A speed disturbance rejection method based on high-order extended state observer

Abstract

This invention discloses a speed disturbance suppression method based on a high-order extended state observer, comprising: Step 1: Taking a three-phase permanent magnet linear synchronous motor as the controlled object, establishing its kinematic model in the three-phase stationary coordinate system, and further constructing its kinematic model in the three-phase stationary coordinate system. d-q Kinematic model in rotating coordinate system; based on d-q The kinematic model of the motor in the coordinate system is constructed using the motor velocity as the state variable, and an extended state observer is built; it is assumed that the system's first... n The rate of change of the second perturbation is negligible, and n takes an integer greater than or equal to 2. This is achieved by considering the addition of additional... n The number of extended state variables constitutes a higher-order extended state observer model to achieve asymptotic convergence of higher-order terms in the disturbance polynomial of the motor motion model. A higher-order disturbance feedforward compensation term is added to the speed closed-loop control to improve the disturbance suppression capability of the speed closed-loop control system. This invention suppresses aperiodic disturbances in the system by converting observed disturbances into feedforward compensation terms at the control input, thereby improving the robustness of speed control without affecting the nominal performance of the system.

Description

Technical Field

[0001] This invention relates to the field of linear motor control technology, and specifically to a speed disturbance suppression method based on a high-order extended state observer. Background Technology

[0002] Permanent magnet linear synchronous motors (PMLSMs) have been widely used in high-precision motion control applications such as CNC machine tools and medical devices due to their advantages of high precision, high response speed, and direct drive. However, the motor's operation process exhibits complex characteristics of multi-stage, time-varying, and nonlinearity, and further improvements in its motion performance still face many challenges.

[0003] To improve the dynamic response performance of motor speed closed-loop control, a speed composite control strategy based on acceleration feedforward is often adopted. However, this method relies heavily on accurate mathematical models and performs poorly when faced with unknown or sudden disturbances. Especially under continuous dynamic operating conditions, the tracking error between the actual trajectory and the planned trajectory will increase significantly, seriously affecting control accuracy. Therefore, it is urgent to enhance the disturbance rejection capability of the PMLSM speed closed-loop control system. Existing robust control strategies often sacrifice the system's control performance under nominal operating conditions. In contrast, disturbance observation-based methods, which focus on observing and compensating for disturbance components, can simultaneously consider both the system's nominal performance and control robustness.

[0004] Among them, the Extended State Observer (ESO) observes system disturbances by expanding them into new state variables and transforming the observed disturbances into compensation terms for the control input, thereby effectively suppressing aperiodic disturbances in the system. ESO does not rely on an accurate system model and is widely used in servo systems, robotics, aircraft control, and other fields. However, ESO cannot guarantee asymptotic observation of time-varying disturbances. To address this, a High-order Extended State Observer (HESO) is constructed by increasing the number of extended states. This guarantees the asymptotic convergence of higher-order terms in the disturbance polynomial, thereby achieving accurate observation and compensation of disturbances and significantly improving the disturbance immunity of the velocity loop. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and to address the problem of speed fluctuations caused by nonlinear disturbances under different operating conditions of motors, which reduce the robustness of the system. This invention proposes a speed disturbance suppression method based on a high-order extended state observer, so as to enable more reliable and accurate closed-loop speed control of the motor.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is: a velocity perturbation suppression method based on a high-order extended state observer, characterized by comprising the following steps: Step 1: Taking a three-phase permanent magnet linear synchronous motor as the controlled object, establish its kinematic model in the three-phase stationary coordinate system, and further construct its kinematic model in... dq Kinematic model in a rotating coordinate system.

[0007] Step Two: Based on dq The kinematic model of the motor in the coordinate system is constructed with the motor speed as the state variable, and an extended state observer is built.

[0008] Step 3: Assume the system's first... n The rate of change of the second perturbation is negligible, and n takes an integer greater than or equal to 2. This is achieved by considering the addition of additional... n The number of extended state variables constitutes the higher-order extended state observer (HESO) to achieve asymptotic convergence of higher-order terms in the perturbation polynomial in the motor motion model. Step 4: Add a high-order disturbance feedforward compensation term to the speed closed-loop control to improve the disturbance suppression capability of the speed closed-loop control system.

