Motor control device and motor control method
The motor control device and method stabilize control systems by limiting voltage corrections to a threshold, addressing the trade-off between responsiveness and stability in electric vehicle motors, ensuring stable operation and preventing oscillation.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- ASTEMO LTD
- Filing Date
- 2025-01-17
- Publication Date
- 2026-07-23
AI Technical Summary
Conventional motor control systems for electric vehicles face a trade-off between increased responsiveness and control stability, particularly in embedded magnet synchronous motors, leading to control oscillation and vibrations due to excessive manipulation of voltage phase in damping ratio control.
A motor control device and method that includes a voltage vector calculation unit, damping ratio control unit, and correction amount limiting unit to generate and limit voltage commands, ensuring the AC voltage supplied to the AC motor matches a command value and preventing excessive correction beyond a predetermined threshold, thereby stabilizing the control system.
The solution achieves both high responsiveness and improved control stability by limiting the correction amount to a threshold, preventing control oscillation and ensuring stable operation even with parameter fluctuations.
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Figure JP2025001446_23072026_PF_FP_ABST
Abstract
Description
Motor control device and motor control method
[0001] The present invention relates to a control device configuration and control method for driving a motor, and more particularly to a technology that is effective when applied to a control device for an in-vehicle motor that requires high responsiveness and stability.
[0002] In conventional gasoline-powered vehicles, the engine and brakes are used for propulsion and braking, respectively, and vehicle motion control is primarily based on the brakes. In contrast, electric vehicles (EVs) can perform both acceleration and deceleration using motors. Motors have a response speed of several milliseconds, which is more than two orders of magnitude faster than engines, and unlike engines, they can accurately grasp the generated torque (rotational force). Therefore, EVs are capable of more advanced motion control than gasoline-powered vehicles.
[0003] Furthermore, with EVs equipped with in-wheel motors, the driving force of all four wheels can be controlled independently, minimizing vertical sway during acceleration and deceleration, as well as lateral sway when cornering, allowing for more stable control of the vehicle's posture.
[0004] As background technology for this field, for example, there is technology such as that described in Patent Document 1. Patent Document 1 discloses a "synchronous machine control device that can properly perform stabilization control of a synchronous machine."
[0005] Japanese Patent Publication No. 2022-144060
[0006] Main motors used in automobiles primarily utilize embedded magnet synchronous motors (IPMSMs), and IPMSMs are required to be not only smaller and more powerful, but also to have even higher responsiveness. While increasing the gain is effective for improving responsiveness, there is a trade-off between increased gain and control stability, and conventional technology has the problem of control oscillation when increasing responsiveness. In particular, when controlling motors with low resistance, such as automotive motors, the motor behaves like an oscillator, and vibrations are easily generated at the resonant frequency.
[0007] Patent Document 1 describes how the voltage phase is manipulated by damping ratio control to suppress vibrations of the magnetic flux Φ. In damping ratio control, vibrations are suppressed by reducing the gain of the resonant frequency component of the IPMSM, and by applying a voltage that provides a magnetic flux in opposite phase to the vibration of the magnetic flux.
[0008] In voltage phase control, which is mainly used in fixed-voltage single-pulse control, the control system is designed on the premise that phase and torque are directly proportional. However, if the voltage phase is greatly manipulated by damping ratio control, the voltage phase may exceed a certain value (stability limit), potentially breaking this direct proportional relationship and leading to instability. Similarly, in general two-axis vector control, the design is based on the premise that the current and voltage of the d and q axes are directly proportional. Even in this case, greatly manipulating the voltage phase by damping ratio control can exceed the stability limit and lead to instability.
[0009] Therefore, the object of the present invention is to provide a motor control device and a motor control method using the same that can achieve both increased gain for high responsiveness and improved control stability.
[0010] To solve the above problems, the present invention provides a motor control device for controlling a power converter to which an AC motor is connected, comprising: a voltage vector calculation unit that generates a voltage command for the power converter so that the AC voltage supplied to the AC motor matches a command value; a damping ratio control unit that calculates the vibration component of the d-axis component or the vibration component of the q-axis component based on the vibration component of the d-axis component of the AC voltage, and generates a correction amount for correcting the voltage command based on the calculated vibration component of the d-axis component or the vibration component of the q-axis component; and a correction amount limiting unit that limits the correction amount to a predetermined threshold if the correction amount exceeds a predetermined threshold.
