PMSM Active Disturbance Rejection Velocity Control Method Based on Adaptive Hybrid State Feedback

Abstract

This invention discloses a PMSM (Active Disturbance Rejection Speed ​​Control) method based on adaptive hybrid state feedback. This method introduces a novel state mixer between the controller and the observer, proportionally mixing the states directly measured by the sensors with the states estimated by the observer to form a new state that is fed back to the controller. Based on the hybrid state feedback strategy, this invention designs a dual-threshold adaptive law combining speed tracking error and disturbance observation derivative, dynamically adjusting the mixing ratio online. This ratio switches to the optimal disturbance rejection performance during system transients and to the optimal noise attenuation performance during steady-state operation. By adjusting the hybrid state feedback, this invention introduces independent zero-point adjustment degrees of freedom for the disturbance rejection and noise attenuation transfer functions without affecting the closed-loop pole configuration, thereby significantly improving the system's dynamic response speed and steady-state accuracy.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to a PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in high-performance speed control systems such as CNC machine tools, robots, and rail transportation due to their high efficiency and high power density. In these applications, the motor system is inevitably affected by internal and external uncertainties such as load disturbances, friction, and parameter changes.

[0003] Active disturbance rejection control (ADRC) has received widespread attention and research in the field of PMSM disturbance rejection control because it does not require an accurate system model and can estimate and compensate for total disturbances online through an extended state observer (ESO).

[0004] Traditional ADRC typically employs two fixed state feedback mechanisms: Measurement State Feedback (MSF) and Observation State Feedback (OSF). MSF (as seen in the literature [Y. Zuo, X. Zhu, L. Quan, C. Zhang, Y. Du, and Z. Xiang, “Active Disturbance Rejection Controller for Speed ​​Control of Electrical Drives Using Phase-Locking Loop Observer,” IEEE Trans. Ind. Electron., vol.66, no. 3, pp. 1748–1759, Mar. 2019]) exhibits good low-frequency disturbance suppression performance but is relatively sensitive to measurement noise. OSF (as seen in the literature [Z. Niu, Y. Zuo, H. Wang, L. Zhang, X. Zhu, and CHTLee, “Improved Low-Frequency Disturbance Rejection Property for PositionControl of PMSM Using Generalized Extended State Observer,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 11, no. 5, pp. 4739–4748, Oct. 2023]) can effectively attenuate high-frequency measurement noise through the filtering characteristics of ESO, but its inherent phase lag weakens the system's dynamic disturbance rejection capability. When the system is simultaneously affected by measurement noise and internal and external disturbances, a single fixed state feedback method is difficult to simultaneously meet the system's comprehensive requirements for dynamic response and steady-state accuracy.

[0005] How to fully exploit the impact of the state information contained in sensors and observers on the closed-loop system without sacrificing the performance of one party, and achieve comprehensive optimization of the dynamic and steady-state performance of the speed control system, is a challenge faced by existing technologies. Summary of the Invention

[0006] In view of the above, the present invention provides a PMSM active disturbance rejection velocity control method based on adaptive hybrid state feedback, which extends the independent zero-point adjustment degree of the closed-loop transfer function of system disturbance suppression and noise attenuation, thereby broadening the performance optimization space of ADRC without affecting pole configuration; by adaptively optimizing the mixing ratio, the overall performance of the system in suppressing high-order time-varying disturbances and attenuating measurement noise is improved.

[0007] A PMSM active disturbance rejection velocity control method based on adaptive hybrid state feedback includes the following steps:

[0008] (1) Establish a dynamic model of a permanent magnet synchronous motor with lumped disturbances;

[0009] (2) Design an extended state observer to estimate the state variables and total disturbance of the dynamic model in real time;

[0010] (3) Construct a hybrid state feedback signal, which is a linear combination of the velocity signal directly measured by the encoder and the velocity signal estimated by the extended state observer through a variable mixing ratio;

[0011] (4) Design a feedback control law and use the hybrid state feedback signal and the lumped disturbance estimated by the extended state observer to calculate the reference values ​​of the stator current on the d-axis and q-axis;

[0012] (5) Design a hybrid ratio adaptive law to dynamically adjust the hybrid ratio online according to the system's operating conditions in order to achieve a balance between disturbance suppression and noise attenuation performance;

[0013] (6) Apply the stator current reference values ​​of the d-axis and q-axis to the motor system to achieve closed-loop speed control.

