Permanent magnet synchronous motor speed control method based on double error correction extended state observer

Abstract

The application discloses a permanent magnet synchronous motor active disturbance rejection speed control method based on a double-error correction extended state observer, a double-error correction extended state observer structure combining a speed estimation error and a position estimation error is constructed, and a speed loop total disturbance observation value is output to a feedback control law. An optimized observer parameter setting strategy is designed based on the control structure of the application, the decoupling configuration of zero points and pole points in a disturbance suppression function is realized, the position of the zero points in the disturbance suppression function is optimized in combination with time domain and frequency domain analysis, and the disturbance suppression performance of the system is enhanced. Therefore, the application has the advantages that the dynamic response and the steady state performance of disturbance suppression are enhanced through an additional zero point moving track without affecting the pole point configuration of an original closed loop system, and the freedom degree of performance adjustment of a linear extended state observer and the upper limit of disturbance suppression performance are widened.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor control, and particularly relates to a permanent magnet synchronous motor active disturbance rejection speed control method based on a double-error correction extended state observer. BACKGROUND

[0002] Permanent magnet synchronous motor (PMSM) is widely used in robots, electric vehicles and other industrial fields due to its high efficiency, high power density and high reliability. In these industrial fields, the motor system needs to effectively suppress the multi-source disturbance 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 document [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. Through the method of designing an extended state observer to estimate the total disturbance and feeding forward compensation to the controller, the tracking response and disturbance suppression performance of the system can be more intuitively and effectively adjusted.

[0004] The parameter tuning methods for linear extended state observer (e.g., [S. Zhu et al., “Robust Speed Control of Electrical Drives With Reduced Ripple Using Adaptive Switching High-Order Extended State Observer,” IEEE Transactions on Power Electronics, vol. 37, no. 2, pp. 2009-2020, Feb. 2022, doi: 10.1109 / TPEL.2021.3105263]) mostly focus on the configuration of the closed-loop system poles, while the observer gain is contained in the zero position at the same time, and the adjustment of the pole position will inevitably change the zero position. At present, few scholars pay attention to the influence of the change of the zero point on the observation performance of the ESO (Extended State Observer), and 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 in the positions that are more optimal for the performance of the system at the same time. Therefore, the design freedom of the linear ESO has not been fully explored, and the influence of the change of the zero point on the performance of the ESO is still in the blank stage. SUMMARY

[0005] In view of the above, the present application provides a permanent magnet synchronous motor active disturbance rejection speed control method based on a double error correction extended state observer, which realizes the decoupling configuration of the zero and the pole, reveals the influence law of the 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 the independent zero point configuration freedom.

[0006] A permanent magnet synchronous motor active disturbance rejection speed control method based on a double error correction extended state observer, comprising the following steps:

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

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

[0009] (3) constructing a double error correction extended state observer and optimizing its parameters;

[0010] (4) estimating the lumped disturbance of the motor system by using the double error correction extended state observer;

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

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

[0013]

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

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

[0016]

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

[0018]

[0019] in: k is the reference value for the mechanical angular velocity. p For proportional gain, This is an estimate of the lumped disturbance.

[0020] Furthermore, the expression for the double-error-corrected extended state observer in step (3) is as follows:

[0021]

[0022] in: Estimated value of lumped disturbance The first derivative, The mechanical angular velocity ω mthe observation value of the mechanical angle θ the observation value of the mechanical angle θ m , ξ is an error correction term, β1-β3 are observer gains, and α is an adjustable gain, and are first derivatives of and respectively.

[0023] Further, after the parameter optimization of the double-error-correction extended state observer in step (3), the expressions of the observer gains β1-β3 and the adjustable gain α are as follows:

[0024]

[0025] where ω o is an observer bandwidth configured by dominant poles, and δ is an adjustable gain configured by dominant zeros.

