Permanent magnet synchronous motor preset time super-spiral sliding mode control method based on extended state observer
By using an extended state observer and a preset-time super-helical sliding mode control method, the robustness and chattering problems of permanent magnet synchronous motors under load disturbances were solved, and the system achieved rapid convergence and high-precision tracking.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-03-17
Smart Images
Figure CN121689918A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of motor control technology, and in particular to a preset-time super-helical sliding mode control method for permanent magnet synchronous motors based on an extended state observer. Background Technology
[0002] As a core actuator in modern control systems, the performance of permanent magnet synchronous motors (PMSMs) directly determines the overall level of high-end equipment. Applications such as CNC machine tools, industrial robots, electric vehicle drives, and aerospace servo systems place near-stringent demands on the dynamic effects, tracking accuracy, and anti-interference capabilities of PMSM control systems. However, as a typical nonlinear, strongly coupled system, the operating environment of a PMSM is fraught with uncertainty. This uncertainty includes sudden changes in load torque, such as the contact between the tool and workpiece during machining, and the instantaneous grasping of the load by the robot. Therefore, developing a robust control strategy that consistently guarantees predetermined high performance under various disturbances is a key technological bottleneck driving the development of high-end equipment.
[0003] In recent years, continuous research on control strategies for permanent magnet synchronous motors has mainly led to two representative methods.
[0004] Firstly, classical PID control is used within the PMSM vector control framework. Field-Oriented Control (FOC), especially with a PI regulator at its core, is currently the standard solution in industry. However, it suffers from inherent drawbacks such as conflicting parameter tuning and insufficient robustness. To achieve a fast dynamic response, the proportional gain needs to be increased, but this amplifies the impact of noise on the system, leading to instability. Conversely, extending the integral time to improve stability reduces the system's ability to suppress disturbances. This trade-off between "speed" and "stability" is particularly pronounced when facing nonlinear disturbances. Furthermore, the design of a PI controller requires an accurate model of the motor at a specific linear operating point. Once motor parameters change or the load experiences severe disturbances, the fixed PI parameters struggle to maintain optimal control performance, resulting in a significant deterioration in system performance. While adaptive PID control can improve this problem to some extent, it also has limitations such as slow response speed and complex controller structure.
[0005] Against this backdrop, sliding mode control, as a robust nonlinear control method, has emerged. It designs a sliding surface and drives the system state trajectory to reach this surface within a finite time. Once reached, the system dynamics "slide" to an equilibrium point; the dynamic characteristics during this process are determined by the sliding surface and are independent of system parameters and disturbances. However, due to its discontinuous switching control law, in practical control systems, limited by the time and space lag of switching devices and unmodeled dynamics, the system state cannot ideally slide on the sliding surface but instead traverses it at high frequencies, resulting in chattering. This not only affects the high-precision positioning and smooth operation of the motor but also amplifies measurement noise, further deteriorating control performance. In severe cases, it can even cause overheating of the motor and driver, damaging the mechanical structure.
[0006] In numerous practical applications, higher demands are placed on the rapid convergence and high-precision tracking performance of motors. With the continuous advancement of the control field, methods such as finite-time control, fixed-time control, and preset-time control have emerged and achieved significant progress. Finite-time control ensures that the system converges to the equilibrium point within a finite time, enhancing the system's transient performance. However, its convergence time heavily depends on initial conditions and system parameters, which are often difficult to accurately obtain in practice. In scenarios such as robot grasping and aircraft docking, strict deadlines are required. Therefore, fixed-time control was proposed. This method introduces fractional-order and odd-order feedback mechanisms to achieve different system dynamics, resulting in an upper bound on the convergence time independent of the initial state. However, the upper bound of fixed-time control typically relies on the design of complex functions, significantly increasing the design difficulty of the controller. To further simplify the design and improve practicality, preset-time control was proposed. By introducing continuous piecewise functions, it not only enables the system to reach the convergence limit within a predetermined time but also significantly reduces the complexity of controller design. This mechanism allows for the preset of the time for the system state to converge to the equilibrium point, which is of great significance in industrial applications with stringent real-time requirements.
