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Motor Controller

Imported: 10 Mar '17 | Published: 27 Nov '08

Shigeki Nagase, Hiroshi Sumasu, Takeshi Ueda

USPTO - Utility Patents

Abstract

A motor controller stores values corresponding to predetermined equivalent resistance which corresponds to power loss generated by switching on and off switching elements. Voltage command values are determined by adding voltage drop values determined from values corresponding to the equivalent resistance and values of current flowing in the switching elements to target applied voltage values corresponding to current command values which correspond to target output of a motor. The switching elements arranged in a power supply line to the motor are switched on and off by control signals generated according to the voltage command values.

Description

FIELD OF THE INVENTION

The present invention relates to a motor controller suitable for controlling, for example, the output of the motor for generating steering assist power in an electric power steering apparatus.

BACKGROUND OF THE INVENTION

In a motor controller comprising switching elements such as MOS-FETs or the like arranged in a power supply line to a motor, current command values corresponding to target output of the motor are determined, target applied voltage values to the motor are calculated based on the current command values, PWM control signals having duty cycle corresponding to the target applied voltage values are generated, and the output of the motor is controlled by switching on and off the switching elements constituting an inverter circuit with the PWM control signals (Japanese Laid-open Patent No. 2001-268980).

SUMMARY OF THE INVENTION

In the motor controller, it is required that the difference between the target output and the actual output of the motor is reduced. However, since the difference is not sufficiently reduced, there is a problem that desirable characteristics cannot be achieved. Especially, when the output of the motor is open-loop controlled, the problem is emphasized. It is an object of the present invention to provide a motor controller that can resolve such a problem.

A motor controller of the present invention for controlling output of a motor by switching on and off switching elements arranged in a power supply line to the motor by control signals comprises a current command value determination part for determining current command values corresponding to a target output of the motor; a calculation part for determining target applied voltage values to the motor corresponding to the current command values; a storage part for storing values corresponding to predetermined equivalent resistance which corresponds to power loss generated by switching on and off the switching elements; a current determination part for determining values of current flowing in the switching elements; a calculation part for determining voltage command values by adding voltage drop values determined from the values corresponding to the equivalent resistance and the values of current flowing in the switching elements to the target applied voltage values; and a signal generating part for generating the control signals according to the voltage command values.

The present invention is based on knowledge that one of causes of the difference between the target output and the actual output of the motor is power loss generated by switching on and off the switching elements. To be more precise, FIG. 12 illustrates an example of relation between the timing of switching on and off the switching elements, power loss of the switching elements and time. Conventionally, it takes no account of such transient power loss generated by switching on and off the switching elements when the voltage command values corresponding to the voltage applied to the motor. Therefore, the voltage applied to the motor drops due to the power loss, so that the difference between the target output and the actual output of the motor is generated.

To the contrary, according to the present invention, the values corresponding to the equivalent resistance which corresponds to the power loss generated by switching on and off the switching elements are predetermined and stored, the voltage command values are determined by adding the voltage drop values determined from the values corresponding to the equivalent resistance and the value flowing in the switching elements to the target applied voltage values, and the output of the motor is controlled by the control signals corresponding to the voltage command values. Therefore, the voltage drop due to the power loss generated by switching on and off the switching elements is compensated, and the difference between the target output and the actual output of the motor can be reduced.

It is preferable that the motor controller of the present invention further comprises a voltage determination part for determining values of voltage applied to the switching elements, wherein values which correspond to the values of current flowing in the switching elements determined by the current determination part and the values of voltage applied to the switching elements determined by the voltage determination part are stored as the values corresponding to the equivalent resistance.

The power loss generated by switching on and off the switching elements varies according to the values of current flowing in the switching elements and the values of voltage applied to the switching elements, so that the difference between the target output and the actual output of the motor can be further reduced by making the values corresponding to the equivalent resistance used to determine the voltage command values correspond to the values of current and the values of voltage.

It is preferable that an output of a three-phase brushless motor is open-loop controlled as the output of the motor via an inverter circuit constituted of the switching elements, U-phase current value, V-phase current value and W-phase current value which are values of current flowing in the respective three-phase coils constituting an armature winding of the motor are determined as values of current flowing in the switching elements, the motor controller further comprises a rotation position determination part for determining rotation positions of a rotor of the motor, a calculation part for calculating an angular velocity of the rotor based on the rotation positions, and a phase current coordinate conversion part for calculating a d-axis current value and a q-axis current value based on the U-phase current value, the V-phase current value, the W-phase current value and the rotation position, in which an axis along the magnetic flux direction of field system of the rotor is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor is taken as the q-axis, the current command value determination part has dq-axes current command value calculation part for determining a d-axis current command value and a q-axis current command value as the current command values based on the target output of the motor, a d-axis equivalent resistance value and a q-axis equivalent resistance value are stored as the values corresponding to the equivalent resistance, a d-axis target applied voltage value Vd and a q-axis target applied voltage value Vq are determined as the target applied voltage values from the following formulas (1) and (2),