[0014] Furthermore, the expression for the dynamic model of the permanent magnet synchronous motor in step (1) is as follows:

[0015]

[0016] in: oh m The mechanical angular velocity of the PMSM for oh m The first derivative, K t The torque constant of the PMSM i q This refers to the q-axis stator current of the PMSM. J and B These are the total inertia coefficient and viscous friction coefficient of PMSM, respectively. T L The load torque of the PMSM This is the reference value for the q-axis stator current. b To control the gain and b = K t / J , b n To control the gain b The nominal value, d This refers to the lumped disturbance of the motor system.

[0017] Furthermore, the extended state observer in step (2) is a fourth-order structure that simultaneously extends the first-order state integral and the first-order perturbation differential observation on the basis of the traditional second-order extended state observer, so as to take into account both the ability to suppress high-order complex perturbations and the ability to attenuate high-frequency measurement noise. The specific expression is as follows:

[0018]

[0019] in: i m For the mechanical angle of PMSM, for i m The actual measured value, for i m The observed values, For mechanical angle estimation error, for The first derivative, mechanical angular velocity oh m The observed values, for The first derivative, For aggregated disturbance d The estimated value, for The first derivative, For the disturbance differential observation, β 1~ β 4 represents the gain coefficient of the observer. for The first derivative.

[0020] Furthermore, the expression for the mixed state feedback signal in step (3) is as follows:

[0021]

[0022] in: oh fd It is a mixed-state feedback signal. oh meas The mechanical angular velocity is directly measured by the encoder. r This refers to the mixing ratio.

[0023] Furthermore, the mixing ratio r Switch between two optimized values: one is the optimal perturbation suppression mixing ratio. r d One value is used to enhance dynamic disturbance rejection performance when the system is under transient conditions; the other value is the optimal noise attenuation mixing ratio. r n It is used to enhance the ability to suppress measurement noise when the system is in steady-state operation.

[0024] Furthermore, when the extended state observer has an extension based on the second-order traditional structure... l Order state integral and k When the general higher-order form of the order perturbation differential observation is used, the optimal noise attenuation mixing ratio is... r n and optimal perturbation suppression mixing ratio r d The expression is:

[0025]

[0026] in: k p For the velocity loop feedback gain, β l and β l+1 The gain coefficient of the observer. l and k It is a natural number.

[0027] Furthermore, the gain coefficient β l and β l+1 The following relationship must be satisfied:

[0028]

[0029] in: oh o For bandwidth parameters, β 0 = 1.

[0030] Furthermore, the expression for the feedback control law in step (4) is as follows:

[0031]

[0032]

[0033] in: This is a reference value for the mechanical angular velocity. em and For velocity tracking error and its observed values ​​and , .

[0034] Furthermore, the hybrid proportional adaptive law in step (5) is based on the velocity tracking error. e m and disturbance differential observations Dual threshold adaptive switching strategy: when e m absolute value | e m | Greater than the first threshold d e At that time, the system is determined to be in a transient state, and the mixing ratio is set to... r = r d When | e m | Less than or equal to the first threshold d e and absolute value Greater than the second threshold d d1 At that time, it was still maintained r = r d When | e m | Less than or equal to the first threshold d e and absolute value Less than or equal to the second threshold d d1 When the system is determined to have reached a steady state, the mixing ratio is set to... r = r n .

[0035] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0036] 1. By introducing hybrid state feedback, this invention provides independent zero-point adjustment freedom for the disturbance suppression and noise attenuation transfer functions without changing the closed-loop pole configuration of the system, thus significantly expanding the performance optimization space of ADRC.

[0037] 2. This invention reveals the scalability and compatibility of the hybrid state feedback strategy in high-order ESOs, and provides a general analytical expression for the hybrid ratio corresponding to the optimal disturbance suppression and noise attenuation performance.

[0038] 3. Through adaptive optimization of the mixing ratio, this invention can achieve both excellent dynamic response and steady-state accuracy under both low-speed and high-speed operating conditions, significantly improving the overall performance of the system in suppressing high-order time-varying disturbances and attenuating measurement noise. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the mixed velocity state structure under different expansion state observer structures in this invention.

[0040] Figure 2 The diagram shows the amplitude-frequency characteristics of the disturbance suppression performance and noise attenuation performance of the present invention under different parameters. The left diagram shows the low-frequency disturbance suppression performance, and the right diagram shows the high-frequency noise attenuation performance.

[0041] Figure 3 This is a schematic diagram of the adaptive switching process for the mixing ratio in this invention.

[0042] Figure 4 This is a structural block diagram of the self-disturbance rejection speed control system of the present invention.