[0007] Currently, sliding mode control based on finite-time convergence is widely used in applications with relatively small disturbances and less stringent requirements for system convergence time. However, with technological advancements, the precision requirements for equipment are increasing, and processes are becoming more complex. Traditional control algorithms are finding it increasingly difficult to meet the demands of complex processes. Therefore, improving the robustness and time controllability of control algorithms is urgently needed and has become a key issue in promoting the development of high-end equipment and ensuring the stable operation of complex systems. Summary of the Invention
[0008] 1. The technical problem that the invention aims to solve To address the challenges of controlling permanent magnet synchronous motors (PMSMs) in real-world industrial environments, such as poor robustness against load torque disturbances, chattering issues inherent in traditional sliding mode control, and the inability to control system convergence time, this invention proposes a preset-time superspiral sliding mode control method for PMSMs based on an extended state observer. This method employs a preset-time extended state observer that ensures rapid convergence and compensation for disturbance estimation errors, guaranteeing timely estimation even under complex disturbances and maintaining system robustness. Furthermore, the convergence time of the disturbance estimation error can be adjusted by modifying the parameters of the preset-time function. Simultaneously, the method utilizes a preset-time superspiral sliding mode controller, significantly reducing chattering through a high-order integral sliding mode approach, and employs preset-time control to ensure rapid convergence of tracking errors, with the upper convergence bound set by parameter adjustment. Moreover, the preset-time extended state observer, preset-time superspiral sliding mode, and sliding surface can be independently adjusted using different preset-time adjustment functions and parameters, improving the system's convergence speed and allowing for flexible adjustments based on actual design requirements.
[0009] 2. Technical Solution To achieve the above objectives, the technical solution provided by this invention is as follows: The present invention provides a preset-time super-helical sliding mode control method for permanent magnet synchronous motors based on an extended state observer, comprising the following steps: Step 1: Obtain the rotor position, rotor angular velocity, and stator current signals of the permanent magnet synchronous motor, and obtain the d-axis current in a two-phase rotating coordinate system through coordinate transformation. i d q-axis current i q Based on q-axis current i q With electromagnetic torque T e The mathematical relationship is used to obtain the electromagnetic torque. T e ; Step 2: Construct a physical model of the rotor position, rotor angular velocity and electromagnetic torque of the permanent magnet synchronous motor, convert the physical model into a state-space expression, and abstract it into a mathematical model to calculate the tracking error between the actual position and the target position of the motor rotor. Step 3: Construct a preset time adjustment function for continuous segments; Step 4: Combine the extended state observer with the preset time adjustment function to construct a preset time extended state observer, estimate the unknown load torque, and estimate and compensate for system disturbances. Step 5: Combine the preset time adjustment function with the sliding surface to construct a preset time sliding surface, and design a preset time super-helical sliding control law based on the sliding surface; Step 6: Convert the electromagnetic torque signal output by the control law into a drive voltage, and control the operation of the permanent magnet synchronous motor through space vector pulse width modulation.
[0010] 3. Beneficial effects Compared with existing known technologies, the technical solution provided by this invention has the following significant advantages: (1) This invention effectively achieves the preset time convergence of the extended state observer. By introducing a continuous piecewise function into the extended state observer, the gain is significantly increased before the preset time is reached, and the gain increases as it approaches the preset time, thereby achieving rapid convergence of the disturbance estimation error. This method accelerates the convergence speed of the system to a certain extent and makes the upper bound of the convergence time of the extended state observer controllable.
[0011] (2) This invention realizes preset time super-helical sliding mode control, which effectively suppresses chattering in traditional sliding mode control and reduces the impact and potential damage to the permanent magnet synchronous motor driver. Furthermore, by introducing a preset time adjustment function, the preset time convergence of the sliding surface and the tracking error is realized, and the upper bound of the convergence time of both can be set and controlled independently.