Vd=(R+PLd)Id*LqIq*(1)


Vq=(R+PLq)Iq*LdId*+(2)

a d-axis voltage drop value Vd and a q-axis voltage drop value Vq are determined as the voltage drop values from the following formulas (3) and (4),


Vd=RdId(3)


Vq=RqIq(4)

a d-axis voltage command value Vd* and a q-axis voltage command value Vq* are determined as the voltage command values from the following formulas (5) and (6),


Vd*=Vd+Vd(5)


Vq*=Vq+Vq(6),

in formulas (1) through (6), Rd stands for a d-axis equivalent resistance value, Rq stands for a q-axis equivalent resistance value, Id stands for a d-axis current value, Iq stands for a q-axis current value, R stands for a predetermined resistance value of the three-phase coils, P stands for a differential operator, Ld stands for a predetermined d-axis self-inductance of the three-phase coils, Lq stands for a predetermined q-axis self-inductance of the three-phase coils, Id* stands for a d-axis current command value, Iq* stands for a q-axis current command value, stands for an angular velocity of the rotor, is a value predetermined by multiplying a maximum value of magnetic flux linkage of the three-phase coils by (3/2)1/2.

As a result, the difference between the target output and the actual output of the three-phase brushless motor open-loop controlled via the inverter circuit can be reduced.

According to the motor controller of the present invention, the difference between the target output and the actual output of the motor can be reduced, so that the motor can be sufficiently performed.

DETAILED DESCRIPTION OF THE INVENTION

An electric power steering device 101 of a rack-pinion type for a vehicle in an embodiment of the present invention, which is shown by FIG. 1, comprises a steering shaft 103 that is rotated by steering operation, a pinion 103a provided on the steering shaft 103, a rack 104 engaged with the pinion 103a, a three-phase brushless motor 1 for generating steering assist power, and a ball screw mechanism 110 for transmitting the output of the motor 1 to the rack 104. Each end of the rack 104 is linked to a wheel (not shown in the figures). When the pinion 103a is rotated by steering operation, the rack 104 moves in the lateral direction of the vehicle, and the steering angle varies due to the movement of the rack 104.

The motor 1 comprises a stator 1a that is fixed to a housing 108 covering the rack 104, a cylindrical rotor 1b that is rotatably supported by the housing 108 via bearings 108a, 108b, and a magnet 1c provided as a field system of the rotor 1b. The stator 1a has U-phase coil, V-phase coil and W-phase coil constituting an armature winding of the motor 1. The rotor 1b surrounds the rack 104. A resolver 2 serves as a rotation position determination part for determining rotation positions of the rotor 1b, and outputs rotation angles of the rotor 1b from a reference position of the stator 1a as the rotation positions.

The ball screw mechanism 110 has a ball screw shaft 110a integrally formed on the outer periphery of the rack 104 and a ball nut 110b engaged with the ball screw shaft 110a via balls. The ball nut 110b is connected to the rotor 1b. As a result, when the motor 1 rotates the ball nut 110b, the steering assist power is provided along the longitudinal direction of the rack 104. The motor 1 is connected to a controller 10.

FIG. 2 is a function block diagram of the controller 10 of the first embodiment. The resolver 2, a torque sensor 7 that detects the steering torque transmitted by the steering shaft 103 and a vehicle velocity sensor 8 that detects the vehicle velocity are connected to the controller 10. The controller 10 has a current determination part 11, a signal processing part 12 and a drive part 13. The drive part 13 has a pair of U-phase MOS-FET 13u1, 13u2, a pair of V-phase MOS-FET 13v1, 13v2 and a pair of W-phase MOS-FET 13w1, FET13w2 as switching elements arranged in a power supply line to the motor 1. The FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 constitute an inverter circuit, and are switched on and off by PWM control signals to open-loop control the output of the motor 1 via the inverter circuit.

The current determination part 11 determines U-phase current value Iu, V-phase current value Iv and W-phase current value Iw, which are values of current flowing in the three-phase coils as values of actual current flowing in the respective FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2. The current detection part 11 of the present embodiment has current detectors 11u, 11v, 11w and AD converter 11u, 11v, 11w that perform AD conversion of current detection signals produced by the current detectors 11u, 11v, 11w. Each of the current detectors 11u, 11v, 11w has a current detection resistance and a detection circuit . Each of the current detection resistor is arranged between the ground terminal and each of the lower arm FETs 13u2, 13v2, 13w2. Each of the detection circuit amplifies the current flowing through the current detection resistor to output the current detection signal.

