rejection control architecture.

[0033] This embodiment provides a theoretical analysis of the stability of the dual-compensation tracking differentiator to prove the global asymptotic stability of the system under the proposed dual-compensation mechanism.

[0034] To prove stability, an error variable is defined. , Assuming the reference signal is constant, the error dynamic equation of the tracking differentiator can be rewritten as equation (6): (6), The following Lyapunov functions are selected as shown in equation (7): (7) The function is positive definite and radially unbounded. Differentiate the function with respect to time along the trajectory of system equation (6), and substitute it into... and The expression, after algebraic simplification, yields equation (8):

[0035] (8) From equation (8), we can see that It is semi-negative definite, and the equality holds if and only if According to the LaSalle invariant set principle, the system will converge to a state satisfying the condition from any initial state. The largest invariant set. Within this set, the system equations can be further derived... Therefore, with the unique invariant set at the origin, the system is globally asymptotically stable. This conclusion applies to any... , This means that regardless of the value of the compensation coefficient (including the case of degenerating into a traditional linear tracking differentiator), the stability of the closed-loop system is strictly guaranteed by theory, providing solid theoretical support for the flexible tuning of parameters in engineering applications.

[0036] like Figure 1As shown, this embodiment provides a position servo active disturbance rejection control system for a permanent magnet synchronous motor. This system is a physical embodiment of the control method, achieving high-performance position servo control through a modular architecture. Specifically, the system includes a dual-compensation tracking differentiator, a linearly extended state observer, a linear state error feedback controller, and a drive unit.

[0037] The dual-compensation tracking differentiator is used to smooth the position reference signal and extract its differential signal based on the linear framework of the traditional linear tracking differentiator by introducing both a finite-time convergence compensation term and an adaptive damping compensation term. Specifically, in Figure 1 In the system architecture shown, the dual-compensation tracking differentiator serves as a reference signal preprocessing module, receiving an externally given position reference signal. This module integrates state equation logic and outputs a smoothed position signal through the coordinated operation of a linear basis and two nonlinear compensation branches. and its corresponding differential signal This structural design enables the system to obtain an ideal reference trajectory that combines fast response and smooth transition characteristics without relying on complex nonlinear algorithm libraries, providing a high-quality input reference for subsequent closed-loop control.

[0038] The linear extended state observer is used to estimate the total disturbance of a system in real time, outputting a state estimate that includes position, velocity, and total disturbance estimates. Specifically, the linear extended state observer treats the permanent magnet synchronous motor as a disturbed integral series object, using the motor's actual position feedback and control input to reconstruct the system's internal state and external disturbances in real time. Its output position estimate... Speed ​​estimates It is not only used for closed-loop feedback, but more importantly, it provides an estimate of the total disturbance. This estimate covers all uncertainties affecting system performance, such as load torque fluctuations, frictional changes, parameter perturbations, and unmodeled dynamics, thus achieving low dependence of the control system on model accuracy.

[0039] The linear state error feedback controller uses the smoothed signal and its derivative signal output from the dual-compensation tracking differentiator as reference inputs. It uses the difference between the smoothed signal and the position estimate, and the difference between the derivative signal and the velocity estimate, as error signals. These are combined with the total disturbance estimate for feedforward compensation to generate the control input. Specifically, the linear state error feedback controller is the core node for information aggregation and decision-making in the system. It receives the ideal trajectory from the dual-compensation tracking differentiator. and the actual state estimate from the linearly extended state observer Internally, the controller first calculates the position error. and speed error The basic feedback control quantity is generated through a proportional-derivative (PD) control law; subsequently, the total disturbance estimate is... The feedforward method is superimposed onto the control loop for real-time cancellation. The final generated control quantity (e.g., q-axis current reference value) The error feedback is sent to the drive unit. This mechanism, which combines error feedback and disturbance feedforward, ensures that the system can accurately track the ideal trajectory while actively suppressing various internal and external disturbances during dynamic processes.

[0040] The drive unit is used to drive the permanent magnet synchronous motor according to the control input. Specifically, the drive unit acts as the power interface between the digital control algorithm and the physical actuator. It receives the control input from the linear state error feedback controller, and after coordinate transformation, pulse width modulation (such as SVPWM), and power inversion, converts it into three-phase voltage or current to drive the stator windings of the permanent magnet synchronous motor. Simultaneously, the drive unit is also responsible for acquiring the actual position and speed information of the motor and feeding it back to the linear extended state observer, forming a complete physical closed loop. It should be understood that although this embodiment describes a surface-mounted permanent magnet synchronous motor as an example, this system architecture is also applicable to embedded permanent magnet synchronous motors or other types of AC servo motors; each functional module can be implemented through software code in an embedded processor, through hardware logic circuits such as FPGAs and ASICs, or through a hardware-software co-operation approach, as long as it has the aforementioned signal processing and transmission functions.

