A reversible inductionless FOC motor control system and method

The sensorless FOC motor control method executed by a microcontroller solves the problems of high drive efficiency and stability in the application of sensorless motors, and achieves fast response and convenient connection, making it suitable for specific production operation scenarios.

CN114696702BActive Publication Date: 2026-08-25GUIZHOU AEROSPACE LINQUAN MOTOR CO LTD
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Patent Information

Application Number
CN202210298673.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-03-22
Publication Date
2026-08-25
Estimated Expiration
2042-03-22

AI Technical Summary

Technical Problem

Existing sensorless FOC motor control algorithms cannot meet the requirements of high drive efficiency, unstable output, slow response speed, poor versatility, and are not easy to connect with other systems in applications of sensorless motors.

Method used

The commutative sensorless FOC motor control method, executed by a microcontroller, receives external signals, processes the motor phase current value, calculates the duty cycle using the FOC vector control algorithm, and performs closed-loop control of current and speed. Combined with a sliding diaphragm observer, the motor rotor angle is corrected in real time to achieve real-time control of rotor direction.

Benefits of technology

It achieves high driving efficiency, stable output, fast response speed, and easy connection with other systems in specific production operations, and has good versatility.

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Abstract

The application discloses a kind of commutatable non-inductive FOC motor control system and method of electrical technology technical field, comprising: receiving external signal;External signal is handled to obtain motor phase current value;Motor phase current value is obtained by FOC vector control algorithm, and the duty cycle of each output pin is obtained;The duty cycle of each output pin is output to carry out motor drive;Current closed loop stage operation and motor speed closed loop control are carried out to the motor after driving;In response to receiving commutation instruction, real-time control is carried out to rotor steering.The application has the characteristics of stable output effect, fast response speed, good versatility and being convenient for connecting with other systems.
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Description

Technical Field

[0001] This invention relates to a commutative sensorless FOC motor control system and method, belonging to the field of electrical technology. Background Technology

[0002] FOC (Field-Oriented Control), also known as vector frequency conversion, is currently the best choice for efficient control of brushless DC motors (BLDC) and permanent magnet synchronous motors (PMSM).

[0003] In existing technologies, sensorless FOC motor control algorithms generally cannot meet the application requirements of high drive efficiency and commutation of sensorless motors in specific production operations. The output effect is unstable, the response speed is slow, the versatility is poor, and it is not convenient to connect with other systems. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a commutative sensorless FOC motor control system and method, which has the characteristics of stable output effect, fast response speed, good versatility and easy connection with other systems.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] In a first aspect, the present invention provides a commutative, sensorless FOC motor control method, executed by a microcontroller, comprising:

[0007] Receive external signals;

[0008] The external signal is processed to obtain the motor phase current value;

[0009] The duty cycle of each output pin is obtained by using the FOC vector control algorithm to measure the motor phase current value.

[0010] The duty cycle of each output pin is output to drive the motor;

[0011] Perform current closed-loop operation and motor speed closed-loop control on the driven motor.

[0012] Upon receiving a commutation command, the rotor direction is controlled in real time.

[0013] Furthermore, the external signal is obtained by amplifying the brushless motor phase current through a sampling operational amplifier circuit and then transmitting it through a sampling power resistor.

[0014] Furthermore, the motor phase current value is used to obtain the duty cycle of each output pin through the FOC vector control algorithm, including:

[0015] Set the preset values ​​for motor speed and motor direction;

[0016] Obtain the U and V phase current values ​​of the motor;

[0017] The U and V phase currents of the motor are subjected to Clark transformation to obtain I. α I β ;

[0018] The rotor angle of the motor is obtained using a sliding diaphragm observer;

[0019] Based on I α I β The actual motor torque component and motor flux linkage component are obtained by performing Park transformation on the motor rotor angle;

[0020] The actual motor torque component, motor flux component, preset motor speed value, and preset motor direction value are calculated using PID.

[0021] The output I is obtained by performing a reverse Park calculation on the calculation result. α I β ;

[0022] Output I α I β The duty cycle of each output pin is then converted using SVPWM.

[0023] Furthermore, the preset values ​​of rotation speed and steering direction are set after being calculated based on the rotation speed and steering direction commands sent to the external communication via the communication protocol. When setting, the microcontroller packages and sends the obtained current, voltage and real-time rotation speed information to the external communication terminal via the communication protocol.