[0026] Further, the adjustable gain δ is adjusted in a range of 0-3, when δ is taken as 0-δ os , the motor control system will not produce secondary overshoot when resisting step disturbance; when δ is taken as δ os -3, the anti-disturbance performance of the motor control system in the low frequency band is further enhanced; when δ=3, the motor control system can realize speed zero-error suppression of ramp disturbance; and the expression of the critical value δ os is as follows:

[0027]

[0028] A computer device comprises a memory and a processor, the memory has a computer program stored therein, and the processor is configured to execute the computer program to implement the above-mentioned permanent magnet synchronous motor active disturbance rejection speed control method based on a double-error-correction extended state observer.

[0029] A computer readable storage medium stores a computer program, and the computer program is executed by a processor to implement the above-mentioned permanent magnet synchronous motor active disturbance rejection speed control method based on a double-error-correction extended state observer.

[0030] Based on the above technical solutions, the present application has the following beneficial technical effects:

[0031] 1. The present application widens the degrees of freedom and flexibility of performance adjustment of the active disturbance rejection speed control system based on the linear extended state observer by moving the zero point trajectory decoupled from the poles.

[0032] 2. The present application discloses the influence law of the zero position on the dynamic response, steady-state performance and stability margin of the active disturbance rejection speed controller, and provides a simple and practical control parameter setting guide.

[0033] 3. The application improves the dynamic response and steady-state disturbance rejection performance of the system and the robustness of the system under parameter variation by optimizing the zero point position without affecting the pole configuration of the active disturbance rejection speed controller. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 Fig. 1 is a speed-current double closed-loop control schematic diagram of a permanent magnet synchronous motor system in an embodiment of the application.

[0035] Figure 2 Fig. 2 is a structural schematic diagram of an active disturbance rejection speed control system of the application.

[0036] Figure 3 Fig. 3 is a Bode plot of a transfer function of a disturbance to an output speed in an embodiment of the application.

[0037] Figure 4 Fig. 4 (a) is an experimental result diagram of a permanent magnet synchronous motor using a conventional active disturbance rejection speed controller under step disturbance.

[0038] Figure 4 Fig. 4 (b) is an experimental result diagram of a permanent magnet synchronous motor using the active disturbance rejection speed controller of the application under step disturbance.

[0039] Figure 5 Fig. 5 (a) is an experimental result diagram of a permanent magnet synchronous motor using a conventional active disturbance rejection speed controller under periodic disturbance.

[0040] Figure 5 Fig. 5 (b) is an experimental result diagram of a permanent magnet synchronous motor using the active disturbance rejection speed controller of the application under periodic disturbance.

[0041] Figure 6 Fig. 6 (a) is an experimental result diagram of a permanent magnet synchronous motor using a conventional active disturbance rejection speed controller under parameter mismatch.

[0042] Figure 6 Fig. 6 (b) is an experimental result diagram of a permanent magnet synchronous motor using the active disturbance rejection speed controller of the application under parameter mismatch. DETAILED DESCRIPTION

[0043] In order to describe the application more specifically, the technical solutions of the application are described in detail below in combination with the drawings and specific embodiments.

[0044] This embodiment 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] As shown in Fig. 1, the speed-current double closed-loop control schematic diagram of the permanent magnet synchronous motor system in the embodiment of the application comprises a motor speed loop and a motor current loop. Figure 1As shown, the permanent magnet synchronous motor system adopts a double-loop control framework based on a field-oriented control strategy, and generally includes a speed loop and a current loop double-loop control structure. The speed loop generates a desired reference torque Motor side speed feedback ω m through a speed loop controller The torque coefficient K T is converted into the reference input of the current loop The current loop controls the output reference voltage through sampling of the motor stator current, and then adjusts the inverter output voltage through SVPWM (Space Vector Pulse Width Modulation) modulation technology to drive the motor. U 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, so the dynamics of the current loop are ignored when designing the speed loop, and it is considered

[0046] To achieve closed-loop control of the speed of the permanent magnet synchronous motor system, the embodiment provides a self-anti-disturbance speed control method based on a double-error correction extended state observer, and the specific process is as follows:

[0047] (1) A dynamic model of the permanent magnet synchronous motor with a lumped disturbance form is established.