[0011] The present invention also relates to a motor control method for controlling a power converter to which an AC motor is connected, the method including: (a) generating a voltage command for the power converter such that an AC voltage supplied to the AC motor matches a command value; (b) calculating a vibration component of the d-axis component or the q-axis component based on a vibration component of dq-axis components of the AC voltage; (c) generating a correction amount for correcting the voltage command based on the vibration component of the d-axis component or the vibration component of the q-axis component calculated in step (b); and (d) limiting the correction amount to a predetermined threshold value when the correction amount exceeds the predetermined threshold value.
[0012] According to the present invention, it is possible to realize a motor control device capable of achieving both an improvement in gain for high responsiveness and an improvement in control stability, and a motor control method using the same.
[0013] Thereby, it is possible to contribute to the improvement of the performance of an in-vehicle motor system.
[0014] Problems, configurations, and effects other than those described above will be clarified by the description of the following embodiments.
[0015] FIG. 1 is a diagram showing a schematic configuration of a motor system according to Embodiment 1 of the present invention. FIG. 2 is a functional block diagram showing the configuration of the controller 5 in FIG. 1. FIG. 3 is a functional block diagram showing the configuration of the voltage control unit 18 in FIG. 2. FIG. 4 is a diagram showing the configuration of the phase limiter 25 in FIG. 3. FIG. 5 is a diagram showing an example of the effect according to Embodiment 1. FIG. 6 is a functional block diagram showing the configuration of the current control unit 15 according to Embodiment 2 of the present invention. FIG. 7 is a diagram showing an example of the effect according to Embodiment 2. FIG. 8 is a diagram showing an example of the effect according to Embodiment 2. FIG. 9 is a flowchart showing the motor control method according to Embodiment 1 of the present invention.
[0016] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the drawings, the same components are denoted by the same reference numerals, and detailed descriptions of overlapping parts are omitted.
[0017] A motor control device according to Embodiment of the present invention and a motor control method using the same will be described with reference to FIGS. 1 to 5 and FIG. 9.
[0018] Figure 1 is a diagram showing the schematic configuration of the motor system of this embodiment. Figure 2 is a functional block diagram showing the configuration of the controller 5 in Figure 1. Figure 3 is a functional block diagram showing the configuration of the voltage control unit 18 in Figure 2. Figure 4 is a diagram showing the configuration of the phase limiter 25 in Figure 3. Figure 5 is a diagram showing an example of the effects of this embodiment. Figure 9 is a flowchart showing the motor control method of this embodiment.
[0019] As shown in Figure 1, the motor system of this embodiment mainly comprises a motor 2 to be controlled, an inverter 1 for driving and controlling the motor 2, and a battery 3 for supplying DC power to the inverter 1. The motor 2 is an AC motor, such as an embedded magnet synchronous motor (IPMSM). The inverter 1 is a DC / AC type power converter that converts the DC power supplied from the battery 3 into AC power and supplies it to the motor 2.
[0020] The inverter 1 comprises a power conversion unit 4, a controller 5, a gate drive circuit 7, a voltage sensor 8, and a current sensor 10. The motor 2 is equipped with a magnetic pole position sensor 11 for measuring the magnetic pole position of the motor 2.
[0021] The power conversion unit 4 consists of six semiconductor switches Q1 to Q6, six diodes D1 to D6, and a smoothing capacitor 12. Each of the diodes D1 to D6 is connected in antiparallel to each other with respect to the semiconductor switches Q1 to Q6.
[0022] A semiconductor switch Q1 and diode D1 form one upper arm, and a semiconductor switch Q2 and diode D2 form one lower arm, with these upper and lower arms forming one leg. Similarly, a semiconductor switch Q3 and diode D3 form one upper arm, and a semiconductor switch Q4 and diode D4 form one lower arm, with these upper and lower arms forming one leg. Similarly, a semiconductor switch Q5 and diode D5 form one upper arm, and a semiconductor switch Q6 and diode D6 form one lower arm, with these upper and lower arms forming one leg. A three-phase AC output is drawn from the connection point of each upper and lower arm and connected to the motor 2 via a current sensor 10.