The constitution of the current determination part 11 is not particularly limited as long as the current flowing through the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 can be determined. For example, each of the current detectors can be arranged in the upstream position of each of the upper arm FETs 13u1, 13v1, 13w1 or in the position between each of the upper arm FETs 13u1, 13v1, 13w1 and each of the lower arm FETs 13u1, 13v1, 13w1. Furthermore, instead of providing three current detectors 11u, 11v, 11w, the respective phase current values Iu, Iv, Iw can be determined by calculation based on switching timing of the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 and detected current with a current detector having a single current detection resistor arranged in either position or position in FIG. 2. Furthermore, the phase current values in one or two of the three-phases can be determined by the current detector, and the remaining phase current values can be determined by calculation.

The signal processing part 12 is comprised of a computer storing a control program, and has a basic target current calculation part 15, a dq-axes current command value calculation part 50, a phase current coordinate conversion part 51, a dq-axes voltage command value calculation part 52, a voltage determination part 53, a voltage coordinate conversion part 54, a storage part 55 and PWM (pulse width modulation) control parts 18u, 18v, 18w for the respective three-phase coils. The storage part 55 can be constituted by an area of a memory device storing the control program or by another memory device.

In the basic target current calculation part 15, a basic target current value I* is calculated based on the steering torque detected by the torque sensor 7 and the vehicle velocity detected by the vehicle velocity sensor 8. The calculation of the basic target current value I* can be performed by a known method; for example, as the value of the steering torque becomes larger and the vehicle velocity becomes smaller, the basic target current value I* becomes larger. Furthermore, the method for determining the basic target current value I* is not particularly limited, and an arbitrary method can be adopted.

The basic target current value I* calculated in the basic target current calculation part 15 is input to the dq-axes current command value calculation part 50. The dq-axes current command value calculation part 50 determines the d-axis current command value Id* and q-axis current command value Iq* as the current command values based on the basic target current value I*. To be more precise, the d-axis current command value Id* for generating magnetic field in the d-axis direction and the q-axis current command value Iq* for generating magnetic field in the q-axis direction are calculated in the dq coordinate system, in which an axis along the magnetic flux direction of the field system (magnet 1c) of the rotor 1b is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor 1b is taken as the q-axis. Here, the q-axis current command value Iq* corresponds to the target output torque of the motor 1. The calculation in the dq-axes current command value calculation part 50 can be performed by using known calculation formulas. Therefore, in the present embodiment, the basic target current calculation part 15 and the dq-axes current command value calculation part 50 serve as the current command value determination part for determining the current command values corresponding to the target output of the motor 1. The constitution of the current command value determination part is not particularly limited as long as the current command values corresponding to the target output of the motor 1 are determined, for example, a constitution which sets constant values as the current command values can be adopted.

The phase current coordinate conversion part 51 calculates the d-axis current value Id and the q-axis current value Iq based on the phase current values Iu, Iv, Iw determined by the current determination part 11 and the rotation positions of the rotor 1b detected by the resolver 2. The calculation in the phase current coordinate conversion part 51 can be performed by using known calculation formulas.

The voltage determination part 53 determines values VE of actual voltage applied to the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2. The voltage determination part 53 in the present embodiment can be constituted by a known voltage detector which outputs signals corresponding to detected values of voltage between the connecting points, which are shown by E1 and E2 in FIG. 2, in the inverter circuit.

The storage part 55 stores predetermined equivalent resistance values which correspond to power loss generated by switching on and off the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2. In the present embodiment, a d-axis equivalent resistance value Rd and a q-axis equivalent resistance value Rq, which corresponds to values of actual current flowing in the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 and values of actual voltage applied to the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2, are stored as the equivalent resistance values. FIG. 3 shows an example of relations between the values of current flowing in the FETs, the values VE of voltage applied to the FETs and the equivalent resistance values, and the values corresponding to such relations are stored. To be more precise, a relation between the d-axis current value Id determined by the phase current coordinate conversion part 51, the voltage value VE determined by the voltage determination part 53 and the d-axis equivalent resistance value Rd is predetermined and stored as a form of table or calculation formula or the like, furthermore, a relation between the q-axis current value Iq determined by the phase current coordinate conversion part 51, the voltage value VE determined by the voltage determination part 53 and the q-axis equivalent resistance value Rq is predetermined and stored as a form of table or calculation formula or the like.

