Permanent magnet synchronous motor active disturbance rejection speed control method based on double-error correction extended state observer

Abstract

The invention discloses a permanent magnet synchronous motor active disturbance rejection speed control method based on a double-error correction extended state observer, and the method comprises the steps: constructing a double-error correction extended state observer structure combining a speed estimation error and a position estimation error, and outputting a speed ring lumped disturbance observation value to a feedback control law. An optimized observer parameter setting strategy is designed based on the control structure, decoupling configuration of a zero point and a pole point in a disturbance suppression function is achieved, the position of the zero point in the disturbance suppression function is optimized by combining time domain and frequency domain analysis, and the disturbance suppression performance of the system is enhanced. Therefore, the method has the advantages that on the premise that pole assignment of an original closed-loop system is not affected, the dynamic response and steady-state performance of disturbance suppression are enhanced through the additional zero-point movement track, and the degree of freedom of performance adjustment of the linear expansion state observer and the upper limit of disturbance suppression performance are widened.

Description

Technical Field

[0001] The invention belongs to the technical field of motor control, and in particular relates to a permanent magnet synchronous motor self-disturbance rejection speed control method based on a dual error correction extended state observer. Background Art

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in robotics, electric vehicles, and other industrial fields due to their high efficiency, high power density, and high reliability. In these industrial fields, motor systems need to effectively suppress multi-source disturbances caused by parameter mismatch, unmodeled dynamics, and load torque.

[0003] Due to the rapid development of control theory, two-degree-of-freedom controllers represented by active disturbance rejection control (such as reference [J. Han, “From PID to Active Disturbance Rejection Control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, Mar. 2009, doi: 10.1109 / TIE.2008.2011621]) have been widely studied and applied. By designing an extended state observer to estimate the total disturbance and feed forward compensation to the controller, it can more intuitively and effectively adjust the tracking response and disturbance suppression performance of the system.

[0004] Most of the parameter tuning methods for linear extended state observers (such as [S.Zhu et al., "RobustSpeed ​​Control of Electrical Drives With Reduced Ripple Using AdaptiveSwitching High-Order Extended State Observer," IEEE Transactions on PowerElectronics, vol.37, no.2, pp.2009–2020, Feb.2022, doi:10.1109 / TPEL.2021.3105263]) focus on the configuration of the poles of the closed-loop system. However, the observer gain is also included in the zero position, and the adjustment of the pole position will inevitably change the zero position. At present, few scholars have paid attention to the impact of the change of the zero point on the observation performance of the ESO (Extended State Observer). The coupling between the zero and the pole makes it impossible to independently adjust the positions of the two under the existing method framework, resulting in the zero and the pole not being able to fall at the same time at a position that is better for system performance. Therefore, for linear ESO, its design freedom has not been fully explored, and the impact of zero point variation on ESO performance is still in a blank stage. Summary of the invention

[0005] In view of the above, the present invention provides a permanent magnet synchronous motor self-disturbance rejection speed control method based on a dual error correction extended state observer, which realizes the decoupling configuration of zero poles, reveals the influence of zero point movement on the dynamic and steady-state performance and stability margin of the control system, and optimizes the dynamic response, steady-state performance and parameter robustness of the system based on independent zero point configuration degrees of freedom.

[0006] A permanent magnet synchronous motor self-disturbance rejection speed control method based on a dual error correction extended state observer comprises the following steps:

[0007] (1) Establish a permanent magnet synchronous motor dynamic model with lumped disturbance form;

[0008] (2) designing a feedback control law in an anti-disturbance speed controller according to the permanent magnet synchronous motor dynamics model;

[0009] (3) Construct a dual error correction extended state observer and optimize its parameters;

[0010] (4) The lumped disturbance of the motor system is estimated using a dual error correction extended state observer;

[0011] (5) The estimated lumped disturbance is substituted into the feedback control law to obtain the dq-axis stator current reference value (the d-axis reference value is 0), thereby performing closed-loop control of the permanent magnet synchronous motor.