[0012] (3) This invention achieves global preset time convergence, and different preset time adjustment functions are used for the extended state observer, sliding surface, and superspiral sliding mode. Therefore, the gain growth rate can be flexibly adjusted according to the actual disturbance situation. By reasonably setting different preset times for each part and adjusting the parameters, priority is given to ensuring that the extended state observer completes convergence in a shorter time, and the disturbance estimation error is ensured to converge and be compensated in a timely manner. This design further effectively improves the overall convergence speed and robustness of the system. Attached Figure Description
[0013] Figure 1 This is a control architecture diagram of the present invention; Figure 2 This is a graph showing the rotor position of the motor in the super-spiral sliding mode comparison experiment of this invention. Figure 3 This is a tracking error curve from a comparative experiment of the superspiral sliding mode of the present invention. Figure 4 This is the output curve of the controller in the super-spiral sliding mode comparison experiment of the present invention; Figure 5 This is a curve of the sliding surface in the comparative experiment of the super-spiral sliding mode of the present invention; Figure 6 This is a graph showing the rotor position of the motor in a comparative experiment of the system of the present invention; Figure 7 This is a comparative experiment tracking error curve of the system of the present invention; Figure 8The output curve of the controller in the comparative experiment of the system of the present invention; Figure 9 This is a comparative experimental sliding surface curve diagram of the system of the present invention; Figure 10 The rotor position curve of the motor was used to experimentally verify the super-spiral sliding mode comparison experiment of this invention. Figure 11 The image shows the rotor position curve of the motor in the comparative experiment of the experimental verification system of this invention. Detailed Implementation
[0014] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments.
[0015] Example 1 This invention employs a permanent magnet synchronous motor to support the platform, and the target position of the motor is... x 1r =30+30 sin (π t (Unit: degrees, load torque is...) T L ( t = 0.1 + 0.1 sin ( πt The parameters, measured in Nm, are sufficient for most demanding industrial environments. The parameters of the permanent magnet synchronous motor are shown in Table 1.
[0016] Table 1. Parameters of Permanent Magnet Synchronous Motor
[0017] Combination Figure 1 The following is a method for preset-time super-helical sliding mode control of a permanent magnet synchronous motor based on an extended state observer, comprising the following steps: Step 1: Read the current rotor position of the motor using the motor encoder. Then the rotor position information Processing to obtain rotor angular velocity The three-phase current during motor rotation is detected by Hall coils. i a , i b , i c Based on Clark transformation, the three-phase current i a , i b , i c Converted to stator current in a two-phase stationary coordinate system i α , i βThen, based on the Park transformation, the stator current is... i α , i β Converted to d-axis current in a two-phase rotating coordinate system i d q-axis current i q It should be noted that during motor control, the d-axis current is usually very small and can be ignored. i d Treat it as 0, and i q Satisfying electromagnetic torque Based on the mathematical relationship, the control input for the subsequent control method design is the electromagnetic torque. T e .
[0018] Step 2: Construct a physical model of the relationship between position, angular velocity and electromagnetic torque of the permanent magnet synchronous motor, convert the physical model into a state-space expression, abstract it into a mathematical model, and calculate the difference between the actual position of the motor and the target position as the tracking error.
[0019] The physical model of a permanent magnet synchronous motor is as follows:
[0020] in, T e Indicates electromagnetic torque. B Indicates the damping coefficient. Indicates the moment of inertia. T L Indicates the load torque. The derivative of the rotor position. This is the derivative of the rotor angular velocity.
[0021] The physical model is transformed into a state-space expression as follows:
[0022] in, , , , , , , for The derivative, for The derivative of . Measuring the actual position of the motor. x 1. The target location is x 1r Therefore, the tracking error between the actual position of the motor and the target position can be defined as follows: , , for The derivative of .
[0023] Step 3: When the motor is first started, the tracking error is relatively large. The controller output can be appropriately increased. However, a higher controller output will affect the control accuracy when the motor is running for a period of time and is in a stable state. Therefore, this invention adds time-varying coefficients to the extended state observer, sliding surface, and super-spiral sliding mode control law to ensure that the controller output is increased at the initial moment to ensure that the control target is reached quickly and that the control accuracy is guaranteed in the stable state.