[0023] The controller 5 receives the torque command value T input from the upper control system * ,
[0025] * and the DC voltage Vdc on the input side of the power conversion unit 4 detected by the voltage sensor 8, the current values iU, iV, iW of each phase (U phase, V phase, W phase) of the three-phase AC output detected by the current sensor 10, and the information regarding the magnetic pole position of the motor 2 (rotor angle θ) detected by the magnetic pole position sensor 11, and generates a gate signal 6 based thereon, and outputs the gate signal 6 to the gate drive circuit 7. The gate drive circuit 7 turns on / off each of the semiconductor switches Q1 to Q6 based on the input gate signal 6.
[0024] The configuration and operation of the controller 5 will be described with reference to FIG. 2. As shown in FIG. 2, the controller 5 includes a torque control unit 13, a current command value calculation unit 14, a current control unit 15, a dq conversion unit 16, a modulation rate calculation control mode determination unit 17, a voltage control unit 18, and a PWM gate control unit 19.
[0025] The torque command value T from the upper control system 0 * is input to the torque control unit 13. The torque control unit 13 calculates the final torque command T 0 * based on the torque command value T and inputs the final torque command T to the current command value calculation unit 14. The current command value calculation unit 14 calculates the dq-axis current command values id<…>is calculated and input to the current control unit 15. The current command value calculation unit 14 calculates the dq-axis current command values id * based on the final torque command T and inputs the dq-axis current command values id * , iq * to the current control unit 15.
[0026] On the other hand, the current values iU, iV, iW detected by the current sensor 10 and the rotor angle θ detected by the magnetic pole position sensor 11 are input to the dq conversion unit 16. The dq conversion unit 16 calculates the dq-axis current command values id, iq based on the current values iU, iV, iW and the rotor angle θ and inputs the dq-axis current command values id, iq to the current control unit 15.
[0027] The current control unit 15 receives the control mode input from the modulation rate calculation control mode determination unit 17 and the dq-axis current command values id * , iq* Based on the dq-axis current command values id and iq from the dq conversion unit 16, the dq-axis voltage command value Vd * , Vq * The value is calculated and input to the voltage control unit 18 and the modulation rate calculation control mode determination unit 17.
[0028] The voltage control unit 18 receives the rotor angle θ detected by the magnetic pole position sensor 11, the DC voltage Vdc detected by the voltage sensor 8, and the dq-axis voltage command value Vd from the current control unit 15. * , Vq * Based on this, the duty cycle signal 9 is calculated and input to the PWM gate control unit 19. The PWM gate control unit 19 generates the gate signal 6 based on the duty cycle signal 9 and outputs it to the gate drive circuit 7.
[0029] Using Figure 3, the configuration and operation of the voltage control unit 18, which is a characteristic part of this embodiment, will be explained. As shown in Figure 3, the voltage control unit 18 includes an integrator 20, a motor inverse model 21, a voltage limiter 22, a coordinate transformation unit 23, an attenuation ratio control unit 24, and a phase limiter 25. The integrator 20 and the motor inverse model 21 function as a voltage vector calculation unit that generates the voltage command for the power conversion unit 4. The voltage vector calculation unit, composed of the integrator 20 and the motor inverse model 21, calculates that the AC voltage supplied to the motor 2 is equal to the torque command value T 0 * The voltage command for the power conversion unit 4 is generated to match the specified value.
[0030] The integrator 20 receives the input d-axis magnetic flux command value φd * And after adding or subtracting the d-axis magnetic flux command value φdc with the adder / subtractor 26, it is integrated with the velocity information ωc with the integrator 28, and then integrated again with the integrator 30 to obtain the d-axis magnetic flux command value φd ** It outputs as follows: Also, the input q-axis magnetic flux command value φq * And after adding or subtracting the q-axis magnetic flux command value φqc with the adder / subtractor 27, it is integrated with the velocity information ωc with the integrator 29, and then integrated again with the integrator 31 to obtain the q-axis magnetic flux command value φq ** Output as follows.
[0031] The motor reverse model 21 receives the input d-axis magnetic flux command value φd **Differentiate it using the differentiator 33. Also, the d-axis magnetic flux command value φd ** The damping amplitude adjustment gain Kec, input from the higher-level control system, is added to or subtracted by the adder / subtractor 32, and the proportionalizer 34 calculates the ratio of the resistance value Rc to the inductance Ldc. The output of the differentiator 33 and the output of the proportionalizer 34 are added together by the adder 38. Furthermore, the d-axis magnetic flux command value φd ** The result is integrated using the velocity information ω1 with the integrator 35.