[0043] Figure 5 The diagram shows the experimental results of the speed of a permanent magnet synchronous motor under different control methods under step disturbance, where (a) corresponds to the traditional linear active disturbance rejection method and (b) corresponds to the improved linear active disturbance rejection method of this invention.

[0044] Figure 6 The diagram shows the experimental results of the speed of a permanent magnet synchronous motor under different control methods under periodic disturbances. (a) corresponds to the traditional linear active disturbance rejection method, and (b) corresponds to the improved linear active disturbance rejection method of this invention.

[0045] Figure 7 The diagram shows the experimental results of the speed of the permanent magnet synchronous motor under different control methods in forward and reverse rotation. (a) corresponds to the traditional linear active disturbance rejection method, and (b) corresponds to the improved linear active disturbance rejection method of this invention. Detailed Implementation

[0046] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0047] This implementation method takes a permanent magnet synchronous motor with a rated power of 3.1kW, a rated torque of 15Nm, and a rated speed of 2000r / min as an example to perform closed-loop control of the motor speed. The specific process is as follows:

[0048] (1) Establish a dynamic model of a permanent magnet synchronous motor with lumped disturbance form.

[0049] 1.1 Establish the mechanical dynamics equations of the permanent magnet synchronous motor.

[0050] The mechanical dynamics equations of a permanent magnet synchronous motor can be described in the following form:

[0051]

[0052] in: i m Indicates mechanical angle, oh m Represents mechanical angular velocity. K t Represents the torque constant. i q This represents the q-axis current in a synchronously rotating coordinate system. J and B Represents the total inertia and coefficient of viscous friction. T L This indicates the load torque.

[0053] 1.2 The dynamic equations of the permanent magnet synchronous motor are transformed into an integral chain structure with lumped disturbance form.

[0054] By retaining only the differential of the velocity state on the left side of the permanent magnet synchronous motor's dynamic equations, and unifying all terms except the reference q-axis current on the right side as lumped disturbances, the mechanical dynamic equations of a permanent magnet synchronous motor with lumped disturbances can be established as follows:

[0055]

[0056] in: This is the q-axis current reference value. b n Indicates control gain b = K t / J The nominal value, total disturbance d Defined as:

[0057]

[0058] in: The disturbance is caused by inertia mismatch. Wow m / J The disturbance is caused by the friction of the motor shaft. T L / J This is a load-side disturbance.

[0059] (2) Design the extended state observer in the active disturbance rejection velocity controller.

[0060] The designed extended state observer is a fourth-order structure that extends the traditional second-order extended state observer with first-order state integrals and first-order perturbation differential observations. This is to balance the ability to suppress high-order complex perturbations and the ability to attenuate high-frequency measurement noise. It can be designed as follows:

[0061]

[0062] in: Represents the observed mechanical angle value. This is the actual measured value of the mechanical angle. Represents the observed mechanical angular velocity. β i ( i =1,2,3,4) represents the observer gain. This represents the estimated disturbance value. This represents the estimated value of the perturbation derivative.

[0063] (3) Design the hybrid state feedback signal in the active disturbance rejection speed controller.

[0064] The hybrid state feedback signal can be designed in the following form:

[0065]

[0066] in: oh meas The speed signal measured by the encoder. r This is the proportion coefficient for the mixed state.

[0067] (4) Design the control law in the active disturbance rejection speed controller.

[0068] The control law in the active disturbance rejection speed controller is designed as the output of the proportional controller minus the lumped disturbance feedforward compensation estimated by the extended state observer, and the feedback state in the proportional controller is a hybrid speed state that fuses the measured speed signal and the observed speed signal, as expressed below:

[0069]

[0070] in: This is a reference value for the mechanical angular velocity.

[0071] (5) Optimize the mixing ratio parameter in the mixed state feedback.

[0072] 5.1 The optimal mixing ratio for setting disturbance suppression performance and noise attenuation performance.

[0073] like Figure 1 As shown, when the extended state observer is extended l Order state integral and kWhen considering the general higher-order structure of the perturbation derivative, the expression for the mixing velocity estimation can be expressed as:

[0074]

[0075] in: , , j = l + k +2, and β 0 = 1.

[0076] The closed-loop transfer function of the system output can be expressed as:

[0077]

[0078] in: Indicates measurement noise. G r ( s ), G d ( s )and G n ( s The transfer functions () represent the system's reference tracking, disturbance suppression, and noise attenuation performance, respectively. .

[0079] As can be seen from the above formula, the mixing ratio r The adjustment does not affect the reference tracking performance of the system, but it expands the degree of freedom of zero adjustment in the closed-loop transfer function of disturbance suppression and noise attenuation and decouples it from pole placement, thereby broadening the optimization space for system performance.