[0024] This embodiment constructs a continuously segmented preset time adjustment function to provide a time-varying gain for the motor control system. The continuously segmented preset time adjustment function is as follows:
[0025] in, t For system uptime, T i For preset time, , These represent the initial and final values of the preset time adjustment function, respectively. A positive integer representing the function bandwidth. The function can be adjusted through parameter settings, which must meet certain requirements. , , , i The integer is positive. Different modules in the motor control system, specifically including: preset-time super-helical sliding mode control, preset-time extended state observer, and preset-time sliding surface, each employ independent preset-time adjustment functions, all using the above-described form but with independently set parameters. When i When the integers are different, they represent the preset time adjustment functions and parameters of different modules.
[0026] Step 4: Unknown load torque exists during motor operation, which may affect motor operation. Therefore, a preset time-extended state observer is constructed to estimate and compensate for the error, reducing the impact of disturbances. The extended state observer is combined with a preset time adjustment function to construct a preset time-extended state observer to estimate the unknown load torque. Its form is as follows:
[0027] in, To The estimate, To The estimate, for The derivative, for The derivative, for The derivative, , To extend the bandwidth of the state observer, this can be achieved by adjusting... L 1 β The parameter 1 adjusts the upper bound of convergence for the preset time-extended state observer estimation error.
[0028] Define control inputs here ,in Let the load torque be the value estimated by the preset time-extended state observer. Then, the original system state equation can be expressed as:
[0029] in, The residual error after estimating the extended state observer.
[0030] Step 5: Combine the preset time adjustment function with the sliding surface to construct a preset time sliding surface, and use this preset time sliding surface to construct a preset time super-spiral sliding mode control law to achieve preset time control of the system. To use sliding mode control, the preset time sliding surface is defined as:
[0031] in, , This refers to the tracking error defined in step two.
[0032] Due to the residual error after the preset time-extended state observer estimation The changes are very small. This can be ignored. To ensure stable convergence of the system, this embodiment designs a desired tracking error convergence trajectory. The designed convergence law is:
[0033] in, For sliding surface s The derivative, For the definition of an auxiliary variable, Its derivative, For a sign function, when When, its value is 1. Its value is -1.
[0034] To ensure the actual sliding surface s To achieve the effect of the designed reaching law, the corresponding control law is designed as follows:
[0035] in, The convergence speed of the control system can be set by the user according to the actual situation. and These are the motor parameters.
[0036] Step Six: As mentioned in Step One, the designed control output is electromagnetic torque. The electromagnetic torque output by the control law is converted into d-axis and q-axis voltages output by the current loop, and then the control voltage is obtained through current loop control. u d , u q The three-phase voltage in the three-phase coordinate system is obtained through the Park inverse transformation, and then modulated and output to the IGBT drive circuit through Space Vector Pulse Width Modulation (SVPWM) to control the permanent magnet synchronous motor and achieve target position tracking.
[0037] To verify the effectiveness of the preset-time super-helical sliding mode control method for permanent magnet synchronous motors based on an extended state observer proposed in this embodiment, the following comparative experiments were conducted.
[0038] Experiment 1: Comparative analysis of three control schemes.
[0039] Group 1 is the Prescribed-time Super Twisting Sliding Mode Controller (PSTSMC) scheme; The second group is a separate Prescribed Time SMC (PTSMC) scheme; Group 3 is a combination of Prescribed Time Sliding Mode Control (PTSMC) and Prescribed Time Extended State Observer (PTESO).
[0040] Under the condition that all other parameters are the same, simulation was performed using Matlab simulation software. The rotor position curves of the motors for the three schemes are shown below. Figure 2 As shown in the figure, the tracking error curve is as follows: Figure 3 As shown, the controller output curve is as follows: Figure 4 As shown, the sliding surface curve diagram is as follows: Figure 5 As shown. It should be noted that, Figure 2 middle x 1r For the target position curve, Figure 4 The upper and lower limits of the ordinate of the first group of schemes are significantly smaller than those of the other two groups.