[0009] Furthermore, the velocity perturbation suppression method based on a high-order extended state observer is characterized in that the kinematic model in the three-phase stationary coordinate system in step one is: , In the above formula, M For secondary total mass, Electromagnetic thrust, The disturbance force experienced by the system Electric angular velocity, electric angular velocity Synchronized speed with motor Existence Relationship: , This refers to the pole pitch of the motor. Electromagnetic thrust. satisfy: , in, It is a permanent magnet flux chain. For electrical angle, For the phase currents of the three-phase windings of the motor, satisfying , , and This refers to the three-phase stator current.

[0010] Furthermore, the velocity perturbation suppression method based on a high-order extended state observer is characterized in that, in step one... dq The electromagnetic thrust equation in the rotating coordinate system is: , , These are the d-axis and q-axis inductances, respectively. Furthermore, the motion model of the three-phase permanent magnet linear synchronous motor with thrust coefficient is expressed as follows: , in, , i q for q Axis current.

[0011] Furthermore, the velocity disturbance suppression method based on a high-order extended state observer is characterized in that the specific method of step two is: defining the system input, output, and state variables as follows: q Shaft reference current i qref ,speed v e and x 1, x 2. Among them, x 1= v e and x 2= f e , f e This represents the extended state. From this, we can obtain the extended state model for the motor motion model: , in, yes f e The differential.

[0012] Furthermore, the velocity disturbance suppression method based on a higher-order extended state observer is characterized in that, in step three, the rate of change of the second disturbance of the system is ignored, and a higher-order extended state model of the motor motion model is constructed by considering the addition of two additional extended state variables: , in, For state variables, express f e The second-order differential.

[0013] Based on the general form of ESO, HESO is represented as: , in, It is a state variable The observed values, For HESO observation gain.

[0014] Furthermore, the velocity perturbation suppression method based on a high-order extended state observer is characterized in that the HESO observation gain in step three... Design using the bandwidth configuration method: , In the formula, denoted as ESO bandwidth, and n represents the order of the observer.

[0015] Based on the higher-order extended state model and observation model of the motor's motion equations, the disturbance is observed. With actual disturbance f e Transfer function between It can be constructed as: , In addition, observation error With actual disturbance f e Transfer function between It can be constructed as: , in, It can reflect the observation capabilities of the enhanced disturbance observer. It can reflect the magnitude of ECDO observation errors.

[0016] Furthermore, in the speed disturbance suppression method based on a higher-order extended state observer, step four considers feedforward compensation for higher-order disturbances, and the speed loop control law designed using a composite control strategy is as follows: , in, v ref and v e These are the speed reference value and the measured value, respectively. k pv and k iv These are the proportional gain and integral gain of the proportional-integral (PI) control, respectively. a ref For acceleration reference value, These are the perturbation observations. Based on the above construction, The expression is: , in, for q Observed values ​​of shaft current.

[0017] Therefore, the disturbance rejection function of the speed closed-loop control system based on HESO Build as: , in, G i (s) represents the approximate transfer function of the current controller delay effect. This indicates a speed loop PI controller that satisfies... , k pv and k iv These are proportional gain and integral gain, respectively. For observing disturbances With actual disturbance f e The transfer function between them.

[0018] The beneficial effects and features of this invention are: (1) The velocity perturbation suppression method based on a high-order extended state observer proposed in this invention achieves asymptotic convergence of the higher-order terms of the perturbation polynomial by introducing two additional extended state variables to construct the HESO model. This HESO can expand the observation range and improve the observation accuracy without increasing the system bandwidth, thereby enhancing the system's perturbation suppression capability and effectively avoiding system oscillation problems that may be caused by excessively large observer bandwidth.

[0019] (2) The velocity disturbance suppression method based on a high-order extended state observer of the present invention improves the velocity loop's anti-disturbance capability by introducing a feedforward compensation term into the velocity loop, thus simultaneously taking into account the nominal performance and robustness of the velocity loop. Compared with the prior art, this method of the present invention not only achieves a fast dynamic response of the velocity closed-loop system under nominal operating conditions, but also improves the system's anti-disturbance capability. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating a preferred embodiment of the present invention; Figure 2 This is a block diagram of the closed-loop control of a ring permanent magnet linear synchronous motor according to a preferred embodiment of the present invention; Figure 3 This is a Bode plot characterizing the HESO observation capability according to a preferred embodiment of the present invention (where (a) is the transfer function). (a) Bode curves at different bandwidths; (b) Bode curves at different bandwidths (Berde curve); Figure 4 This is a preferred embodiment of the velocity composite control block diagram based on HESO. Figure 5 This is a Bode plot representing the velocity closed-loop disturbance rejection capability of a preferred embodiment of the present invention. Detailed Implementation 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.