[0080] Figure 2 The following is given when the extended state observer is l = k =1, a fourth-order structure and k p When =100, different mixing ratio factors are available. r and different bandwidth parameters oh o Low-frequency disturbance suppression performance G d ( s and high-frequency noise attenuation performance G n ( s The amplitude-frequency characteristics of the signal were determined, with the disturbance frequency set to 20 rad / s and the high-frequency measurement noise frequency set to 6000 rad / s. Figure 2 As can be seen from this, in each bandwidth parameter oh o Each of the following corresponds to an optimal mixing ratio. r This optimizes disturbance suppression or noise attenuation performance. r =1, meaning that the system achieves optimal noise attenuation performance when the controller's state feedback is simply selected as the observed state of ESO. Let this be denoted as... r The value is r n When adjusting r Make the perturbation suppression function G d ( s When one of the zeros in the polynomial is moved to the origin, the system exhibits optimal disturbance suppression performance. Q ( s The constant term in ) is 0, that is:

[0081]

[0082] Therefore, the optimal disturbance rejection performance at this point can be solved. r Value, denoted as r d ,but r n and r d It can be represented as:

[0083]

[0084] in: β l and β l+1 The parameter selection satisfies ,and β 0 = 1.

[0085] 5.2 Design of the adaptive law for the mixing ratio.

[0086] To enhance the system's noise attenuation performance under steady-state conditions, thereby reducing steady-state speed fluctuations, and to improve its ability to suppress internal and external disturbances under dynamic conditions, thereby reducing transient errors and recovery time, the hybrid proportional adaptive law is designed as a mechanism based on speed tracking error. and the observational differential of the disturbance Dual threshold adaptive switching strategy, such as Figure 3 As shown. When the absolute value of the speed tracking error is | e m | Greater than the first threshold d e At that time, the system is determined to be in a transient state, and the mixing ratio is set to... r = r d When the absolute value of the speed tracking error is | e m |Not greater than the first threshold d e At this point, the system initially enters a steady state. Further analysis is then conducted based on the observed differential values ​​of the disturbances. To determine the severity of the disturbance change, if the absolute value of the observed differential value of the disturbance... Not greater than the second threshold d d1 To determine if the system has reached a steady state, set the mixing ratio... r = r n .like Greater than d d1 This indicates that although the velocity error at the current moment is small, there are still transient disturbances in the system, which can easily cause the velocity error to fluctuate again. To maintain robustness, the velocity error should be maintained. r = r d .

[0087] In summary, the self-disturbance rejection speed control system of this invention can be constructed as follows: Figure 4 As shown.

[0088] (6) Experimental verification.

[0089] Figure 5 Experimental waveforms of the conventional active disturbance rejection speed control method and the control method of this invention are shown when a step load torque of 8 Nm is applied at 1.5 s, given a speed command of 500 r / min. Figure 5 As can be seen, during a sudden step disturbance, the maximum speed fluctuation of the traditional active disturbance rejection speed control method is 134.9 r / min, while the maximum speed fluctuation of the method of this invention is 70.2 r / min. Compared with the traditional method, the active disturbance rejection speed control method of this invention can quickly detect the increase in tracking error and determine it as a transient condition at the moment the disturbance occurs, thereby reducing the mixing ratio. r Automatically switch to the optimal disturbance suppression value r d This allows the q-axis current to be adjusted and compensated at a faster rate, resulting in a smaller speed drop and a faster recovery time.

[0090] Figure 6 Experimental waveforms of the conventional active disturbance rejection speed control method and the control method of this invention are shown when a periodic sinusoidal load torque with a frequency of 10 Hz and an amplitude of 5 Nm is applied, given a speed command of 500 r / min as a reference speed. From... Figure 6As can be seen, during the application of periodic sinusoidal disturbances, the maximum velocity fluctuation of the traditional active disturbance rejection velocity control method is 104 r / min, while the maximum velocity fluctuation of the method of the present invention is 34.62 r / min. Compared with the traditional method, the method of the present invention significantly improves the ability to suppress periodic time-varying disturbances.

[0091] Figure 7 The given values ​​are: amplitude 50 r / min and slope 2.1 rad / s. 2 The experimental results of dynamic tracking under the trapezoidal wave reference velocity command are used to evaluate the tracking accuracy in the low-speed and zero-crossing regions and the ability to suppress complex disturbances such as nonlinear friction. Figure 7 As can be seen, the maximum error during the dynamic tracking of the trapezoidal wave reference speed occurs in the zero-crossing region of the speed in both forward and reverse directions. The traditional active disturbance rejection speed control method generates a large speed tracking error when suppressing high-order friction disturbances, with a maximum speed error of 5.20 r / min. In contrast, the maximum speed tracking error of the method of the present invention is 2.21 r / min, indicating that the method of the present invention can effectively suppress the influence of high-order time-varying friction disturbances in the low-speed zero-crossing region.