[0041] Depend on Figure 2 and Figure 3 It can be seen that the second group using a separate PTSMC stabilizes the system in about 1.7 seconds, but the tracking error... Z There is a steady-state error of about 2°; the third group, using a combination of PTSMC and PTESO control, achieves system stability in about 0.8 seconds, but the tracking error remains. Z There is an oscillation problem of about 1°; the first group using PSTSMC stabilizes the system in about 1.3 seconds, and the system tracking error... Z 1 is almost zero and there is no obvious oscillation. Comparing groups 2 and 3, it can be seen that PTESO significantly improves the system's convergence speed, but oscillations still exist after the system stabilizes. Comparing groups 1 and 2, it can be seen that PSTSMC is significantly better than PTSMC in terms of steady-state performance.
[0042] Depend on Figure 4 and Figure 5 It can be seen that the chattering amplitude of group 2 is between 50Nm and -50Nm; the chattering amplitude of group 3 is also between 50Nm and -50Nm, but the chattering frequency is significantly higher than that of group 2; the chattering amplitude of group 1 is between 0.5Nm and -0.5Nm, which is almost negligible. The comparison shows that PSTSMC significantly suppresses chattering and effectively improves the stability of the system.
[0043] Experiment 2: Comparative analysis of system state and tracking error under three different parameters.
[0044] Group 1 is a combination control of PSTSMC and PTESO, with different preset times and parameters set for the controller and the observer; The second group uses a combination of PSTSMC and PTESO control, but employs the same preset time and parameters; Group 3 is a control group consisting of a combination of STSMC and ESO without preset time.
[0045] Under the condition that all other parameters are the same, simulation was performed using Matlab simulation software. The rotor position curves of the motors for the three schemes are shown below. Figure 6 As shown in the figure, the tracking error curve is as follows: Figure 7 As shown, the controller output curve is as follows: Figure 8 As shown, the sliding surface curve diagram is as follows: Figure 9 As shown.
[0046] Experiment 2 results show that the third group, using the STSMC and ESO combined control without preset time, achieved a system stabilization time of approximately 1.1 seconds. The second group, using the PSTSMC and PTESO combined control strategy but with the same preset time parameter, achieved a system stabilization time of approximately 0.7 seconds, but experienced a sudden oscillation at 1 second before stabilizing again. The first group, using the PSTSMC and PTESO combined control strategy with different preset time parameters, achieved a system stabilization time of approximately 0.5 seconds, with no oscillation after stabilization. It should be noted that the oscillation at 1 second in the second group was due to the PTESO not taking effect before the preset time, but rapidly taking effect at 1 second, causing a brief oscillation. Therefore, using different preset time parameters can significantly improve the system's convergence time and stability.
[0047] Experiment 3: Comparative analysis of three control schemes.
[0048] Group 1 is the PTSMC solution used alone; The second group of control schemes combines PTES and PTSMC; Group 3 is the PSTSMC scheme.
[0049] Under otherwise identical conditions, experiments were conducted on a platform supported by a permanent magnet synchronous motor. The rotor position curves of the three schemes are shown below. Figure 10 As shown.
[0050] Experiment 3 shows that the second group, using only preset-time sliding mode control, struggles to track the target position under time-varying load torque. The third group, employing a combination of preset-time sliding mode and a preset-time extended state observer, can essentially achieve target position tracking with a tracking error within ±20° and a convergence speed of approximately 3 seconds. The first group, using preset-time super-spiral sliding mode, has a tracking error within ±8° and a convergence speed of approximately 2 seconds. Furthermore, its chattering is significantly less than that of the second and third groups. Therefore, the preset-time super-spiral sliding mode control scheme is significantly superior to the other two schemes.
[0051] Experiment 4: Comparative analysis of system states under two sets of different parameters.
[0052] Group 1 uses a combination of PSTSMC and PTESO control, and employs the same preset time and parameters. The second group uses a combination of PSTSMC and PTESO control, but with different preset times and parameters.
[0053] Under the condition that all other parameters are the same, experimental verification was carried out on the permanent magnet synchronous motor platform. The rotor position curves of the two schemes are shown in the figure below. Figure 11 As shown.
[0054] Experiment 4 shows that the first group, using the same preset time and parameters, had a convergence time of 1.5s and a chattering amplitude of about 5°, while the second group, using different preset time and parameters, had a convergence time of 1s and a chattering amplitude of 1°. Therefore, the control scheme using different preset time and parameters is significantly better than the other scheme.
