High-frequency motor driving self-adaptive multi-rate control system and method
By using recursive least squares method and adaptive expansion state observer in high-frequency motor drivers, combined with multi-rate improvement model, adaptive multi-rate control of high-frequency motor drives in the case of nonlinear perturbation and parameter mismatch is achieved, which solves the problem of poor control effect at high switching frequency and improves the robustness and dynamic tracking performance of the system.
Patent Information
- Application Number
- CN202510207755.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-25
- Publication Date
- 2025-05-27
AI Technical Summary
SiC-based high-frequency motor drivers are difficult to achieve effective control at high switching frequencies, and are limited by the interrupt task processing capabilities of the digital signal processor, resulting in insufficient robustness and dynamic tracking performance in the case of nonlinear perturbations and parameter mismatch.
The predicted current error compensation value is obtained by using the recursive least squares method, and an adaptive expansion state observer is designed as a motor model, and the adaptive multi-rate control of high-frequency motor drive is realized by combining the multi-rate improvement model.
In the case of parameter mismatch and nonlinear perturbation, the system has good robustness and dynamic tracking performance, which can effectively exert the advantages of SiC switching devices, reduce system harmonic distortion, and improve system power density.
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Figure CN120049780A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of motor control. More specifically, it relates to an adaptive multi-rate control system and method for a high-frequency motor driver based on SiC. Background Art
[0002] In recent years, with the emergence of switching devices based on wide bandgap (WBG) materials, such as silicon carbide (SiC) and gallium nitride (GaN), compared with silicon (Si), they have a higher breakdown field, faster switching speed, and lower conduction loss, which can effectively reduce harmonic distortion and improve system power density. Therefore, they play a unique advantage in converter applications that require high switching frequency, high efficiency, and high density. In particular, high switching frequency can reduce current ripple, thereby reducing the filter size requirement and improving system efficiency. For example, bulky DC electrolytic capacitors can be replaced with thin-film capacitors to reduce the overall volume and cost of electric vehicle drivers. In addition, high-speed machines with more pole numbers bring high power density, which requires high switching frequency control. However, although WBG devices have great advantages, their expected high switching frequency is always a huge challenge for controller design because the sampling (interrupt) interval is too short for the digital signal processor to complete heavy interrupt tasks, making the advantages provided by WBG devices not fully realized in the industry.
[0003] Currently, the traditional solution is to design a lower sampling frequency to easily implement interrupt tasks; at the same time, increase the control frequency so that the switching state can be updated multiple times within each sampling period, thereby increasing the switching frequency. In addition, in the control scheme, most are combined with model predictive control, which has a faster response speed, an intuitive concept, and multi-variable control capabilities. However, in actual situations, uncertain influences such as high and low temperatures, strong vibrations, and complex electromagnetic environments cause changes in internal motor parameters such as inductance and magnetic flux, generating non-linear disturbances, which seriously affect control performance. The reason is that, on the one hand, model predictive control heavily relies on model parameters, and on the other hand, high control frequency will amplify error effects. Therefore, a new control method is urgently needed for high-frequency motor drivers based on SiC. Summary of the Invention
[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide an adaptive multi-rate control system and method for high-frequency motor drive. The predicted current error compensation value is obtained by the recursive least squares method, and an adaptive extended state observer is designed as the motor model based on this. Finally, the multi-rate is combined to improve the model to achieve adaptive multi-rate control of high-frequency motor drive, so that it can still have good robustness and dynamic tracking performance under the conditions of parameter mismatch and non-linear disturbance, and give full play to the advantages of SiC switching devices.