[0048] 1.1 The mechanical dynamics equation of the permanent magnet synchronous motor is established and described as follows:

[0049]

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

[0051] 1.2 The dynamics equation of the permanent magnet synchronous motor is converted into an integral chain structure with a lumped disturbance form:

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

[0053]

[0054] wherein: is the reference value of the q-axis current, b n represents the control gain b = K t / J is the nominal value of the speed;

[0055] The total disturbance d is defined as:

[0056]

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

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

[0059] As shown in Figure 2 , the feedback control law in the active disturbance rejection speed controller can be designed as the output of the proportional controller minus the estimated lumped disturbance of the extended state observer, and the expression is as follows:

[0060]

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

[0062] (3) Design the double error correction extended state observer structure in the active disturbance rejection speed control.

[0063] As shown in Figure 2 , the double error correction extended state observer in the active disturbance rejection speed control can be designed as follows:

[0064]

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

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

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

[0068]

[0069] Where: ω o represents the observer bandwidth of the dominant pole configuration, and δ represents the adjustable gain of the dominant zero point configuration. Combined with 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 double error correction extended state observer, the zero-pole of the closed-loop system can be obtained as:

[0070]

[0071] Where: p 1,2,3,4 represents the pole of the disturbance suppression closed-loop transfer function, and z 1,2,3 represents the zero point of the disturbance suppression closed-loop transfer function. In the double error correction structure of the present application, the position of the closed-loop system pole p 2,3,4 is only related to the parameter ω o , and the position of the zero point z 2,3 is determined by the parameters ω o and δ. By configuring the position of the closed-loop system pole p 2,3,4 with ω o , the position of the closed-loop system zero point z 2,3 can be further adjusted by δ. Therefore, through the design of the present application, the active disturbance rejection speed control system has the ability to adjust the system performance through independent zero point configuration, and the freedom of performance adjustment of the original active disturbance rejection speed control system is expanded.

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

[0073]

[0074] The coefficient of the s term in the numerator of the disturbance suppression transfer function G DR (s) simultaneously determines the amplitude-frequency characteristic of the low frequency band ω oThe parameter δ determines the system's anti-interference performance in the low-frequency band, and adjusting δ can further influence this performance. Figure 3 As shown in the Bode plot of the disturbance-to-output speed transfer function in the active disturbance rejection speed control method of this invention, it can be seen that as δ increases from 0 to 3, the system's disturbance rejection performance in the mid-to-low frequency range gradually improves; when δ = 3, the system's disturbance rejection performance in the mid-to-low frequency range 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 system's disturbance rejection performance in the mid-to-low frequency range begins to gradually decline, reducing the system's stability margin. The method of this invention can achieve [something] while maintaining the observer bandwidth parameter ω. o Without changing the parameters, the disturbance suppression performance of the system in the low-frequency band can be further adjusted by using the rated zero-point configuration parameter δ.

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

[0076]

[0077] The location of the poles determines the modes of free motion of the system during the dynamic process of suppressing disturbances. Zeros, while not constituting modes in the time-domain response, affect the weighting coefficients of each mode in the response. The closer the zero of the closed-loop transfer function is to the imaginary axis, the higher its weighting in each modal response. When the zero z2 is moved to the pole -k by adjusting the parameter δ... p When on the left side, the polarity of the response component coefficient A1 corresponding to the dominant pole p1 changes from positive to negative. At this point, the corresponding velocity response begins to produce overshoot. Setting A1 = 0, the critical value δ for overshoot can be calculated as follows:

[0078]

[0079] Taking into account the system's dynamic response to disturbance suppression, steady-state performance, and stability margin, the parameter δ for optimizing the system's disturbance suppression performance is selected within the range of 0 to 3, where δ ranges from 0 to 3. os When δ is taken as δ, no secondary overshoot will occur when resisting step disturbances; when δ is taken as δ os When δ = 3, the system’s anti-interference performance in the low-frequency band is further enhanced as δ increases; when δ = 3, slope disturbance suppression without steady-state error can be achieved.