[0055] In summary, the method of the present invention is superior to the existing solutions in both suppressing chattering and improving convergence speed and system robustness.
Claims
1. A preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer, characterized in that, The method comprises the following steps: Step one, get the rotor position, rotor angular velocity and stator current signal of permanent magnet synchronous motor, get the d-axis current in two-phase rotating coordinate system through coordinate transformation i d , q-axis current i q , based on the mathematical relationship between q-axis current i q and electromagnetic torque T e , get electromagnetic torque T e ; Step two, a physical model of the permanent magnet synchronous motor rotor position, rotor angular velocity and electromagnetic torque is built, the physical model is converted into a state space expression, and is abstracted into a mathematical model to calculate the tracking error of the actual position and the target position of the motor rotor; Step three, a preset time adjustment function is built in continuous segments; Step four, a preset time extended state observer is built by combining the extended state observer with the preset time adjustment function, unknown load torque is estimated, and system disturbance is estimated and compensated; Step five, a preset time sliding mode surface is constructed by combining the preset time adjustment function with the sliding mode surface, and a preset time super-hyperbolic sliding mode control law is designed based on the sliding mode surface; Step six, the electromagnetic torque signal output by the control law is converted into a driving voltage to control the permanent magnet synchronous motor to operate through space vector pulse width modulation.
2. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 1, characterized in that: In step one, the motor rotor position is read through the motor encoder, and the rotor angular velocity is obtained after processing; the three-phase current is detected through the Hall sensor, and the d-axis current and q-axis current in the two-phase rotating coordinate system are obtained through Clark transformation and Park transformation processing in sequence.
3. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 2, characterized in that: In step two, the physical model of the permanent magnet synchronous motor is: wherein T e denotes the electromagnetic torque, B denotes the damping coefficient, denotes the moment of inertia, T L denotes the load torque, is the derivative of the rotor position, is the derivative of the rotor angular velocity; The physical model is converted into a state space expression as follows: wherein , , , , , , is the derivative of , is the derivative of ; the actual position of the motor is measured as x 1, and the target position is x 1r ; the tracking error of the actual and target positions of the motor rotor is defined as , , is the derivative of .
4. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 3, characterized in that: In step three, the preset time adjustment function has the following form: wherein, t is the system running time, T i is the preset time, , respectively represent the initial value and the final value of the preset time adjustment function, and satisfy , , , i is a positive integer, is a positive integer.
5. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 4, characterized in that: The preset time extended state observer, the preset time sliding mode surface, and the preset time super-hyperbolic sliding mode control law respectively adopt independent preset time adjustment functions.
6. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 5, characterized in that: In step four, the preset time extended state observer has the following form: wherein is an estimate of , is an estimate of , is a derivative of , is a derivative of , is a derivative of , , is a bandwidth of the extended state observer, which is adjusted by adjusting L 1 in β 1 adjusts a convergence upper bound of the preset time extended state observer estimation error on the parameters of 7. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 6, characterized in that: In step five, the preset time sliding mode surface is defined as: wherein, , is the tracking error defined in step two, is the preset time adjustment function corresponding to the sliding surface.
8. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 7, characterized in that: In step five, the reaching law is designed based on the super-hyperbolic algorithm as: wherein is the derivative of the sliding surface s , is a helper variable defined as is the derivative of is the sign function, which has the value 1 when -1.
9. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 8, characterized in that: In step five, the preset time super-hyperbolic sliding mode control law is designed according to the sliding mode surface and the reaching law, and specifically is: wherein, to control the convergence speed of the system, and are motor parameters.
10. The preset time super-twisting sliding mode control method for permanent magnet synchronous motor based on extended state observer according to claim 9, characterized in that: In step six, the electromagnetic torque is converted into the d-axis and q-axis voltages output by the current loop, the d-axis and q-axis control voltages are generated after current loop control, and then the driving signals are generated through Park inverse transformation and space vector pulse width modulation, the insulated gate bipolar transistor driving circuit is controlled, and then the permanent magnet synchronous motor is driven.