[0005] To achieve the above-mentioned invention purpose, an adaptive multi-rate control system driven by a high-frequency motor according to the present invention is characterized by comprising: a high-frequency motor driver based on SiC, a three-phase AC motor, a DC power supply, a voltage stabilizing capacitor, a current sampling module, and an adaptive multi-rate controller;
[0006] The high-frequency motor driver based on SiC includes a first bridge arm, a second bridge arm, and a third bridge arm. Among them, the DC ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to the DC power supply; the output ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to the current sampling module;
[0007] The first bridge arm includes a first switching tube S a1 , a second switching tube S a2 ; the second bridge arm includes a third switching tube S b1 , a fourth switching tube S b2 ; the third bridge arm includes a fifth switching tube S c1 , a sixth switching tube S c2 ; the drains of S a1 , S b1 , S c1 are all connected to the positive pole of the DC power supply; the substrates of S a2 , S b2 , S c2 are connected together and then connected to the negative pole of the DC power supply;
[0008] The three-phase AC motor includes a first stator winding, a second stator winding, and a third stator winding. The fundamental wave electromotive forces of the three stator windings are 120° electrical angle apart from each other;
[0009] The voltage stabilizing capacitor is connected in parallel across the DC power supply;
[0010] The input ends of the current sampling module are respectively connected to the drains of S a2 , S b2 , S c2 , and its output end is connected to the output end of the three-phase AC motor, and is used to collect the three-phase currents i a , i b , i c generated by the high-frequency motor driver based on SiC;
[0011] The adaptive multi-rate controller includes a position encoding module, a speed calculation module, a speed PI control module, a difference operation unit, a limiting module, a T 1 coordinate transformation unit, a T 2 coordinate transformation unit, an adaptive multi-rate boosting model, a boosting control law, and space vector pulse width modulation;
[0012] Among them, the input end of the position encoding module is connected to the three-phase AC motor, and its output end is connected to the T 1The coordinate transformation unit is connected to the input end of the speed calculation module; the output of the speed calculation module is the actual rotational speed ω e and the reference rotational speed ω e * As the input of the difference operation unit, calculate the reference rotational speed ω e * The difference between the difference value and the actual rotational speed ω e is used as the input of the rotational speed PI module; the output end of the rotational speed PI module is connected to the input end of the limiter module, and the output of the limiter module is i q * is connected to the input end of the boost control law; T 1 The coordinate transformation unit converts the three-phase stationary coordinate system into a two-phase rotating coordinate system through the input of three-phase currents i a 、i b 、i c and the position θ, and outputs the actual dq-axis currents i d 、i q ; the input end of the adaptive multi-rate boost model is connected to the output end of the T 1 coordinate transformation unit, and the output end is connected to the input end of the boost control law; the output end of the boost control rate u d * 、u q * is connected to the input end of the T 2 coordinate transformation unit; the T 2 coordinate transformation unit converts the two-phase rotating coordinate system into a two-phase stationary coordinate system and outputs u α * 、u β * is connected to the input end of the space vector pulse width modulation; the space vector pulse width modulation outputs a driving signal to control the switching tubes of the SiC-based high-frequency motor driver to achieve precise control of the three-phase AC motor.
[0013] The invention purpose of the present invention is achieved as follows:
[0014] A high-frequency motor drive adaptive multi-rate control system of the present invention calculates the q-axis reference current through the rotational speed PI loop; based on the adaptive law of the recursive least squares algorithm, obtains the disturbance estimation parameters, and combines them with the absolute current error to obtain the predicted current error compensation value, and designs an adaptive extended state observer; based on the observer, divides each sampling interval T s into N control intervals with a time scale of T c to establish an adaptive multi-rate boost model; based on the multi-rate control law, obtains the optimal reference control voltage; finally, generates the switching signal of the high-frequency motor driver through the space vector pulse width modulation to control the switching tubes to achieve the final control effect.
[0015] Meanwhile, the high-frequency motor-driven adaptive multi-rate control system and method of the present invention also have the following
[0016] Advantages:
[0017] (1) The multi-rate control used in the present invention enables the entire system to have a higher control frequency at a lower sampling frequency, can easily implement the control algorithm in a relatively long interruption period, and maintain sufficient computational margin, effectively reducing system harmonic distortion, increasing system power density, reducing device conduction loss, and giving full play to the unique advantages of SiC.