[0032] Furthermore, the motor inverse model 21 receives the input q-axis magnetic flux command value φq ** The output is integrated by the velocity information ω1 using the integrator 36, and then added or subtracted by the output of the adder 38 using the adder / subtractor 39 to obtain the d-axis voltage command value Vd. * It outputs as follows: Also, the q-axis magnetic flux command value φq ** The proportional control unit 37 calculates the ratio of the resistance Rc to the inductance Lqc. The output of the proportional control unit 37 is added to the output of the integrator 35 by the adder 40 to obtain the q-axis voltage command value Vq. * Output as follows.
[0033] The voltage limiter 22 receives the dq-axis voltage command value Vd from the motor reverse model 21. * , Vq * Set limit values for each, and the dq axis limit voltage command value Vdlim * ,Vqlim * This is output to the coordinate transformation unit 23.
[0034] The damping ratio control unit 24 calculates the vibration component of the d-axis or q-axis based on the vibration component of the dq-axis component of the AC voltage, and sets the dq-axis limiting voltage command value Vdlim based on the calculated vibration component of the d-axis or q-axis component. * ,Vqlim * A correction amount Δθd is generated to correct for the error.
[0035] The phase limiter 25 limits the correction amount Δθd generated by the attenuation ratio control unit 24 to a predetermined threshold Δθ if the correction amount Δθd exceeds a predetermined threshold Δθ, and outputs it as a limit correction amount Δθdlim. The coordinate transformation unit 23 receives the dq axis limit voltage command value Vdlim from the voltage limiter 22. * ,Vqlim *This is corrected by the limit correction amount Δθdlim input from the phase limiter 25, and the dq axis correction voltage command value Vd ** , Vq ** Output as follows.
[0036] The predetermined threshold Δθ mentioned above is calculated using one of the following equations (1) to (4).
[0037]
[0038]
[0039]
[0040] Here, 2ζ is twice the damping coefficient of the IPMSM, Ld is the d-axis inductance, Lq is the q-axis inductance, R is the resistance, φd is the magnetic flux in the d-axis, φq is the magnetic flux in the q-axis, and id is the d-axis current. In equations (1) to (4), the terms excluding 2ζ correspond to the amplitude components of the vibration. Therefore, the threshold Δθ should be set by the ratio of the amplitude to be suppressed multiplied by 2ζ.
[0041] The configuration and operation of the phase limiter 25 will be explained using Figure 4. As shown in Figure 4, the phase limiter 25 includes a comparator 41 that compares an input upper limit value (limit upper limit 2ζ×K) with a predetermined value and sets a lower limit value (limit lower limit - 2ζ×K), and a limiter that limits the correction amount Δθd to the above threshold value based on the upper limit value (limit upper limit 2ζ×K), the lower limit value (limit lower limit - 2ζ×K), and the correction amount Δθd generated by the attenuation ratio control unit 24. Although Figure 4 shows an example where the comparator 41 is placed outside the limiter, the phase limiter 25 may also be configured with the comparator 41 placed inside the limiter.
[0042] Here, K is the damping amplitude adjustment gain. The damping amplitude adjustment gain K sets the ratio to the magnetic flux amplitude. For example, setting the damping amplitude adjustment gain K to "1" means that the vibration component will be suppressed to the same level as the magnetic flux amplitude.
[0043] A typical motor control method of the present invention will be explained using Figure 9.
[0044] First, in step S1, the AC voltage supplied to the motor 2 is set to the torque command value T. 0 * The voltage command for the power conversion unit 4 is generated to match the specified value.
[0045] Next, in step S2, the vibration component of the d-axis or the vibration component of the q-axis is calculated based on the vibration component of the dq-axis component of the AC voltage supplied to the motor 2.
[0046] Next, in step S3, a correction amount Δθd is generated to correct the voltage command based on the vibration component of the d-axis or the vibration component of the q-axis calculated in step S2.
[0047] Finally, in step S4, if the correction amount Δθd exceeds a predetermined threshold Δθ, the correction amount Δθd is limited to the threshold Δθ.