[0041] Through the above system architecture, this embodiment organically integrates the signal conditioning advantages of the dual-compensation tracking differentiator, the anti-interference advantages of the linear extended state observer, and the simplicity of the linear state error feedback controller. The signal flow between modules is clear, and the functional decoupling is well-defined, making it easy to debug and maintain in engineering, and establishing a robust structure-function correspondence at the legal level, effectively supporting the comparison and determination of infringement of controller products.

[0042] To verify the effectiveness of the proposed active disturbance rejection position servo control method for permanent magnet synchronous motors under actual working conditions, and to further illustrate the performance advantages of the dual-compensation tracking differentiator compared to the traditional linear tracking differentiator, this embodiment is based on... Figure 3 and Figure 4 The simulation or experimental results shown are compared and analyzed. It should be understood that the test conditions, motor parameters, and load conditions described below are only an exemplary application scenario of this application and are not intended to limit the scope of protection of this application. In practical applications, those skilled in the art can adjust the relevant parameters according to the specific requirements of the servo system. As long as the dual-compensation control architecture described in the foregoing embodiments of this application is adopted, similar performance improvement effects can be obtained.

[0043] In the test environment of this embodiment, a surface-mount permanent magnet synchronous motor was used as the controlled object, and the same controller bandwidth parameters were set to ensure the fairness of the comparison. The test covered two typical operating conditions: step signal response and sinusoidal signal dynamic tracking, which were used to evaluate the transient response quality and steady-state tracking accuracy of the system, respectively. The comparison algorithms included the traditional linear active disturbance rejection control (LADRC) and the active disturbance rejection control based on a dual-compensation tracking differentiator (DC-TD-ADRC) proposed in this application.

[0044] like Figure 3 As shown, the difference between the two control strategies can be clearly observed in the step signal position tracking response test. While the response curve of the traditional LADRC algorithm exhibits a certain speed on the rising edge, visible overshoot and subsequent adjustment oscillations appear near the target value. This reflects that the traditional linear tracking differentiator inevitably sacrifices smoothness in pursuit of fast response, causing the system to consume additional time at the end of the transient process to eliminate residual errors. In contrast, the response curve of the DC-TD-ADRC algorithm of this application shows superior transient performance. Specifically, its rising edge is steeper, indicating that the finite-time convergence compensation term provides a stronger driving torque than linear feedback in the larger error phase, significantly shortening the response time. Simultaneously, the curve smoothly enters steady state near the target position, with almost no overshoot or oscillation. This phenomenon strongly demonstrates that the adaptive damping compensation term plays a crucial role in the high-speed and deceleration phases; its equivalent damping coefficient automatically increases with speed, effectively absorbing the system's kinetic energy, thus completely suppressing overshoot without sacrificing response speed. This decoupling of speed and smoothness is a direct manifestation of how this application resolves the inherent contradictions in the prior art.

[0045] like Figure 4 As shown, the advantages of this application in dynamic continuous trajectory tracking were further verified in the sinusoidal signal tracking and error comparison test. Figure 4The top image shows the position tracking waveform, and the bottom image shows the corresponding position tracking error waveform. Looking at the amplitude of the error waveform, the maximum peak position tracking error of the traditional LADRC algorithm is approximately 0.54 rad, while the maximum peak position tracking error of the DC-TD-ADRC algorithm in this application is reduced to approximately 0.43 rad, a reduction of about 20%. Furthermore, observing the phase relationship, the tracking curve of this application has a higher degree of fit with the reference signal and less phase lag. This is because the dual compensation mechanism not only optimizes the generation quality of the reference signal but also improves the response bandwidth of the closed-loop system to time-varying signals through finite-time convergence characteristics, enabling the system to more sensitively follow high-frequency changing commands. It should be understood that although the figures show error data at specific frequencies and amplitudes, the tracking accuracy improvement brought by this application is universal. Under different speed and load disturbance conditions, the dual-compensation tracking differentiator can maintain tracking performance superior to traditional linear methods through its inherent nonlinear compensation mechanism.