[0018] (2) The improved adaptive multi-rate predictive control method of the present invention still has good robustness and dynamic response in the case of environmental changes and parameter mismatches, and can achieve precise output control of high-frequency motors. Description of the Drawings
[0019] Figure 1 is the schematic diagram of a high-frequency motor-driven adaptive multi-rate control system of the present invention;
[0020] Figure 2 is the flowchart of a high-frequency motor-driven adaptive multi-rate control method of the present invention;
[0021] Figure 3 is the structural schematic diagram of an adaptive extended state observer;
[0022] Figure 4 is the time scale schematic diagram of an adaptive multi-rate control system;
[0023] Figure 5 is the digital implementation of an adaptive multi-rate algorithm. Detailed Embodiments
[0024] The following describes the specific embodiments of the present invention with reference to the drawings, so that those skilled in the art can better understand the present invention. It should be particularly noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.
[0025] Embodiment
[0026] In this embodiment, as Figure 1 shown, a high-frequency motor-driven adaptive multi-rate control system of the present invention is characterized by comprising: a high-frequency motor driver 1 based on SiC, a three-phase AC motor 2, a DC power supply 3, a voltage stabilizing capacitor 4, a current sampling module 5, and an adaptive multi-rate controller 6;
[0027] The SiC-based high-frequency motor driver 1 includes a first bridge arm, a second bridge arm, and a third bridge arm. Among them, the DC ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to the DC power supply 3; the output ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to the current sampling module 5;
[0028] The first bridge arm includes a first switching tube S a1 , a second switching tube S a2 ; The second bridge arm includes a third switching tube S b1 , a fourth switching tube S b2 ; The third bridge arm includes a fifth switching tube S c1 , a sixth switching tube S c2 ; The drains of S a1 , S b1 , S c1 are all connected to the positive pole of the DC power supply; the substrates of S a2 , S b2 , S c2 are connected together and then connected to the negative pole of the DC power supply;
[0029] The three-phase AC motor 2 includes a first stator winding, a second stator winding, and a third stator winding. The fundamental wave electromotive forces of the three stator windings are 120° electrical angle apart from each other;
[0030] The voltage stabilizing capacitor 4 is connected in parallel across the DC power supply;
[0031] The input ends of the current sampling module 5 are respectively connected to the drains of S a2 , S b2 , S c2 , and its output end is connected to the output end of the three-phase AC motor 2 for collecting the three-phase currents i a , i b , i c generated by the SiC-based high-frequency motor driver 1;
[0032] The adaptive multi-rate controller 6 includes a position encoding module 7, a speed calculation module 8, a speed PI control module 9, a difference operation unit 16, a limiting module 10, a T 1 coordinate transformation unit 11, a T 2 coordinate transformation unit 12, an adaptive multi-rate boosting model 13, a boosting control law 14, and a space vector pulse width modulation 15;
[0033] Among them, the input end of the position encoding module 7 is connected to the three-phase AC motor 2, and its output end is connected to the input ends of the T 1 coordinate transformation unit 11 and the speed calculation module 8; the actual rotational speed ω e output by the speed calculation module 8 and the reference rotational speed ω e *As the input of the difference operation unit 16, calculate the reference speed ω e * The difference between the difference value and the actual speed ω e is used as the input of the speed PI module 9; the output end of the speed PI module 9 is connected to the input end of the limiting module 10, and the output of the limiting module 10 is i q * is connected to the input end of the boost control law 14; T 1 The coordinate transformation unit 11 converts the three-phase static coordinate system into a two-phase rotating coordinate system by inputting the three-phase currents i a 、i b 、i c and the position θ, and outputs the actual dq-axis currents i d 、i q ; the input end of the adaptive multi-rate boost model 13 is connected to the output end of the T 1 coordinate transformation unit 11, and the output end is connected to the input end of the boost control law 14; the output end of the boost control law 14 is u d * 、u q * is connected to the input end of the T 2 coordinate transformation unit 12; the T 2 coordinate transformation unit 12 converts the two-phase rotating coordinate system into a two-phase static coordinate system and outputs u α * 、u β * is connected to the input end of the space vector pulse width modulation 15; the space vector pulse width modulation 15 outputs a drive signal to control the switching tubes of the SiC-based high-frequency motor driver 1 to achieve precise control of the three-phase AC motor.
[0034] In this embodiment, the materials of the switching tubes S a1 、S a2 、S b1 、S b2 、S c1 、S c2 are all SiC.