[0012] Furthermore, the expression of the permanent magnet synchronous motor dynamics model in step (1) is as follows:

[0013]

[0014] Where: m is the mechanical angular velocity of the PMSM, ω m The first derivative of K t is the torque constant of PMSM, i q is the q-axis stator current of PMSM, J and B are the total inertia and viscous friction coefficient of PMSM respectively; T d =T L +T R , T L is the load torque of PMSM, T R is the torque ripple of PMSM, T d represents the total disturbance torque including load torque and torque ripple, is the q-axis stator current reference value, b is the control gain and b=K t / J,b n is the nominal value of the control gain b, and d is the lumped disturbance of the motor system.

[0015] Furthermore, the expression of the lumped disturbance d is as follows:

[0016]

[0017] Furthermore, the expression of the feedback control law in step (2) is as follows:

[0018]

[0019] in: is the reference value of mechanical angular velocity, k p is the proportional gain, is the estimated value of the lumped disturbance.

[0020] Furthermore, the expression of the dual error correction extended state observer in step (3) is as follows:

[0021]

[0022] in: is the lumped disturbance estimate The first derivative of is the mechanical angular velocity ω mThe observed value of is the mechanical electrical angle θ m The observed value, ξ is the error correction term, β1~β3 are the observer gains, α is the adjustable gain, and They are and The first derivative of .

[0023] Furthermore, after the parameters of the dual error correction extended state observer are optimized in step (3), the expressions of the observer gains β1-β3 and the adjustable gain α are as follows:

[0024]

[0025] Where: o is the observer bandwidth of the dominant pole configuration, and δ is the adjustable gain of the dominant zero configuration.

[0026] Furthermore, the adjustable gain δ has an adjustment range of 0 to 3. os When δ is δ, the motor control system will not produce secondary overshoot when resisting step disturbance; os When δ = 3, the anti-interference performance of the motor control system in the low frequency band is further enhanced; when δ = 3, the motor control system can achieve speed zero static error to suppress ramp disturbance; the critical value δ os The expression is as follows:

[0027]

[0028] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor is used to execute the computer program to implement the above-mentioned permanent magnet synchronous motor self-disturbance rejection speed control method based on a dual error correction extended state observer.

[0029] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method for controlling the permanent magnet synchronous motor's self-disturbance rejection speed based on a dual error correction extended state observer is implemented.

[0030] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0031] 1. The present invention broadens the freedom and flexibility of performance adjustment of the self-disturbance rejection speed control system based on the linear extended state observer by moving the zero-point trajectory decoupled from the pole.

[0032] 2. The present invention reveals the influence of the zero position on the dynamic response, steady-state performance and stability margin of the anti-disturbance speed controller, and provides a concise and practical guide for control parameter setting.

[0033] 3. The present invention improves the dynamic response and steady-state disturbance suppression performance of the system and the robustness of the system under parameter changes by optimizing the zero point position without affecting the pole configuration of the anti-disturbance speed controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of speed-current dual closed-loop control of a permanent magnet synchronous motor system in an embodiment of the present invention.

[0035] Figure 2 It is a schematic diagram of the structure of the automatic anti-disturbance speed control system of the present invention.

[0036] Figure 3 It is a Bode diagram of the transfer function of disturbance to output speed in the implementation mode of the present invention.

[0037] Figure 4 (a) is the experimental result diagram of permanent magnet synchronous motor using traditional anti-disturbance speed controller under step disturbance.

[0038] Figure 4 (b) is a graph showing the experimental results of a permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under step disturbance.

[0039] Figure 5 (a) is the experimental result diagram of permanent magnet synchronous motor using traditional anti-disturbance speed controller under periodic disturbance.

[0040] Figure 5 (b) is a graph showing the experimental results of a permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under periodic disturbances.

[0041] Figure 6 (a) is the experimental result diagram of permanent magnet synchronous motor using traditional anti-disturbance control speed controller under parameter mismatch.

[0042] Figure 6 (b) is a graph showing the experimental results of a permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under parameter mismatch. DETAILED DESCRIPTION

[0043] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0044] This implementation method takes a permanent magnet synchronous motor with a rated power of 3.1 kW, a rated torque of 15 Nm, and a rated speed of 2000 r / min as an example to perform closed-loop control on the motor speed.