[0046] In summary, the comparison and verification of the step response and sinusoidal tracking fully demonstrate that the permanent magnet synchronous motor active disturbance rejection position servo control method provided in this application has significant progress in practical applications. This method successfully overcomes the trade-off between response speed and signal smoothness in traditional linear active disturbance rejection control. While ensuring simplicity in engineering implementation, it achieves dynamic performance and steady-state accuracy comparable to or even surpassing complex nonlinear control algorithms, effectively responding to the technical needs of the high-precision servo drive field.

[0047] The above inventions are merely a few specific embodiments of the present invention. However, the embodiments of the present invention are not limited thereto, and any variations that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A method for self-disturbance rejection position servo control of a permanent magnet synchronous motor, characterized in that, include: Acquire the reference position signal and the motor feedback signal of the permanent magnet synchronous motor; The reference position signal is smoothed by a dual-compensation tracking differentiator to obtain a smoothed position signal and a smoothed velocity signal. The dual-compensation tracking differentiator is based on the linear tracking differentiator framework. It introduces a finite-time convergence compensation term based on the position tracking error in the error forward channel and an adaptive damping compensation term based on the smoothed velocity signal in the velocity feedback channel. The position tracking error is determined based on the smoothed position signal and the reference position signal. Based on the smooth position signal, the smooth speed signal, and the motor feedback signal, a control command is generated by an active disturbance rejection controller to drive the permanent magnet synchronous motor.

2. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 1, characterized in that, The finite-time convergence compensation term is configured such that as the position tracking error approaches zero, its gain decays more slowly than that of the linear term, maintaining high gain to accelerate error convergence. The adaptive damping compensation term is configured to increase the damping coefficient as the smooth speed signal increases, so as to adaptively enhance damping and suppress overshoot in the high-speed stage.

3. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 2, characterized in that, The expression for the finite-time convergence compensation term includes a fractional power function based on the position tracking error; The expression for the adaptive damping compensation term includes a velocity squared saturation function based on the smoothed velocity signal; The expression for the finite-time convergence compensation term includes... The expression for the adaptive damping compensation term includes... ,in, This refers to the position tracking error; and For compensation coefficient, After smoothing , For reference position signal, for The derivative of Let Sgn(e) be the tracking factor, and Sgn(e) be the sign function.

4. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 3, characterized in that, The state equation of the dual-compensation tracking differentiator is: in and They represent and The first derivative with respect to time.

5. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 4, characterized in that, When the compensation coefficient and When both are zero, the dual-compensation tracking differentiator degenerates into a linear tracking differentiator.

6. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 1, characterized in that, The active disturbance rejection controller includes a linear extended state observer and a linear state error feedback control law; The method further includes: estimating the mechanical angle of the permanent magnet synchronous motor in real time based on the position signal contained in the control command and the motor feedback signal using the linearly extended state observer. Mechanical angular velocity and aggregate disturbance The state estimate is obtained; The step of generating control commands through an active disturbance rejection controller includes: generating the control commands based on the smoothed position signal and the state estimate using the linear state error feedback control law.

7. The method for self-disturbance rejection position servo control of a permanent magnet synchronous motor as described in claim 6, characterized in that, The state equation of the linearly extended state observer is: ， in, , , They are mechanical angles Mechanical angular velocity and aggregate disturbance The estimated value, To control the amount, i.e. For q-axis current, , , Let represent the first derivatives of the three estimates with respect to time, and let represent the rate of change of the state estimate over time. For position estimation error, , , For observer gain, This is the inherent coefficient of the velocity loop.

8. A position servo self-disturbance rejection control system for a permanent magnet synchronous motor, characterized in that, include: The signal acquisition unit acquires the reference position signal and the motor feedback signal of the permanent magnet synchronous motor; A dual-compensation tracking differentiator smooths the reference position signal to obtain a smoothed position signal and a smoothed velocity signal. Based on the linear tracking differentiator framework, the dual-compensation tracking differentiator introduces a finite-time convergence compensation term based on the position tracking error in the error forward channel and an adaptive damping compensation term based on the smoothed velocity signal in the velocity feedback channel. The position tracking error is determined based on the smoothed position signal and the reference position signal. The active disturbance rejection controller generates control commands based on the smoothed position signal, the smoothed speed signal, and the motor feedback signal to drive the permanent magnet synchronous motor.

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