[0048] Figure 5 shows an example of the effects of this embodiment. Here, the waveforms are shown when the controller gain is gradually increased from 1x to simulate fluctuations in the control parameters. As explained above, the motor control device and motor can be operated stably simply by setting a limit (threshold Δθ) for the damping ratio control.
[0049] In conventional technology, when parameter fluctuations occurred, the phase Δθd of the damping ratio control increased, causing a large manipulation of the voltage phase. This prevented the voltage limiter and anti-windup used in the two-axis vector control from functioning correctly, resulting in control oscillation. As in this embodiment, by limiting Δθd, control oscillation can be prevented when parameter fluctuations occur. The limit value can be set by multiplying the desired amplitude ratio by the gain 2ζ, allowing for design without affecting normal operation. Furthermore, even when parameter fluctuations occur, control oscillation does not occur, and gain margin is ensured.
[0050] Referring to Figures 6 to 8, a motor control device and a motor control method using the same according to Embodiment 2 of the present invention will be described. In this embodiment, in addition to the configuration and operation of Embodiment 1, an embodiment using flux-based cascade vector control, which controls the current using an inverse model of the motor 2 based on magnetic flux, will be described.
[0051] Figure 6 is a functional block diagram showing the configuration of the current control unit 15 in this embodiment. Figures 7 and 8 show an example of the effects of this embodiment. The current control unit 15 in Figure 6 corresponds to the current control unit 15 in Figure 2.
[0052] As shown in Figure 6, the current control unit 15 of this embodiment mainly comprises a magnetic flux base cascade vector control unit 42, an attenuation ratio control unit 43, a limiter 44, a voltage phase control unit 45, and a coordinate transformation unit 47.
[0053] The current control unit 15 receives the dq axis current command value id from the current command value calculation unit 14. * , IQ * Based on the dq-axis current command values id and iq input from the dq conversion unit 16 and the control mode input from the modulation rate calculation control mode determination unit 17, the dq-axis voltage command value Vd is determined by flux-based cascade vector control. * , Vq * Calculate and output the result.
[0054] The magnetic flux base cascade vector control unit 42 controls the dq axis current command value id * , IQ * Based on the dq-axis current command values id and iq, and the control mode, the dq-axis voltage command value Vd is controlled by flux-based cascade vector control. ** , Vq ** It calculates and outputs the dq-axis magnetic flux command value φd * , φq * The dq-axis magnetic flux command values φdc and φqc are calculated and output.
[0055] The damping ratio control unit 43 receives the dq-axis magnetic flux command value φd output from the magnetic flux base cascade vector control unit 42. * , φq * Based on the dq-axis magnetic flux command values φdc and φqc, the correction amount θd is calculated and output by the same process as the damping ratio control unit 24 in Example 1 (Figure 3). The correction amount θd is input to the limiter 44, which calculates and outputs the limiting correction amount θdlim by the same process as the phase limiter 25 in Example 1 (Figure 3).
[0056] The voltage phase control unit 45 controls the dq axis current command value id * , IQ * Based on the dq axis current command values id and iq and the control mode, a correction amount θv1 is calculated and output by voltage phase control. The correction amount θv1 is added with the limiting correction amount θdlim in the adder 46 and output as the correction amount θv.
[0057] The coordinate transformation unit 47 receives the dq-axis voltage command value Vd from the magnetic flux-based cascade vector control unit 42. ** , Vq ** Then, based on the correction amount θv input from the adder 46, the dq-axis voltage command value Vd is calculated using the formula shown in Figure 6. * , Vq * The value is calculated and input to the voltage control unit 18 and the modulation rate calculation control mode determination unit 17 (see Figure 2).
[0058] In the configuration shown in Figure 6, when voltage phase control is performed, the dq-axis voltage command value Vd ** , Vq ** The value is fixed at the time of switching, and the correction amount θv1 is set to 0 during flux-based cascade vector control operation.
[0059] In this embodiment, the voltage vector calculation unit, which consists of an integrator 20 and a motor inverse model 21 (see Figure 3), converts the dq-axis voltage command value Vd in the flux-based cascade vector control unit 42. ** , Vq ** Based on this, the dq-axis voltage command value Vd of the power conversion unit 4 * , Vq * Generates.