[0035] In addition, the present invention also provides a high-frequency motor drive adaptive multi-rate control method, as Figure 2 shown, including the following steps:
[0036] (1), Obtain the reference current of the three-phase AC motor;
[0037] (1.1), Given the reference speed ω e * ;
[0038] (1.2) Obtain the position angle θ of the three-phase AC high-frequency motor through the position encoder module, input θ into the speed calculation module, and calculate the actual speed ω of the three-phase AC high-frequency motor. e ;
[0039] (1.3) Take the difference between ω e * and ω e as the input, and output the q-axis reference current i q * through the speed PI loop. Additionally, set the d-axis reference current i d * to 0;
[0040] (2) Establish an adaptive multi-rate lifting model for current prediction;
[0041] (2.1) Through the current sampling module, transform the three-phase currents i a , i b , i c through the T 1 coordinate transformation to obtain the actual stator currents i d and i q on the dq axis;
[0042] In this embodiment, the formula for the T 1 coordinate transformation is:
[0043]
[0044] (2.2) Design an adaptive extended state observer, whose structure is as Figure 3 shown, and is specifically expressed as follows:
[0045]
[0046] Among them, the superscript "·" represents the first derivative, is the estimated value of the actual stator current , is the estimated value of the lumped disturbance , δ id and δ iq are respectively the dq-axis components of the lumped disturbance δ, u d and u q are respectively the actual output stator voltages on the dq axis, is the current error estimate value and R s is the stator resistance, L sd and L sq are respectively the dq-axis stator inductances, ω e is the electrical angular velocity of the rotor, ψf is the permanent magnet magnetic flux, l is a positive value and should be one order of magnitude higher than the eigenvalue of the three-phase AC high-frequency motor system; F(·) is the adaptive disturbance variable, is the predicted current error compensation value, K is the sampling time, m is the prediction coefficient; sgn(·) is the sign function;
[0047] In this embodiment, the predicted current error compensation value y(K+m) is used to feedback the disturbance trend in advance, and its design equation is:
[0048]
[0049] where m is the prediction coefficient, E lim is the disturbance constraint, is the disturbance estimation parameter;
[0050] And the disturbance estimation parameter is obtained based on the adaptive law of the recursive least squares algorithm, and the design equation is:
[0051]
[0052] where, n is the number of sampling periods after model mismatch occurs, represents the absolute current error, P(K) is the gain matrix; is the estimation parameter of the linear equation , Y = [y(1), y(2), …, y(K)] T , and the superscript T represents transpose;
[0053] (2.3), Divide the sampling period T s into N intervals on average, and each small interval is defined as a control interval with a length of T c ;
[0054] In this embodiment, Figure 4 shows the time scale of the adaptive multi-rate control system. The adaptive multi-rate boosting model is a mathematical model designed according to the mechanism of the high-frequency circuit, and the boosting model is established based on the circuit mathematical model. The sampling frequency remains at a low speed, while the control output is updated at the time scale of multi-rate;
[0055] (2.4), Based on the control interval T c , establish an adaptive multi-rate boosting model using the forward Euler method based on the expression of the adaptive extended observer, which is specifically expressed as follows:
[0056]
[0057] where K is the sampling instant, and kT c |K represents the k-th control instant at the K-th sampling instant, where k = 0, 1, 2, …, N-1; is the discrete lumped disturbance at the K-th sampling instant;
[0058] In this embodiment, the discrete lumped disturbance is calculated by the formula:
[0059]
[0060] where x(K) is the actual stator current at the K-th sampling instant, is the current estimated value at the K-th sampling instant,
[0061] (3) Design a multi-rate adaptive control law;
[0062] Replace with the reference current and substitute it into the adaptive multi-rate boost model to obtain the optimal reference control voltage u (kT * (kT c |K):
[0063]
[0064] In this embodiment, Figure 5 shows the digital implementation of the adaptive multi-rate algorithm. Np is the prediction range; within each sampling period, the frequency of the triangular carrier is increased to the same as the control frequency, the sampling period is kept N times the control period, and the reference voltage of the input space vector pulse width modulation is updated multiple times. Therefore, a high switching frequency can be achieved at a lower sampling frequency, and the computational burden of the system is small;
[0065] (4) Generate drive inverter switching signals based on the optimal reference control voltage;
[0066] (4.1) Represent the optimal reference control voltage u * (kT c |K) in the form of dq-axis components as: Then perform T 2 coordinate transformation on the dq-axis components respectively to obtain the voltage representation u α * (kT c |K) and u β * (kT c |K) in the two-phase stationary coordinate system, where α, β represent the two phases in the stationary coordinate system;
[0067] In this embodiment, T 2 The formula for coordinate transformation is:
[0068]
[0069] (4.2) Based on u α * (kT c |K) and u β * (kT c |K) perform space vector pulse width space modulation to generate the drive signals G x1 and G x2 , where the drive signal G x1 controls the switch tube S x1 , G x2 is the complementary drive signal of G x1 to control the switch tube S x2 , x represents phases a, b, c, S x1 and S x2 are respectively the upper and lower tubes of the corresponding bridge arm.