[0024] Furthermore, the motor rotor angle is obtained through a sliding diaphragm observer, including:

[0025] The sliding diaphragm cross section is set according to the brushless motor parameters;

[0026] The sliding mode observer model is approximated to the actual motor model through real-time calibration;

[0027] When the observer model is completely consistent with the actual motor model, the motor back EMF is estimated by the sliding diaphragm section, and the motor rotor angle is obtained by back-tangent calculation.

[0028] Furthermore, the driven motor undergoes current closed-loop operation and motor speed closed-loop control, wherein:

[0029] The current closed-loop operation includes:

[0030] Reference values ​​for the motor torque component and motor flux linkage component are set based on external signals;

[0031] Determine whether the difference between the reference and actual values ​​of the motor torque component and the motor flux linkage component is within the allowable error range;

[0032] When the difference is within the allowable error, the motor flag changes from the current loop flag to the current and speed closed loop flag.

[0033] Motor speed closed-loop control includes:

[0034] The preset value of motor speed is transformed into a preset value of motor torque component through mapping calculation;

[0035] The actual motor torque component value is gradually brought to the preset value of the motor torque component through PID calculation.

[0036] Furthermore, in response to receiving a commutation command, the rotor rotation direction is controlled in real time, including: upon receiving the commutation command, when the original motor rotation direction is axial counterclockwise, the motor wiring is changed via software, and the V-phase output bridge arm and U-phase output bridge arm in the drive circuit are redefined as U-phase output bridge arm and V-phase output bridge arm, respectively.

[0037] Secondly, the present invention provides a commutative sensorless FOC motor control system, comprising:

[0038] Signal receiving module: Used to receive external signals;

[0039] Motor phase current value calculation module: used to process external signals to obtain the motor phase current value;

[0040] Duty cycle output module: used to obtain the duty cycle of each output pin by using the FOC vector control algorithm to obtain the motor phase current value;

[0041] Motor drive module: Used to output the duty cycle of each output pin to drive the motor;

[0042] Motor control module: used for current closed-loop operation and motor speed closed-loop control of the driven motor;

[0043] Rotor steering control module: Used to control the rotor steering in real time in response to receiving a commutation command.

[0044] Thirdly, the present invention provides a commutative sensorless FOC motor control device, including a processor and a storage medium;

[0045] The storage medium is used to store instructions;

[0046] The processor is configured to operate according to the instructions to perform the steps of the method according to any of the foregoing.

[0047] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of any of the methods described above.

[0048] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0049] This invention discloses a commutative sensorless FOC motor controller and its control method, which can be applied to specific production operations to meet the application requirements of high drive efficiency and commutation of sensorless motors. It features stable output, fast response speed, good versatility, and easy connection with other systems. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the motor controller provided in Embodiment 1 of the present invention;

[0051] Figure 2 This is the overall control flowchart of the motor controller provided in Embodiment 1 of the present invention;

[0052] Figure 3 This is a control flowchart of the commutation section of the motor controller provided in Embodiment 1 of the present invention. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0054] Example 1:

[0055] To address the need for high conversion efficiency and commutation of sensorless motors in specific production processes, this invention patent designs a commutable sensorless FOC motor controller (hereinafter referred to as the controller) and its control method. It can be applied to specific production processes to meet the application requirements of high drive efficiency and commutation of sensorless motors. It features stable output, fast response speed, good versatility, and easy connection with other systems.

[0056] This solution includes a hardware platform and software control components. The hardware platform consists of a main control circuit, a control power supply circuit, a power supply circuit, an inverter circuit, and a feedback sampling circuit, among which:

[0057] The main control circuit consists of a microcontroller, microcontroller peripheral support circuits, and a communication interface. The microcontroller and the microcontroller peripheral support circuits work together to enable the microcontroller to perform calculations and operations smoothly. The communication interface is connected to the microcontroller and is responsible for communicating with other external control systems, making it easy for external control systems to read and modify the internal parameters of the microcontroller.

[0058] The control power supply circuit consists of a control power input interface, reverse connection protection components, filter capacitors, and a power module. When the controller's control power input passes through its corresponding control power input interface and the reverse connection protection components, if the control power is connected in reverse, the reverse connection protection components will not conduct, thus protecting the downstream components. The current finally reaches the power module, which converts the external input control power into the driving voltage required by the microcontroller, providing power to the microcontroller.

[0059] The power supply circuit is responsible for providing power to the controller as a whole. It consists of a power supply input interface, a power supply reverse connection protection component, and a supporting capacitor. The power supply is input through the power supply input interface, passes through the power supply reverse connection protection component, and is deactivated if the power supply is connected in reverse. This is used to protect the downstream components. After being filtered by the supporting capacitor, the power supply is transmitted to the inverter circuit.

