Dual-error-correction extended state observer-based active disturbance rejection speed control method for permanent magnet synchronous motor

Abstract

Disclosed in the present invention is a dual-error-correction extended state observer-based active disturbance rejection speed control method for a permanent magnet synchronous motor. By constructing a dual-error-correction extended state observer structure that combines a speed estimation error with a position estimation error, an observed value of lumped disturbance in a speed loop is outputted to a feedback control law. On the basis of the control structure of the present invention, an optimized observer parameter tuning strategy is designed, implementing the decoupled configuration of zeros and poles in a disturbance rejection function; moreover, zero positions in the disturbance rejection function are optimized by combining time-domain analysis with frequency-domain analysis, thereby improving the disturbance rejection performance of a system. Therefore, the present invention achieves the advantages of enhancing the dynamic response and steady-state performance of disturbance rejection by means of an additional zero-moving trajectory without affecting the pole placement of an original closed-loop system, and increasing the degree of freedom of performance adjustment and the upper limit of the disturbance rejection performance for linear extended state observers.

Description

A Permanent Magnet Synchronous Motor Active Disturbance Rejection Speed ​​Control Method Based on a Dual Error Correction Extended State Observer Technical Field

[0001] This invention belongs to the field of motor control technology, specifically relating to a method for active disturbance rejection speed control of a permanent magnet synchronous motor based on a dual error correction extended state observer. Background Technology

[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 (e.g., [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 it forward to compensate the controller, it can more intuitively and effectively adjust the tracking response and disturbance rejection performance of the system.

[0004] Most parameter tuning methods for linear extended state observers (such as those in the literature [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]) focus on configuring the poles of the closed-loop system. However, the observer gain is also included in the zero position, and adjusting the pole position will inevitably change the zero position. Currently, few scholars have paid attention to the impact of zero changes on the observation performance of ESO (Extended State Observer). The coupling between zeros and poles makes it impossible to adjust their positions independently under the existing method framework, resulting in zeros and poles not simultaneously falling in positions that are more conducive to system performance. Therefore, the design freedom of linear ESOs has not been fully explored, and the impact of zero-point changes on ESO performance is still in its infancy. Summary of the Invention

[0005] In view of the above, the present invention provides a method for active disturbance rejection speed control of permanent magnet synchronous motor based on a dual-error correction extended state observer, which realizes the decoupled configuration of zero and pole, reveals the influence law of zero movement on the dynamic 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 configuration degrees of freedom.

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

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

[0008] (2) Design the feedback control law in the self-disturbance rejection speed controller based on the dynamic model of the permanent magnet synchronous motor;

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

[0010] (4) The lumped disturbance of the motor system is estimated using a double-error-corrected 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] 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.

[0014] Furthermore, the expression for the lumped disturbance d is as follows:

[0015] Furthermore, the expression for the feedback control law in step (2) is as follows:

[0016] in: k is the reference value for the mechanical angular velocity. p For proportional gain, This is an estimate of the lumped disturbance.

[0017] Furthermore, the expression for the double-error-corrected extended state observer in step (3) is as follows:

[0018] in: Estimated value of lumped disturbance The first derivative, The mechanical angular velocity ω m The observed values, For mechanical electrical angle θ m The observed values ​​are given, where ξ is the error correction term, β1~β3 are the observer gains, and α is the adjustable gain. and They are respectively and The first derivative.

[0019] Furthermore, after optimizing the parameters of the double-error-corrected extended state observer in step (3), the expressions for the observer gains β1~β3 and the adjustable gain α are as follows:

[0020] Where: ω o δ is the observer bandwidth configured for the dominant poles, and δ is the adjustable gain configured for the dominant zeros.

[0021] Furthermore, the adjustable gain δ has an adjustment range of 0 to 3. When δ is 0 to 3, the adjustment range is... os When δ is taken as δ, the motor control system will not produce a secondary overshoot when resisting a step disturbance; os When δ = 3, the anti-interference performance of the motor control system in the low-frequency range is further enhanced; when δ = 3, the motor control system can achieve zero static error in speed suppression of ramp disturbances; among which the critical value δ os The expression is as follows:

[0022] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described active disturbance rejection speed control method for a permanent magnet synchronous motor based on a dual error correction extended state observer.

[0023] A computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described active disturbance rejection speed control method for a permanent magnet synchronous motor based on a dual-error correction extended state observer.

[0024] Based on the above technical solution, the present invention has the following beneficial technical effects:

[0025] 1. This invention expands the degrees of freedom and flexibility of performance adjustment of the active disturbance rejection velocity control system based on the linear extended state observer by moving the zero-point trajectory decoupled from the poles.

[0026] 2. This invention reveals the influence of zero position on the dynamic response, steady-state performance and stability margin of an active disturbance rejection speed controller, and provides a concise and practical guide for control parameter tuning.

[0027] 3. Without affecting the pole configuration of the active disturbance rejection speed controller, this invention improves the dynamic response and steady-state disturbance suppression performance of the system by optimizing the zero position, and enhances the robustness of the system under parameter changes. Attached Figure Description

[0028] Figure 1 is a schematic diagram of the speed-current dual closed-loop control of the permanent magnet synchronous motor system in an embodiment of the present invention.