[0021] Feedforward control systems can control the system based on the principle of compensation according to changes in disturbances or setpoints. When a disturbance occurs, the system controls the system according to the magnitude of the disturbance to compensate for its impact on the controlled object. However, due to inaccurate speed fluctuation modeling, difficulty in identification, and time-varying model parameters in actual systems, the compensation effect through speed fluctuation modeling is limited. It is necessary to indirectly suppress disturbances in the motor motion system from the perspective of disturbance observation. ESO (Electronic Stability Optimization) can treat internal uncertainties and external disturbances as a "total disturbance," and suppress aperiodic disturbances by converting the "total disturbance" into a compensation term at the control input. However, ESO has a slow dynamic response at low bandwidths, resulting in incomplete disturbance compensation. In conclusion, improving the disturbance rejection capability of the motor motion control system is particularly important for the reliable and robust operation of the motor system.

[0022] Please refer to Figure 1 The embodiments of the present invention relate to a velocity perturbation suppression method based on a high-order extended state observer, comprising the following steps: Step 1: Taking a three-phase permanent magnet linear synchronous motor as the controlled object, establish its kinematic model in the three-phase stationary coordinate system, and further construct its kinematic model in... dq Kinematic model in a rotating coordinate system.

[0023] Step 2: Based on dq The kinematic model of the motor in the coordinate system is constructed with the motor speed as the state variable, and an extended state observer is built.

[0024] Step 3: Assume the system's... n The rate of change of the second perturbation is negligible; by considering the addition of an additional... n The number of extended state variables constitutes a higher-order extended state observer to achieve asymptotic convergence of higher-order terms in the perturbation polynomial in the motor motion model.

[0025] Step 4: Add a high-order disturbance feedforward compensation term to the speed closed-loop control to improve the disturbance suppression capability of the speed closed-loop control system.

[0026] The closed-loop control block diagram of the permanent magnet linear synchronous motor in a specific embodiment of the present invention is as follows: Figure 2 As shown. The control principle of this linear motor mainly includes the following aspects: (1) The motor system adopts vector closed-loop drive control. Specifically, the outer loop uses HESO-based speed feedforward composite control, and the inner loop uses... i d = 0 vector control. Outer loop output. q shaft current i qref The voltage output from the inner current loop serves as the reference input for the inverter, and the motor drive voltage is obtained through the Space Vector Pulse Width Modulation (SVPWM) algorithm.

[0027] (2) Using acceleration as the target, the motor trajectory is planned according to the residual area method (also known as the trapezoidal velocity curve or S-curve). The residual area method adjusts the acceleration by calculating the remaining area to be moved (i.e., displacement) at the current speed, so that the speed is exactly zero when reaching the target position, and a smooth acceleration and deceleration process is achieved. If there is no jerk limit, trapezoidal acceleration (i.e., the velocity curve is trapezoidal and the acceleration is rectangular) or triangular acceleration (when the speed cannot reach the maximum set speed) can usually be used. If the jerk limit is considered, the acceleration curve is trapezoidal and the velocity curve is S-shaped.

[0028] Figure 3 This section analyzes the observation performance of a high-order extended state observer under different bandwidths. Based on... and , Figure 4 Bandwidth plotted The Bode curves are shown for speeds of 100 rad / s, 200 rad / s, 300 rad / s, and 400 rad / s, respectively. Figure 3 (a) is the transfer function Bode curves at different bandwidths. As can be seen from the figure, with... The increased bandwidth leads to faster system response, indicating that ECDO's observation capabilities improve with increased bandwidth. Figure 3 (b) provides the bandwidth under different conditions. The Bird curve. As shown in the graph, with... As the value increases, the phase delay and low-frequency gain of the Bode curve decrease, meaning that the observation error is smaller under the same disturbance input.

[0029] Figure 4 This is a block diagram of the speed composite control based on HESO. A high-order extended state observer can be used to observe various disturbances in the speed closed-loop system and feed them into the control channel, thereby improving the speed loop's anti-interference capability.