[0080] Figure 4 (a) and Figure 4(b) shows the experimental waveforms of the traditional active disturbance rejection speed control method and the anti-disturbance performance enhanced active disturbance rejection speed control method of the application when a 5Nm step form load torque is applied at 1.0s under the speed command given by the reference speed of 500r / min. As can be seen from the figure, during the process of sudden step disturbance, the maximum speed fluctuation of the traditional method and the method of the application is 62r / min and 37r / min respectively, and the time required for the speed to return to the set value is 254ms and 123ms respectively. Compared with the traditional active disturbance rejection speed control method, the active disturbance rejection speed control method of the application re-optimizes the zero point position under the premise of keeping the system pole position unchanged, and adjusts the proportion coefficient of the speed response modal component, so that the maximum speed fluctuation and the speed recovery time in the process are superior to the traditional method.

[0081] Figure 5 (a) and Figure 5 (b) shows the experimental waveforms of the traditional active disturbance rejection speed control method and the anti-disturbance performance enhanced active disturbance rejection speed control method of the application 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. The disturbance rejection transfer function G DR (s) is the first order coefficient of the dominant low frequency amplitude-frequency characteristic in the molecule, so it 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 application is 74r / min, which has a smaller speed fluctuation under periodic load disturbance.

[0082] Figure 6 (a) and Figure 6 (b) shows the experimental waveforms of the traditional method and the method of the application under inertia mismatch when the inertia set value in the controller is less than twice the actual inertia value of the system. As can be seen from the figure, compared with the traditional active disturbance rejection speed control method, the method of the application can produce smaller overshoot when tracking the step speed command under inertia mismatch and transition to steady state faster; and can better suppress the influence of step disturbance on the actual speed.

[0083] The above description of the embodiments is to facilitate those skilled in the art to understand and apply the application, and 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 labor. Therefore, the application is not limited to the above embodiments, and the improvements and modifications of the application made by those skilled in the art according to the disclosure of the application should be within the scope of protection of the application.

Claims

1. A dual error correction extended state observer based active disturbance rejection speed control method for permanent magnet synchronous motor, comprising the following steps: (1) establishing a dynamic model of permanent magnet synchronous motor with lumped disturbance form; (2) designing a feedback control law in the active disturbance rejection speed controller according to the dynamic model of permanent magnet synchronous motor; (3) constructing a dual error correction extended state observer and optimizing its parameters; the expression of the dual error correction extended state observer is as follows: wherein: a first derivative of the lumped disturbance estimate value an observation value of the mechanical angular velocity ω m an observation value of the mechanical electrical angle θ m b n a nominal value of the control gain b a q-axis stator current reference value, ζ is an error correction term, β1 to β3 are observer gains, and α is an adjustable gain and a first derivative of the lumped disturbance estimate value and a first derivative of the lumped disturbance estimate value​​ (4) estimating the lumped disturbance of the motor system by using the dual error correction extended state observer; (5) substituting the estimated lumped disturbance into the feedback control law to obtain the reference value of dq-axis stator current, thereby performing closed-loop control on the permanent magnet synchronous motor.

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

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

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

5. The active disturbance rejection speed control method of permanent magnet synchronous motor according to claim 1, characterized in that: After optimizing the parameters of the dual error correction extended state observer in the step (3), the expressions of the observer gains β1-β3 and the adjustable gain α are as follows: where: ω o is the observer bandwidth configured for the dominant pole, and δ is the adjustable gain configured for the dominant zero.

6. The active disturbance rejection speed control method of permanent magnet synchronous motor according to claim 5, characterized in that: The adjustable gain delta is adjusted in a range of 0-3, when delta is in a range of 0-delta os , the motor control system will not produce secondary overshoot when resisting step disturbance; when delta is in a range of delta os -3, the anti-disturbance performance of the motor control system in the low frequency band is further enhanced; when delta=3, the motor control system can realize speed no-static error suppression ramp disturbance; wherein the expression of the critical value delta os is as follows: where: k p is a proportional gain.

7. A computer device comprising a memory and a processor, said memory having stored therein a computer program, characterized in that: The processor is used to execute the computer program to realize the active disturbance rejection speed control method for permanent magnet synchronous motor as claimed in any one of claims 1-6.

8. A computer readable storage medium storing a computer program, characterized in that: The computer program is executed by the processor to realize the active disturbance rejection speed control method for permanent magnet synchronous motor as claimed in any one of claims 1-6.

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