[0045] like Figure 1As shown in the figure, the permanent magnet synchronous motor system adopts a dual-loop control framework based on the magnetic field oriented control strategy, which generally includes a speed loop and a current loop control structure. The speed loop is based on the reference speed signal. Motor side speed feedbackω m , the desired reference torque is generated by the speed loop controller Through the torque coefficient K T Converted to the reference input of the current loop The current loop controls the output reference voltage by sampling the motor stator current, and then adjusts the inverter output voltage to drive the motor through SVPWM (Space Vector Pulse Width Modulation) modulation technology. DC is the DC voltage of the inverter. When the current loop bandwidth is high enough, the output torque can completely track the reference torque in a very short time. Therefore, the dynamics of the current loop is ignored when designing the speed loop.

[0046] In order to realize closed-loop control of the speed of a permanent magnet synchronous motor system, this embodiment provides an auto-disturbance rejection speed control method based on a dual error correction extended state observer, and the specific process is as follows:

[0047] (1) Establish a permanent magnet synchronous motor dynamic model with lumped disturbance form.

[0048] 1.1 Establish the mechanical dynamics equation of permanent magnet synchronous motor as follows:

[0049]

[0050] Where: m Indicates the mechanical angle; θ m Indicates mechanical angular velocity; K t represents the torque constant; i q represents the q-axis current in the synchronously rotating coordinate system; J and B represent the total inertia and viscous friction coefficients; T d =T L +T R , T L Indicates load torque, T R Represents torque ripple, T d Represents the total disturbance torque of load torque and torque ripple.

[0051] 1.2 Convert the dynamic equation of the permanent magnet synchronous motor into an integral chain structure with a lumped disturbance form:

[0052] By retaining only the differential of the speed state on the left side of the permanent magnet synchronous motor dynamics equation and classifying the terms other than the reference q-axis current on the right side of the equation as lumped disturbances, the mechanical dynamics equation of the permanent magnet synchronous motor in the form of lumped disturbance can be established and expressed as follows:

[0053]

[0054] in: is the q-axis current reference value, b n Indicates control gain b = K t / Nominal value of J;

[0055] The total disturbance d is defined as:

[0056]

[0057] in: is the disturbance caused by inertia mismatch, Bω m / J is the disturbance caused by the friction of the motor shaft, T L / J is the load side disturbance; d r =-T R / J represents the torque ripple disturbance caused by non-ideal factors such as sensor scaling / offset errors, inverter dead-time effects, and non-sinusoidal flux distribution of the motor.

[0058] (2) Design the feedback control law in the anti-disturbance speed controller.

[0059] like Figure 2 As shown in Figure 2, the feedback control law in the ADRC speed controller can be designed as the output of the proportional controller minus the lumped disturbance estimated by the extended state observer, expressed as follows:

[0060]

[0061] Where: k p Represents the proportional gain in the speed loop proportional controller, Indicates the reference value of speed, represents the estimate of the lumped disturbance by the extended state observer.

[0062] (3) Design a dual error correction extended state observer structure in self-disturbance rejection speed control.

[0063] like Figure 2 As shown in Figure 2, the dual error correction extended state observer in the ADRC speed control can be designed as follows:

[0064]

[0065] in: Represents the mechanical angle observation value, represents the mechanical angular velocity observation value, β i (i=1,2,3) represents the observer gain, represents the derivative of the disturbance estimate, ξ represents the proposed error correction term, and α represents the proportional adjustable gain.

[0066] (4) Optimize the parameters of the dual error correction extended state observer.