[0029] Figure 2 is a schematic diagram of the self-disturbance rejection speed control system of the present invention.

[0030] Figure 3 is a Bode plot of the transfer function of the disturbance to the output speed under the embodiment of the present invention.

[0031] Figure 4(a) shows the experimental results of a permanent magnet synchronous motor using a traditional active disturbance rejection speed controller under step disturbance.

[0032] Figure 4(b) shows the experimental results of the permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under step disturbance.

[0033] Figure 5(a) shows the experimental results of a permanent magnet synchronous motor using a traditional active disturbance rejection speed controller under periodic disturbances.

[0034] Figure 5(b) shows the experimental results of the permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under periodic disturbance.

[0035] Figure 6(a) shows the experimental results of a permanent magnet synchronous motor using a traditional active disturbance rejection speed controller under parameter mismatch.

[0036] Figure 6(b) shows the experimental results of the permanent magnet synchronous motor using the self-disturbance rejection speed controller of the present invention under parameter mismatch. Detailed Implementation

[0037] 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.

[0038] This embodiment 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 on the motor speed.

[0039] As shown in Figure 1, this permanent magnet synchronous motor system adopts a dual-loop control framework based on a field-oriented control strategy. The overall structure includes a speed loop and a current loop. The speed loop operates based on a reference speed signal. Motor-side speed feedback ω m The desired reference torque is generated through the speed loop controller. Through the torque coefficient K T Reference input converted to 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 using SVPWM (Space Vector Pulse Width Modulation) modulation technology. DCThis represents the DC voltage of the inverter. When the current loop bandwidth is sufficiently high, the output torque can completely track the reference torque in a very short time. Therefore, the dynamics of the current loop are ignored when designing the speed loop, and it is assumed that...

[0040] To achieve closed-loop speed control of a permanent magnet synchronous motor system, this embodiment provides an active disturbance rejection speed control method based on a dual-error correction extended state observer, the specific process of which is as follows:

[0041] (1) Establish a dynamic model of a permanent magnet synchronous motor with lumped disturbance form.

[0042] 1.1 The mechanical dynamics equations of the permanent magnet synchronous motor are described as follows:

[0043] Where: ω m Represents a mechanical angle; θ m Represents mechanical angular velocity; K t Indicates torque constant; i q The current represents the q-axis current in a synchronously rotating coordinate system; J and B represent the total inertia and the coefficient of viscous friction, respectively; T d =T L +T R T L T represents the load torque. R Indicates torque pulsation, T d It represents the total disturbance torque of the load torque and torque pulsation.

[0044] 1.2 The dynamic equations of the permanent magnet synchronous motor are transformed into an integral chain structure with lumped disturbances:

[0045] 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 in the form of lumped disturbances can be established as follows:

[0046] in: This is the q-axis current reference value, b n This indicates that the control gain b = K t The nominal value of / J;

[0047] The total disturbance d is defined as:

[0048] in: Bω is the disturbance caused by inertia mismatch. m / J represents the disturbance caused by frictional force on the motor shaft, and T represents the disturbance caused by the frictional force on the motor shaft. L / J represents load-side disturbance; d r =-TR / J indicates torque pulsation disturbance caused by non-ideal factors such as sensor scaling / offset error, inverter dead zone effect, and non-sinusoidal flux distribution of the motor.

[0049] (2) Design the feedback control law in the active disturbance rejection speed controller.

[0050] 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 lumped disturbance estimated by the extended state observer, as expressed below:

[0051] Where: k p This represents the proportional gain in the speed loop proportional controller. A reference value representing speed. This represents the estimate of the lumped disturbance by the extended state observer.

[0052] (3) Design the structure of the dual error correction extended state observer in active disturbance rejection speed control.

[0053] As shown in Figure 2, the dual-error-corrected extended state observer in active disturbance rejection speed control can be designed as follows:

[0054] in: Represents the observed mechanical angle value. β represents the observed mechanical angular velocity. i (i = 1, 2, 3) represents the observer gain. Let ξ represent the derivative of the perturbation estimate, ξ represent the proposed error correction term, and α represent the proportionally adjustable gain.

[0055] (4) Optimize the parameters of the double-error correction extended state observer.

[0056] In a dual-error-corrected extended state observer, to achieve decoupling of the zeros and poles in the output velocity transfer function from the disturbance and to expand the degrees of freedom in adjusting the observer's performance, the observer's parameters can be configured as follows:

[0057] Where: ω o Let δ represent the observer bandwidth of the dominant pole placement and δ represent the adjustable gain of the dominant zero placement. Combining the mechanical dynamics model of the permanent magnet synchronous motor in the form of lumped disturbances, the feedback control law of the active disturbance rejection speed controller, and the double-error-corrected extended state observer, the zeros and poles of the closed-loop system can be obtained as follows:

[0058] Where: p 1,2,3,4 z represents the poles of the disturbance suppression closed-loop transfer function. 1,2,3This represents the zero point of the disturbance suppression closed-loop transfer function. Under the dual-error correction structure of this invention, the closed-loop system pole p... 2,3,4 The position is only related to the parameter ω o Related to, and zero point z 2,3 The position is also determined by the parameter ω o And δ determines, through ω o Configure the poles p of the closed-loop system 2,3,4 After positioning, the zero point z of the closed-loop system can be further adjusted via δ. 2,3 The position of the position, therefore, through the design of the present invention, enables the active disturbance rejection speed control system to have the ability to adjust the system performance through independent zero-point configuration, thus expanding the degree of freedom of the original active disturbance rejection speed control system performance adjustment.