[0060] Figures 7 and 8 show an example of the effects of this embodiment. In this embodiment, as in Embodiment 1, the motor control device and the motor can be operated stably simply by setting a limit (threshold Δθ) for the damping ratio control.
[0061] It should be noted that the present invention is not limited to the embodiments described above, and various modifications are included. For example, the embodiments described above are described in detail to make the present invention easier to understand, and are not necessarily limited to those having all the configurations described. Furthermore, it is possible to replace parts of the configuration of one embodiment with the configuration of another embodiment, and it is also possible to add configurations from other embodiments to the configuration of one embodiment. In addition, it is possible to add, delete, or replace parts of the configuration of each embodiment with other configurations.
[0062] 1...Inverter, 2...Motor, 3...Battery, 4...Power conversion unit, 5...Controller, 6...Gate signal, 7...Gate drive circuit, 8...Voltage sensor, 9...Duty signal, 10...Current sensor, 11...Magnetic pole position sensor, 12...Smoothing capacitor, 13...Torque control unit, 14...Current command value calculation unit, 15...Current control unit, 16...dq conversion unit, 17...Modulation rate calculation control mode determination unit, 18...Voltage control unit, 19...PWM gate control unit, 20...Integrator, 21 ...Motor inverse model, 22...Voltage limiter, 23, 47...Coordinate transformation unit, 24, 43...Attenuation ratio control unit, 25...Phase limiter, 26, 27, 32, 39...Adder / subtractor, 28, 29, 30, 31, 35, 36...Integrator, 33...Differentiator, 34, 37...Proportional, 38, 40, 46...Adder, 41...Comparator, 42...Flux-based cascade vector control unit, 44...Limiter, 45...Voltage phase control unit, Q1-Q6...Semiconductor switches, D1-D6...Diodes.
Claims
1. A motor control device for controlling a power converter to which an AC motor is connected, comprising: a voltage vector calculation unit that generates a voltage command for the power converter so that the AC voltage supplied to the AC motor matches a command value; a damping ratio control unit that calculates the vibration component of the d-axis component or the vibration component of the q-axis component based on the vibration component of the d-axis component of the AC voltage, and generates a correction amount for correcting the voltage command based on the calculated vibration component of the d-axis component or the vibration component of the q-axis component; and a correction amount limiting unit that limits the correction amount to a predetermined threshold if the correction amount exceeds a predetermined threshold.
2. A motor control device according to claim 1, wherein the correction amount limiting unit comprises a comparator that compares an input upper limit value with a predetermined value to set a lower limit value, and a limiter that limits the correction amount to the threshold value based on the upper limit value, the lower limit value, and the correction amount generated by the damping ratio control unit.
3. A motor control device according to claim 1, wherein the correction amount limiting unit sets the threshold by multiplying the ratio of the desired vibration amplitude of the vibration component by a predetermined gain.
4. A motor control device according to claim 1, comprising a flux-based cascade vector control unit that controls current using an inverse model of the AC motor based on magnetic flux, wherein the voltage vector calculation unit generates a voltage command for the power converter based on the dq axis voltage command converted by the flux-based cascade vector control unit.
5. A motor control method for controlling a power converter to which an AC motor is connected, comprising: (a) a step of generating a voltage command for the power converter such that the AC voltage supplied to the AC motor matches a command value; (b) a step of calculating the vibration component of the d-axis component or the vibration component of the q-axis component based on the vibration components of the d-axis components of the AC voltage; (c) a step of generating a correction amount for correcting the voltage command based on the vibration component of the d-axis component or the vibration component of the q-axis component calculated in step (b); and (d) a step of limiting the correction amount to a predetermined threshold if the correction amount exceeds a predetermined threshold.
6. A motor control method according to claim 5, characterized in that, in step (d), (d1) a step of setting a lower limit by comparing an input upper limit with a predetermined value, and (d2) a step of limiting the correction amount to the threshold based on the upper limit, the lower limit, and the correction amount generated in step (c).
7. A motor control method according to claim 5, characterized in that in step (d), the threshold is set by multiplying the ratio of the desired vibration amplitude of the vibration component by a predetermined gain.
8. A motor control method according to claim 5, characterized in that, in step (a), a voltage command for the power converter is generated based on a dq-axis voltage command converted by flux-based cascade vector control.