[0070] Although the above-described illustrative specific embodiments of the present invention have been described to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.
Claims
1. A high frequency motor drive adaptive multi-rate control system, characterized in that: include: SiC-based high-frequency motor driver, three-phase AC motor, DC power supply, voltage stabilizing capacitor, current sampling module and adaptive multi-rate controller; The SiC-based high-frequency motor driver comprises a first bridge arm, a second bridge arm, and a third bridge arm, wherein the DC ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to a DC power supply; and the output ports of the first bridge arm, the second bridge arm, and the third bridge arm are connected to a current sampling module; The first bridge arm includes a first switch tube S a1 , the second switch tube S a2 The second bridge arm includes a third switch tube S b1 , the fourth switch tube S b2 The third bridge arm includes a fifth switch tube S c1 , the sixth switch tube S c2 ; S a1 , S b1 , S c1 The drain of S is connected to the positive pole of the DC power supply; a2 , S b2 , S c2 The substrate is connected to the source electrode, and then connected to the negative electrode of the DC power supply; The three-phase AC motor comprises a first stator winding, a second stator winding and a third stator winding, and the fundamental wave potentials of the three stator windings differ by 120° electrical angle from each other; The voltage stabilizing capacitor is connected in parallel at both ends of the DC power supply; The input terminals of the current sampling module are respectively connected to S a2 , S b2 , S c2 The drain terminal of the SiC-based high-frequency motor driver is connected to the output terminal of the three-phase AC motor to collect the three-phase current i generated by the SiC-based high-frequency motor driver. a 、i b 、i c ; The adaptive multi-rate controller includes a position encoding module, a speed calculation module, a speed PI control module, a difference operation unit, a limit module, a T1 coordinate transformation unit, a T2 coordinate transformation unit, an adaptive multi-rate boost model, a boost control law and space vector pulse width modulation; The input end of the position encoding module is connected to the three-phase AC motor, and the output end is connected to the T1 coordinate transformation unit and the input end of the speed calculation module; the output of the speed calculation module is the actual speed ω e With reference speed ω e * As the input of the difference operation unit, the reference speed ω is calculated e * Difference and actual speed ω e The difference is used as the input of the speed PI module; the output of the speed PI module is connected to the input of the limit module, and the limit module outputs i q * Connected to the input terminal of the lifting control law; T1 coordinate transformation unit inputs three-phase current i a 、i b 、i c With position θ, the three-phase stationary coordinate system is converted into a two-phase rotating coordinate system, and the actual dq axis current i is output d 、i q ; The input end of the adaptive multi-rate boost model is connected to the output end of the T1 coordinate transformation unit, and the output end is connected to the input end of the boost control law; the boost control rate output end u d * 、u q * Connected to the input end of the T2 coordinate transformation unit; the T2 coordinate transformation unit converts the two-phase rotating coordinate system into a two-phase stationary coordinate system and outputs u α * 、u β * Connected to the space vector pulse width modulation input terminal; the space vector pulse width modulation output drive signal controls the switch tube of the SiC-based high-frequency motor driver to achieve precise control of the three-phase AC motor.
2. The high frequency motor drive adaptive multi-rate control system according to claim 1, characterized in that: The switch tube S a1 , S a2 , S b1 , S b2 , S c1 , S c2 The material is SiC.