[0060] The inverter circuit consists of a motor output interface, the driver chip, and six driver power transistors. The driver chip receives the drive signal from the microcontroller at its input terminal, amplifies the current and voltage, and sends it to the six driver power transistors to drive the motor. The driver power module receives the drive signal at its base and drives the collector and emitter to turn on or off, thus outputting the drive signal. The six driver power transistors are combined in pairs to form upper and lower arm bridges, with three driver power transistors in the upper arm bridge and three in the lower arm bridge. The emitter of the upper arm bridge is connected to the motor output interface, and the collector is connected to a power resistor. The emitter of the lower arm bridge is connected to a power sampling resistor, and the collector is connected to the motor output interface.

[0061] The feedback sampling circuit consists of an operational amplifier module, an operational amplifier amplification resistor, and the power sampling resistor. One end of the power sampling resistor is connected to the lower arm bridge transmitter of the driving power transistor, and the other end is grounded. It is responsible for converting the current driving the brushless motor into a voltage signal and transmitting it to the operational amplifier module. The operational amplifier module interacts with the operational amplifier amplification resistor to amplify the voltage signal generated by the power sampling resistor and transmit the processed voltage signal to the microcontroller.

[0062] The software control section is responsible for processing external signals and determining the brushless motor phase current value based on the processed results. By combining the motor phase current value with motor parameters, the actual position of the motor rotor is obtained, thereby determining the rotor angle and achieving the goal of determining the position of the brushless motor rotor without position sensors. The external signal source is the sampling power resistor, which amplifies the brushless motor phase current through a sampling operational amplifier circuit before transmitting it to the microcontroller.

[0063] The overall motor drive algorithm in the software section is implemented via the microcontroller's PWM interrupt. The overall control method of the software control section adopts the FOC vector control algorithm, specifically, it controls the U and V phase currents I of the brushless motor. u I v By using Clark transforms Iα and Iβ (where Iα and Iβ are the static α-axis and β-axis current values, respectively), the motor rotor angle is obtained through a sliding diaphragm observer, and then Park transforms it into Iα. q I d According to the vector component situation, I q I is the torque component of the motor. d I is the motor flux linkage component. q and I d The actual operating state of the motor rotor can be obtained by vector combination, and the actual value I q and I d Perform PID calculations with preset values, and then perform inverse Park calculations on the results to obtain the required output I. α I β , will I α I β The SVPWM calculator converts the duty cycle of each output pin of the microcontroller into the actual duty cycle, thereby enabling motor drive.

[0064] The motor rotor angle is obtained using a sliding mode observer. Specifically, based on the brushless motor parameters, a sliding mode cross-section is set. The actual motor current model includes the magnitude of the extended back electromotive force (EMF). The sliding mode observer model can gradually approximate the actual motor model through real-time correction. When the observer model and the actual motor model are completely consistent, the extended back EMF parameter in the observer model is the required actual motor extended back EMF. The motor back EMF E is estimated using the sliding mode cross-section. α E β The obtained back electromotive force is used to calculate the estimated angle of the current motor rotor through back shearing.

[0065] The main idea of ​​SVPWM is to use the ideal flux linkage circle of the stator of a three-phase symmetrical motor under three-phase symmetrical sinusoidal voltage supply as a reference standard, and to appropriately switch different switching modes of the three-phase inverter to form a PWM wave. The actual flux linkage vector formed is then used to track its accurate flux linkage circle. Specifically, the SVPWM interval is determined by calculating the phase current. The duty cycle of each PWM channel in each interval is different. By controlling the duty cycle of each channel, the on-state of each drive power transistor is controlled, thereby achieving the purpose of outputting a sinusoidal current waveform by the drive circuit.

[0066] The speed and direction inputs of the software part are obtained by the communication interface part through external communication. Specifically, the external communication sends speed and direction commands to the microcontroller through a communication protocol. The microcontroller sets the preset speed and rotation direction by solving the communication commands. At the same time, the microcontroller packages the obtained current, voltage and real-time speed information and sends it to the external communication terminal through the communication protocol to realize full-duplex communication.

[0067] The overall process of the software control section is divided into three stages: the strong drag stage, the current closed-loop operation stage, and the current and speed closed-loop stage. The three stages are carried out in time. After the previous stage ends, a flag appears and the next stage begins.

[0068] The motor flag is set to stop by default. When the microcontroller receives the run command, it begins the software control process.

[0069] During the forced drag phase, the output of the high bridge arm of one phase of the drive circuit is set to a fixed value, while the low bridge arms of the other two phases are grounded. After setting, the rotor angle of the motor is forcibly dragged to a fixed angle, which is set as 0° for the motor. The forced drag time is set to a delay. After the forced drag ends, the delay ends and the motor flag changes to the current loop flag, and the control proceeds to the current closed loop phase.