[0067] In the dual error correction extended state observer, in order to achieve the zero-pole decoupling configuration in the disturbance-to-output speed transfer function and expand the freedom of observer performance adjustment, the observer parameters can be configured as follows:

[0068]

[0069] Where: o represents the observer bandwidth of the dominant pole configuration, δ represents the adjustable gain of the dominant zero configuration, and the zero poles of the closed-loop system can be obtained by combining the mechanical dynamics model of the permanent magnet synchronous motor in the form of lumped disturbance, the feedback control law of the active disturbance rejection speed controller and the dual error correction extended state observer:

[0070]

[0071] Where: p 1,2,3,4 represents the pole of the disturbance rejection closed-loop transfer function, z 1,2,3 In the dual error correction structure of the present invention, the closed-loop system pole p 2,3,4 The position of o The zero point z 2,3 The position of o and δ, through ω o Configure the poles p of the closed-loop system 2,3,4 After the position is obtained, the closed-loop system zero point z can be further adjusted by δ 2,3 position, thus the design of the present invention enables the self-disturbance rejection speed control system to have the ability to adjust the system performance through an independent zero point configuration, thereby expanding the degree of freedom of performance adjustment of the original self-disturbance rejection speed control system.

[0072] The actual total disturbance d in the closed-loop system to the system output ω m The closed-loop transfer function can be expressed as:

[0073]

[0074] In the disturbance rejection transfer function G DR The coefficient of the first-order term s that dominates the low-frequency amplitude-frequency characteristics in the numerator (s) is simultaneously given by ω oand δ, the adjustment of parameter δ can further affect the anti-interference performance of the system in the low frequency band, such as Figure 3 As shown, it can be seen from the Bode diagram of the transfer function of disturbance to output speed in the self-disturbance rejection speed control method of the present invention that when δ increases from 0 to 3, the anti-disturbance performance of the system in the medium and low frequency bands gradually increases; when δ=3, the anti-disturbance performance of the corresponding system in the medium and low frequency bands is maximized; when δ is greater than 3, the control system changes from a minimum phase system to a non-minimum phase system, and the disturbance suppression performance of the system in the medium and low frequency bands begins to gradually decay and reduce the stability margin of the system. The method of the present invention can be achieved while maintaining the observer bandwidth parameter ω o Under the premise of unchanged, the disturbance suppression performance of the system in the low frequency band is further adjusted by the rated zero configuration parameter δ.

[0075] Under step disturbance, the time domain step response expression of the disturbance suppression function can be obtained as follows:

[0076]

[0077] The position of the pole determines the mode of free motion of the system in the dynamic process of system disturbance suppression. The zero point does not constitute the mode of time domain response, but affects the proportion coefficient of each mode in the response. When the position of the zero point of the closed-loop transfer function is closer to the imaginary axis, the proportion of the zero point in each modal response is higher. When the zero point z2 is moved to the pole -k by adjusting the parameter δ p When the left side is on, the polarity of the response component coefficient A1 corresponding to the dominant pole p1 changes from positive to negative. At this time, the corresponding speed response begins to overshoot. Let A1 = 0, and the critical value of δ that produces overshoot can be obtained as:

[0078]

[0079] Considering the system's disturbance suppression dynamic response, steady-state performance and stability margin, the selection range of the parameter δ for optimizing the system's disturbance suppression performance is 0 to 3, where δ is 0 to δ os When δ is δ, no secondary overshoot will occur when resisting step disturbance; os When δ=3, as δ increases, the anti-interference performance of the system in the low frequency band is further enhanced; when δ=3, the slope disturbance can be suppressed without static error.

[0080] Figure 4 (a) and Figure 4(b) shows the experimental waveforms of the traditional anti-disturbance speed control method and the anti-disturbance speed control method with enhanced anti-disturbance performance of the present invention when a step-shaped load torque of 5Nm is applied at 1.0s under a speed command of a reference speed of 500r / min. It can be seen from the figure that in the process of sudden step disturbance, the maximum speed fluctuations of the traditional method and the method of the present invention are 62r / min and 37r / min respectively, and the time required for the speed to recover to the set value is 254ms and 123ms respectively. Compared with the traditional anti-disturbance speed control method, the anti-disturbance speed control method of the present invention re-optimizes the zero point position under the premise that the system pole position remains unchanged, and then adjusts the weight coefficient of each modal component of the speed response, so that the maximum speed fluctuation and speed recovery time in the process are better than those of the traditional method.