[0030] Figure 5Bode plots characterizing the disturbance rejection capabilities of different velocity closed-loop control systems are presented. The disturbance rejection function of the HESO-based velocity closed-loop control system is: , If HESO disturbance suppression compensation is not considered in the speed closed-loop control system, then the actual speed of the speed composite control system is... v e With system disturbance f e The transfer function between them is expressed as: , Figure 5 In this configuration, the HESO bandwidth is set to 300 rad / s. From... Figure 5 As can be seen, the amplitude gain of the HESO-based composite control system decreases significantly in the low-frequency band, indicating that the addition of the HESO disturbance suppression method significantly improves the anti-interference capability of the velocity closed-loop system. These results also demonstrate the effectiveness of HESO in disturbance suppression.

[0031] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A velocity perturbation suppression method based on a high-order extended state observer, characterized in that, Includes the following steps: Step 1: Taking a three-phase permanent magnet linear synchronous motor as the controlled object, establish its kinematic model in the three-phase stationary coordinate system, and further construct its kinematic model in... dq Kinematic model in a rotating coordinate system; Step Two: Based on dq The kinematic model of the motor in the coordinate system is constructed with the motor speed as the state variable, and an extended state observer is built. Step 3: Assume the system's first... n The rate of change of the second perturbation is negligible, and n takes an integer greater than or equal to 2. This is achieved by considering the addition of additional... n The number of extended state variables constitutes a higher-order extended state observer model, in order to achieve asymptotic convergence of higher-order terms in the perturbation polynomial in the motor motion model. Step 4: Add a high-order disturbance feedforward compensation term to the speed closed-loop control to improve the disturbance suppression capability of the speed closed-loop control system.

2. The velocity perturbation suppression method based on a high-order extended state observer according to claim 1, characterized in that, The kinematic model in the three-phase stationary coordinate system in step one is as follows: ， In the above formula, M For secondary total mass, Electromagnetic thrust, For various disturbance forces in the system, Electric angular velocity, electric angular velocity Synchronized speed with motor Existence Relationship: , Motor pole pitch; electromagnetic thrust satisfy: ， in, It is a permanent magnet flux linkage. For electrical angle, For the phase currents of the three-phase windings of the motor, satisfying , , and This refers to the three-phase stator current.

3. The velocity perturbation suppression method based on a high-order extended state observer according to claim 2, characterized in that, In step one dq Electromagnetic thrust in rotating coordinate system for: ， , These are the d-axis and q-axis inductances, respectively. Furthermore, the motion model of the three-phase permanent magnet linear synchronous motor is represented as follows: ， Among them, thrust coefficient , i q for q Axis current.

4. The velocity perturbation suppression method based on a high-order extended state observer according to claim 1, characterized in that, The specific method for step two is as follows: Define the system input, output, and state variables as follows: q Shaft reference current i qref ,speed v e and x 1, x 2； in, x 1= v e and x 2= f e , fe We treat the various disturbances in the system as states to be extended to construct an extended state model; thus, we can obtain an extended state model for the motor motion model: ， in, yes f e The differential, u e The system input variable is the q-axis current i. q .

5. The velocity perturbation suppression method based on a high-order extended state observer according to claim 4, characterized in that, In step three, it is assumed that the system's first... n Neglecting the rate of change of the second disturbance, when n is 2, i.e. ignoring the rate of change of the second disturbance of the system, a higher-order extended state observer model of the motor motion model is constructed by considering the addition of two extra extended state variables: ， in, For state variables, express f e The second derivative; Based on the general form of ESO, HESO is represented as: ， in, It is a state variable The observed values, For HESO observation gain.

6. The velocity perturbation suppression method based on a high-order extended state observer according to claim 5, characterized in that, HESO observation gain Design using the bandwidth configuration method: ， In the formula, denoted as ESO bandwidth, and n represents the order of the observer.

7. The velocity disturbance suppression method based on a high-order extended state observer according to claim 5, wherein the specific method of step four is as follows: considering feedforward compensation for high-order disturbances, and simultaneously employing a composite control strategy, the velocity loop control law is designed as follows: ， in, v ref and v e These are the speed reference value and the measured value, respectively. k pv and k iv These are the proportional gain and integral gain of the proportional-integral (PI) control, respectively. a ref For acceleration reference value, For the perturbation observation, 1 / s represents the integration operation; Based on the above construction, The expression is: ， in, for q Observed values ​​of shaft current; Therefore, the disturbance rejection function of the speed closed-loop control system based on HESO Build as: ， in, G i (s) represents the approximate transfer function of the current controller delay effect. This indicates a speed loop PI controller that satisfies... , k pv and k iv These are proportional gain and integral gain, respectively. For observed disturbances and actual disturbances f e The transfer function between them.

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