3. A high-frequency motor drive adaptive multi-rate control method, characterized in that: The following steps are involved: (1) Obtain the reference current of the three-phase AC motor; (1.1), given the reference speed ω of the three-phase AC motor e * ; (1.2) Obtain the position angle θ of the three-phase AC high-frequency motor through the position encoder module, input θ into the speed calculation module, and calculate the actual speed ω of the three-phase AC high-frequency motor e ; ( 1.3) e * With ω e The difference is used as input, and the q-axis reference current i is obtained through the speed PI loop output. q * , and the d-axis reference current i d * Set to 0; (2) Establish an adaptive multi-rate boost model for current prediction; (2.1) The three-phase current i is sampled by the current sampling module a 、i b 、i c After T1 coordinate transformation, the actual stator current i of the dq axis is obtained d with i q ; (2.2) Design an adaptive extended state observer, which is specifically expressed as follows: The superscript "·" indicates the first-order derivative. is the actual stator current The estimated value of Lumped disturbance The estimated value of id With δ iq are the dq axis components of the lumped disturbance δ, u d with u q They are the actual output stator voltages of the dq axes, is the current error estimate and R s is the stator resistance, L sd With L sq are the dq axis stator inductance, ω e is the electrical angular velocity of the rotor, ψ f is the permanent magnet flux, l is a positive value and should be one order of magnitude higher than the characteristic value of the three-phase AC high-frequency motor system; F(·) is the adaptive disturbance variable, is the predicted current error compensation value, K is the sampling time, m is the prediction coefficient; sgn(·) is the sign function; (2.3), the sampling period T s Divide into N intervals evenly, each small interval is defined as a control interval with a length of T c ; (2.4), in the control interval T c Based on the expression of the adaptive extended observer, the adaptive multi-rate boosting model is established using the forward Euler method, which is specifically expressed as follows: Where K is the sampling time, kT c |K represents the kth control moment at the Kth sampling moment, k = 0, 1, 2, ..., N-1; is the discrete lumped disturbance at the Kth sampling moment; (3) Design multi-rate adaptive control law; With reference current replace Substitute it into the adaptive multi-rate boost model to obtain the optimal reference control voltage u * (kT c |K): (4) generating a driving inverter switch signal based on the optimal reference control voltage; (4.1), the optimal reference control voltage u * (kT c |K) is expressed in the form of dq axis components as follows: Then, the dq axis components are transformed into T2 coordinates respectively to obtain the voltage representation u in the two-phase stationary coordinate system: α * (kT c |K) and u β * (kT c |K), α, β represent the two phases in the stationary coordinate system; (4.2), based on u α * (kT c |K) and u β * (kT c | K) performs space vector pulse width modulation to generate a drive signal G for the inverter switch tube x1 With G x2 , where the driving signal G x1 Control switch tube S x1 , G x2 G x1 The complementary driving signal controls the switch tube S x2 , x represents phase a, b, c, S x1 With S x2 They are the upper tube and the lower tube corresponding to the bridge arm respectively.
4. The high frequency motor drive adaptive multi-rate control method according to claim 3, characterized in that: The predicted current error compensation value The calculation formula is: Among them, m is the prediction coefficient, E lim is the perturbation constraint, is the disturbance estimation parameter; The disturbance estimation parameters The calculation is performed using the adaptive law of the recursive least squares method, and the calculation formula is: in, n is the number of sampling cycles after the model mismatch occurs, represents the absolute current error, P(K) is the gain matrix; For linear equations The estimated parameters of , Y = [y(1), y(2), …, y(K)] T , and The superscript T indicates transpose.
5. The high frequency motor drive adaptive multi-rate control method according to claim 3, characterized in that: The discrete lumped disturbance The calculation formula is: Where x(K) is the actual stator current at the Kth sampling moment, is the estimated current value at the Kth sampling time, 6. The high frequency motor drive adaptive multi-rate control method according to claim 3, characterized in that: The formula for the T1 coordinate transformation is:
7. The high frequency motor drive adaptive multi-rate control method according to claim 3, characterized in that: The formula for the T2 coordinate transformation is:
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