[0070] After the motor flag changes to the current loop flag, the current closed-loop stage begins. First, the rotation direction and preset speed of the brushless motor are input via external communication. (Setting I) q I d The reference value is a fixed value, independent of the preset value. It is calculated by the FOC (Freedom of Control) to drive the motor to rotate. When the set I... d With actual I d When the difference is within the allowable error, the motor flag changes from the current loop flag to the current and speed closed loop flag, the current closed loop stage ends, and the control program enters the current and speed closed loop stage.

[0071] When the control program enters the current and speed closed-loop stage, it begins closed-loop control of the motor speed. The preset motor speed value is transformed into I through mapping calculation. q The preset value is used to calculate the actual I using PID control. q The value gradually reaches the I value. q The preset value is used to achieve the preset speed of the motor.

[0072] This method differs from general sensorless FOC motor control algorithms in that, upon receiving a commutation command, the microcontroller can perform real-time control of the rotor's direction of rotation. Specifically, when the original motor rotation direction is CCW (axial counter-clockwise rotation), the microcontroller will use the I signal collected by the feedback sampling circuit.u I v Current is redefined as I v I u This involves changing the motor wiring via software and redefining the V-phase and U-phase output bridge arms in the drive circuit as U-phase and V-phase output bridge arms, respectively, to achieve a software-based commutation effect that changes the original CCW (clockwise rotation) to CW (axial clockwise rotation). When the microcontroller receives a stop signal, all PWM output channels of the microcontroller stop outputting PWM signals, and the motor flag changes to the stop position, awaiting the next run command.

[0073] Example 2:

[0074] A commutative sensorless FOC motor control system, which can implement the commutative sensorless FOC motor control method described in Embodiment 1, includes:

[0075] Signal receiving module: Used to receive external signals;

[0076] Motor phase current value calculation module: used to process external signals to obtain the motor phase current value;

[0077] Duty cycle output module: used to obtain the duty cycle of each output pin by using the FOC vector control algorithm to obtain the motor phase current value;

[0078] Motor drive module: Used to output the duty cycle of each output pin to drive the motor;

[0079] Motor control module: used for current closed-loop operation and motor speed closed-loop control of the driven motor;

[0080] Rotor steering control module: Used to control the rotor steering in real time in response to receiving a commutation command.

[0081] Example 3:

[0082] This invention also provides a commutative sensorless FOC motor control device, which can realize the commutative sensorless FOC motor control method described in Embodiment 1, including a processor and a storage medium;

[0083] The storage medium is used to store instructions;

[0084] The processor is configured to operate according to the instructions to perform the steps of the following method:

[0085] Receive external signals;

[0086] The external signal is processed to obtain the motor phase current value;

[0087] The duty cycle of each output pin is obtained by using the FOC vector control algorithm to measure the motor phase current value.

[0088] The duty cycle of each output pin is output to drive the motor;

[0089] Perform current closed-loop operation and motor speed closed-loop control on the driven motor.

[0090] Upon receiving a commutation command, the rotor direction is controlled in real time.

[0091] Example 4:

[0092] This invention also provides a computer-readable storage medium that implements the commutative sensorless FOC motor control method described in Embodiment 1. The medium stores a computer program that, when executed by a processor, performs the steps of the following method:

[0093] Receive external signals;

[0094] The external signal is processed to obtain the motor phase current value;

[0095] The duty cycle of each output pin is obtained by using the FOC vector control algorithm to measure the motor phase current value.

[0096] The duty cycle of each output pin is output to drive the motor;

[0097] Perform current closed-loop operation and motor speed closed-loop control on the driven motor.

[0098] Upon receiving a commutation command, the rotor direction is controlled in real time.