[0059] In a closed-loop system, the actual total disturbance d is transferred to the system output ω. m The closed-loop transfer function can be expressed as:

[0060] In the perturbation suppression transfer function G DR The coefficient of the first-order s-term in the (s) molecule, which dominates the low-frequency amplitude-frequency characteristics, is simultaneously determined by ω. o The disturbance rejection performance of the system in the low-frequency range can be further affected by adjusting the parameter δ, as shown in Figure 3. From 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 when δ increases from 0 to 3, the disturbance rejection performance of the system in the mid-to-low frequency range gradually increases; when δ = 3, the disturbance rejection performance of the system 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 disturbance suppression performance of the system in the mid-to-low frequency range begins to gradually decay and the stability margin of the system decreases. The method of this invention can achieve the goal of 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.

[0061] Under step perturbation, the time-domain step response expression of the perturbation suppression function can be obtained as follows:

[0062] 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:

[0063] 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.

[0064] Figures 4(a) and 4(b) show the experimental waveforms of the conventional active disturbance rejection speed control (ADRC) method and the ADRC method with enhanced disturbance rejection performance of the present invention when a step load torque of 5 Nm is applied at 1.0 s, given a speed command of 500 r / min. As can be seen from the figures, during the sudden step disturbance, the maximum speed fluctuation of the conventional method and the method of the present invention are 62 r / min and 37 r / min, respectively, and the time required for the speed to recover to the set value is 254 ms and 123 ms, respectively. Compared with the conventional ADRC method, the ADRC method of the present invention, by re-optimizing the zero-point position while keeping the system pole position unchanged, and thus adjusting the weight coefficients of each modal component of the speed response, results in better maximum speed fluctuation and speed recovery time during the process.

[0065] Figures 5(a) and 5(b) show the experimental waveforms of the conventional active disturbance rejection speed control method and the disturbance rejection performance-enhanced active disturbance rejection speed control method of this invention, under a speed command of 500 r / min and an applied periodic trapezoidal wave load torque with a frequency of 2.5 Hz, an amplitude of 8 Nm, and a slope of 50 Nm / s. The method of this invention modifies the disturbance rejection transfer function G based on the conventional method. DR The coefficients of the first-order term that dominate the low-frequency amplitude-frequency characteristics in the (s) molecule result in a faster perturbation estimation rate. Under periodic trapezoidal wave load perturbation, the steady-state velocity fluctuation of the conventional method is 125 r / min, while the steady-state velocity fluctuation of the method of this invention is 74 r / min, exhibiting a smaller velocity fluctuation under periodic load perturbation.

[0066] Figures 6(a) and 6(b) show the experimental waveforms of the conventional method and the method of this invention tracking step speed and resisting step load torque under inertia mismatch when the inertia setpoint in the controller is less than twice the actual system inertia. As can be seen from the figures, compared with the conventional active disturbance rejection speed control method, the method of this invention can generate a smaller overshoot and transition to steady state more quickly when tracking step speed commands under inertia mismatch; and it can better suppress the impact of step disturbances on the actual speed.

[0067] 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 method for active disturbance rejection speed control of a permanent magnet synchronous motor based on a dual-error correction extended state observer, comprising the following steps: (1) Establish a dynamic model of a permanent magnet synchronous motor with lumped disturbance form; (2) Design the feedback control law in the self-disturbance rejection speed controller based on the dynamic model of the permanent magnet synchronous motor; (3) Construct a dual-error-corrected extended state observer and optimize its parameters; (4) The lumped disturbance of the motor system is estimated using a double-error-corrected extended state observer; (5) Substitute the estimated lumped disturbance into the feedback control law to obtain the reference value of the dq axis stator current, thereby performing closed-loop control of 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 the permanent magnet synchronous motor in step (1) is as follows: where: ω m is 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. is the q-axis stator current reference value, b is a control gain and b = K t / J, b n is a nominal value of the control gain b, d is a 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 perturbation 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 step (2) is as follows: wherein: is the reference value for the mechanical angular velocity, k p is the proportional gain, This is an estimate of the lumped disturbance.

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

6. The active disturbance rejection speed control method of permanent magnet synchronous motor according to claim 5, characterized in that: After the parameter optimization of the double error correction expanding state observer in 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.

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

8. 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 implement the automatic disturbance rejection speed control method for permanent magnet synchronous motors as described in 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 the processor, it implements the automatic disturbance rejection speed control method for permanent magnet synchronous motors as described in any one of claims 1 to 7.

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