[0092] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback, characterized in that, Includes the following steps: (1) Establish a dynamic model of a permanent magnet synchronous motor with lumped disturbances; (2) Design an extended state observer to estimate the state variables and total disturbance of the dynamic model in real time; (3) Construct a hybrid state feedback signal, which is a linear combination of the velocity signal directly measured by the encoder and the velocity signal estimated by the extended state observer through a variable mixing ratio; (4) Design a feedback control law and use the hybrid state feedback signal and the lumped disturbance estimated by the extended state observer to calculate the reference values ​​of the stator current on the d-axis and q-axis; (5) Design a hybrid ratio adaptive law to dynamically adjust the hybrid ratio online according to the system's operating conditions in order to achieve a balance between disturbance suppression and noise attenuation performance; (6) Apply the stator current reference values ​​of the d-axis and q-axis to the motor system to achieve closed-loop speed control.

2. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 1, characterized in that, The expression for the dynamic model of the permanent magnet synchronous motor in step (1) is as follows: in: ω m The mechanical angular velocity of the PMSM for ω m The first derivative, K t The torque constant of the PMSM i q This refers to the q-axis stator current of the PMSM. J and B These are the total inertia coefficient and viscous friction coefficient of PMSM, respectively. T L The load torque of the PMSM This is the reference value for the q-axis stator current. b To control the gain and b = K t / J , b n To control the gain b The nominal value, d This refers to the lumped disturbance of the motor system.

3. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 2, characterized in that, The extended state observer in step (2) is a fourth-order structure that extends the traditional second-order extended state observer with both first-order state integral and first-order perturbation differential observations, in order to balance the ability to suppress high-order complex perturbations and the ability to attenuate high-frequency measurement noise. The specific expression is as follows: in: θ m For the mechanical angle of PMSM, for θ m The actual measured value, for θ m The observed values, For mechanical angle estimation error, for The first derivative, mechanical angular velocity ω m The observed values, for The first derivative, For aggregated disturbance d The estimated value, for The first derivative, For the disturbance differential observation, β 1~ β 4 represents the gain coefficient of the observer. for The first derivative.

4. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 3, characterized in that, The expression for the mixed state feedback signal in step (3) is as follows: in: ω fd It is a mixed-state feedback signal. ω meas The mechanical angular velocity is directly measured by the encoder. ρ This refers to the mixing ratio.

5. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 4, characterized in that, The mixing ratio ρ Switch between two optimized values: one is the optimal perturbation suppression mixing ratio. ρ d One value is used to enhance dynamic disturbance rejection performance when the system is under transient conditions; the other value is the optimal noise attenuation mixing ratio. ρ n It is used to enhance the ability to suppress measurement noise when the system is in steady-state operation.

6. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 5, characterized in that, When the extended state observer has an extension based on the second-order conventional structure l Order state integral and k When the general higher-order form of the order perturbation differential observation is used, the optimal noise attenuation mixing ratio is... ρ n and optimal perturbation suppression mixing ratio ρ d The expression is: in: k p For the velocity loop feedback gain, β l and β l+1 The gain coefficient of the observer. l and k It is a natural number.

7. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 6, characterized in that, The gain coefficient β l and β l+1 The following relationship must be satisfied: in: ω o For bandwidth parameters, β 0 = 1.

8. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 6, characterized in that, The expression for the feedback control law in step (4) is as follows: in: This is a reference value for the mechanical angular velocity. e m and For velocity tracking error and its observed values ​​and , .

9. The PMSM active disturbance rejection speed control method based on adaptive hybrid state feedback according to claim 8, characterized in that, The hybrid proportional adaptive law in step (5) is based on velocity tracking error. e m and disturbance differential observations Dual threshold adaptive switching strategy: when e m absolute value | e m | Greater than the first threshold δ e At that time, the system is determined to be in a transient state, and the mixing ratio is set to... ρ = ρ d When | e m | Less than or equal to the first threshold δ e and absolute value Greater than the second threshold δ d1 At that time, it was still maintained ρ = ρ d When | e m | Less than or equal to the first threshold δ e and absolute value Less than or equal to the second threshold δ d1 When the system is determined to have reached a steady state, the mixing ratio is set to... ρ = ρ n .

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