[0099] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0100] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0101] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0102] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0103] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A commutative sensorless FOC motor control method, executed by a microcontroller, characterized in that, include: Receive external signals; The external signal is processed to obtain the motor phase current value; The duty cycle of each output pin is obtained by using the FOC vector control algorithm to measure the motor phase current value. The duty cycle of each output pin is output to drive the motor; Perform current closed-loop operation and motor speed closed-loop control on the driven motor. Upon receiving a commutation command, the rotor direction is controlled in real time. The motor phase current value is used to obtain the duty cycle of each output pin through the FOC vector control algorithm, including: Set the preset values ​​for motor speed and motor direction; Obtain the U and V phase current values ​​of the motor; The U and V phase currents of the motor are subjected to Clark transformation to obtain Iα and Iβ; The motor rotor angle is obtained using a sliding diaphragm observer; Based on Iα, Iβ and the motor rotor angle, Park transformation is performed to obtain the actual motor torque component and motor flux component. The actual motor torque component, motor flux component, preset motor speed value, and preset motor direction value are calculated using PID. The calculation results are then subjected to inverse Park calculation to obtain the outputs Iα and Iβ. The outputs Iα and Iβ are converted into the duty cycle of each output pin through SVPWM; The driven motor is subjected to current closed-loop operation and motor speed closed-loop control, wherein: The current closed-loop operation includes: Reference values ​​for the motor torque component and motor flux linkage component are set based on external signals; Determine whether the difference between the reference and actual values ​​of the motor torque component and the motor flux linkage component is within the allowable error range; When the difference is within the allowable error, the motor flag changes from the current loop flag to the current and speed closed loop flag. Motor speed closed-loop control includes: The preset value of motor speed is transformed into a preset value of motor torque component through mapping calculation; The actual motor torque component value is gradually brought to the preset value of the motor torque component through PID calculation.

2. The commutative sensorless FOC motor control method according to claim 1, characterized in that, The external signal is obtained by amplifying the phase current of the brushless motor through a sampling operational amplifier circuit and then transmitting it through a sampling power resistor.

3. The commutative sensorless FOC motor control method according to claim 1, characterized in that, The preset values ​​of speed and direction are set after being calculated based on the speed and direction commands sent to the external communication via the communication protocol. When setting, the microcontroller packages the obtained current, voltage and real-time speed information and sends it to the external communication terminal via the communication protocol.

4. The commutative sensorless FOC motor control method according to claim 1, characterized in that, The rotor angle of the motor is obtained through a sliding diaphragm observer, including: The sliding membrane cross section is set according to the brushless motor parameters; The sliding mode observer model is approximated to the actual motor model through real-time calibration; When the observer model is completely consistent with the actual motor model, the motor back EMF is estimated by the sliding diaphragm section, and the motor rotor angle is obtained by back-tangent calculation.

5. The commutative sensorless FOC motor control method according to claim 1, characterized in that, In response to receiving a commutation command, the rotor direction is controlled in real time, including: after receiving the commutation command, when the original motor rotation direction is axial counterclockwise, the motor wiring is changed through software, and the V-phase output bridge arm and U-phase output bridge arm in the drive circuit are redefined as U-phase output bridge arm and V-phase output bridge arm, respectively.

6. A commutative, sensorless FOC motor control system, characterized in that, include: Signal receiving module: Used to receive external signals; Motor phase current value calculation module: used to process external signals to obtain the motor phase current value; Duty cycle output module: used to obtain the duty cycle of each output pin by using the FOC vector control algorithm to obtain the motor phase current value; Motor drive module: Used to output the duty cycle of each output pin to drive the motor; Motor control module: used for current closed-loop operation and motor speed closed-loop control of the driven motor; Rotor steering control module: used to control the rotor steering in real time in response to receiving a commutation command; The motor phase current value is used to obtain the duty cycle of each output pin through the FOC vector control algorithm, including: Set the preset values ​​for motor speed and motor direction; Obtain the U and V phase current values ​​of the motor; The U and V phase currents of the motor are subjected to Clark transformation to obtain Iα and Iβ; The motor rotor angle is obtained using a sliding diaphragm observer; Based on Iα, Iβ and the motor rotor angle, Park transformation is performed to obtain the actual motor torque component and motor flux component. The actual motor torque component, motor flux component, preset motor speed value, and preset motor direction value are calculated using PID. The calculation results are then subjected to inverse Park calculation to obtain the outputs Iα and Iβ. The outputs Iα and Iβ are converted into the duty cycle of each output pin through SVPWM; The driven motor is subjected to current closed-loop operation and motor speed closed-loop control, wherein: The current closed-loop operation includes: Reference values ​​for the motor torque component and motor flux linkage component are set based on external signals; Determine whether the difference between the reference and actual values ​​of the motor torque component and the motor flux linkage component is within the allowable error range; When the difference is within the allowable error, the motor flag changes from the current loop flag to the current and speed closed loop flag. Motor speed closed-loop control includes: The preset value of motor speed is transformed into a preset value of motor torque component through mapping calculation; The actual motor torque component value is gradually brought to the preset value of the motor torque component through PID calculation.

7. A commutative, sensorless FOC motor control device, characterized in that, Including processor and storage media; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1 to 5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 5.

Citation Information

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