[0081] Figure 5 (a) and Figure 5 (b) shows the experimental waveforms of the traditional automatic anti-disturbance speed control method and the automatic anti-disturbance speed control method with enhanced anti-disturbance performance of the present invention when a periodic trapezoidal wave load torque with a frequency of 2.5Hz, an amplitude of 8Nm, and a slope of 50Nm / s is applied under a speed command of a reference speed of 500r / min. The method of the present invention changes the disturbance suppression transfer function G on the basis of the traditional method. DR The first-order coefficient of the dominant low-frequency amplitude-frequency characteristic in the numerator (s) has a faster disturbance estimation rate. Under the periodic trapezoidal wave load disturbance, the steady-state speed fluctuation of the traditional method is 125r / min, while the steady-state speed fluctuation of the method of the present invention is 74r / min, with a smaller speed fluctuation under the periodic load disturbance.

[0082] Figure 6 (a) and Figure 6 (b) shows the experimental waveforms of the conventional method and the method of the present invention tracking the step speed and resisting the step load torque under inertia mismatch when the inertia setting value in the controller is less than twice the actual inertia value of the system. It can be seen from the figure that compared with the conventional self-disturbance rejection speed control method, the method of the present invention can produce a smaller overshoot and a faster transition to a steady state when tracking the step speed command under inertia mismatch; and can better suppress the influence of the step disturbance on the actual speed.

[0083] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A permanent magnet synchronous motor self-disturbance rejection speed control method based on a dual error correction extended state observer, comprising the following steps: (1) Establish a permanent magnet synchronous motor dynamic model with lumped disturbance form; (2) designing a feedback control law in an anti-disturbance speed controller according to the permanent magnet synchronous motor dynamics model; (3) Construct a dual error correction extended state observer and optimize its parameters; (4) The lumped disturbance of the motor system is estimated using a dual error correction extended state observer; (5) The estimated lumped disturbance is substituted into the feedback control law to obtain the dq-axis stator current reference value, thereby performing closed-loop control of the permanent magnet synchronous motor.

2. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 1 is characterized in that: The expression of the permanent magnet synchronous motor dynamics model in step (1) is as follows: Where: m is the mechanical angular velocity of the PMSM, ω m The first derivative of K t is the torque constant of PMSM, i q is the q-axis stator current of PMSM, J and B are the total inertia and viscous friction coefficient of PMSM respectively; T d =T L +T R , T L is the load torque of PMSM, T R is the torque ripple of PMSM, T d represents the total disturbance torque including load torque and torque ripple, is the q-axis stator current reference value, b is the control gain and b=K t / J,b n is the nominal value of the control gain b, and d is the lumped disturbance of the motor system.

3. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 2 is characterized in that: The expression of the lumped disturbance d is as follows:

4. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 2 is characterized in that: The expression of the feedback control law in step (2) is as follows: in: is the reference value of mechanical angular velocity, k p is the proportional gain, is the estimated value of the lumped disturbance.

5. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 4 is characterized in that: The expression of the double error correction extended state observer in step (3) is as follows: in: is the lumped disturbance estimate The first derivative of is the mechanical angular velocity ω m The observed value of is the mechanical electrical angle θ m The observed value, ξ is the error correction term, β1~β3 are the observer gains, α is the adjustable gain, and They are and The first derivative of .

6. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 5, characterized in that: After the parameters of the dual error correction extended state observer are optimized in step (3), the expressions of the observer gains β1-β3 and the adjustable gain α are as follows: Where: o is the observer bandwidth of the dominant pole configuration, and δ is the adjustable gain of the dominant zero configuration.

7. The permanent magnet synchronous motor self-disturbance rejection speed control method according to claim 6 is characterized in that: The adjustable gain δ has an adjustment range of 0 to 3. os When δ is δ, the motor control system will not produce secondary overshoot when resisting step disturbance; os When δ = 3, the anti-interference performance of the motor control system in the low frequency band is further enhanced; when δ = 3, the motor control system can achieve speed zero static error to suppress ramp disturbance; the critical value δ os The expression is as follows:

8. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: The processor is used to execute the computer program to implement the permanent magnet synchronous motor self-disturbance rejection speed control method according to any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method for self-disturbance rejection speed control of a permanent magnet synchronous motor as claimed in any one of claims 1 to 7 is implemented.

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