Furthermore, resistance R of the three-phase coils, d-axis self-inductance Ld, q-axis self-inductance Lq, a value obtained by multiplying a maximum value of magnetic flux linkage of the three-phase coils by (3/2)1/2 in the above-mentioned formulas (1) and (2) are predetermined and stored in the storage part 55.

The dq-axes voltage command value calculation part 52 determines the voltage command values by adding the voltage drop values determined from the above-mentioned equivalent resistance values and values of current flowing in the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 to the target applied voltage values determined from the current command values and the relation expressed by the formulas (1) and (2). To be more precise, the dq-axes voltage command value calculation part 52 determines the d-axis target applied voltage value Vd and q-axis target applied voltage value Vq which are target applied voltage values, from the d-axis current command value Id* and q-axis current command value Iq* determined by the dq-axes current command value calculation part 50 and the formulas (1) and (2), so that it serves as a calculation part for determining the target applied voltage values of the motor 1 corresponding to the current command values. Furthermore, the dq-axes voltage command value calculation part 52 determines a d-axis voltage drop value Vd and a q-axis voltage drop value Vq as voltage drop values from the d-axis current value Id and q-axis current value Iq determined by the phase current coordinate conversion part 51 and the above-mentioned formulas (3) and (4), and determines the d-axis voltage command value Vd* and q-axis voltage command value Vq* as the voltage command values from the above-mentioned formulas (5) and (6). Here, the dq-axes voltage command value calculation part 52 serves as a calculation part for calculating angular velocity of the rotor 1b based on the rotation positions of the rotor 1b inputted in time series from the resolver 2, and read the d-axis equivalent resistance value Rd and q-axis equivalent resistance value Rq from the storage part 55 based on the voltage value VE determined by the voltage determination part 53 and the d-axis current value Id and q-axis current value Iq determined by the phase current coordinate conversion part 51.

In the present embodiment, the voltage coordinate conversion part 54 and PWM control parts 18u, 18v, 18w serve as the signal generating part for generating the PWM control signals for switching on and off the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 according to the d-axis voltage command value Vd* and q-axis voltage command value Vq* which are voltage command values.

To be more precise, in the voltage coordinate conversion part 54, the U-phase voltage command value Vu*, V-phase voltage command value Vv* and W-phase voltage command value Vw* are calculated based on the d-axis voltage command value Vd*, the q-axis voltage command value Vq* and the rotation positions of the rotor 1b detected by the resolver 2. The calculation in the voltage coordinate conversion part 54 can be performed by using known calculation formulas.

The respective PWM control parts 18u, 18v, 18w generates PWM control signals that are pulse signals having duty cycle corresponding to the voltage command values Vu*, Vv*, Vw* of the respective phases. The FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 of the drive part 13 are switched on and off by the PWM control signals so that the voltage applied by a battery E to the coils of respective phases of the motor 1 corresponds to the voltage command values Vu*, Vv*, Vw*. To be more precise, in the U-phase of the inverter circuit, when the PWM control signal inputted to the gate of one of the upper arm FET 13u1 and the lower arm FET 13u2 is high pulse, the PWM control signal inputted to the gate of the other is low pulse, and dead time is set between the falling edge of one of the PWM control signals and the rising edge of the other. It's same in the V-phase and W-phase. As a result, voltage corresponding to the target output is applied to the three-phase coils of the motor, and the motor is driven.

The flowchart of FIG. 4 shows a control procedure with the controller 10 of the first embodiment for the motor 1. First, the detected values by the resolver 2, the torque sensor 7, the vehicle velocity sensor 8, the current detectors 11u, 11v, 11w, and the voltage determination part 53 are read (step S1), and the basic target current value I* is calculated based on the detected torque and vehicle velocity (step S2). The d-axis current command value Id* and q-axis current command value Iq* corresponding to the basic target current value I* are calculated (step S3), the d-axis current value Id and q-axis current value Iq corresponding to the detected phase current values Iu, Iv, Iw and rotation positions of the rotor 1b are calculated (step S4), and the angular velocity of the rotor 1 is calculated based on the rotation positions of the rotor 1b determined in time series (step S5). The d-axis equivalent resistance value Rd and q-axis equivalent resistance value Rq corresponding to the calculated d-axis current value Id, calculated q-axis current value Iq and detected voltage value VE are read from the storage part 55 (step S6). Next, the d-axis voltage command value Vd* and q-axis voltage command value Vq* are calculated based on the calculated d-axis current command value Id*, calculated q-axis current command value Iq*, calculated d-axis current value Id, calculated q-axis current value Iq, calculated angular velocity , read d-axis equivalent resistance value Rd, read q-axis equivalent resistance value Rq, and relation expressed by formulas (1) through (6) (step S7). The U-phase voltage command value Vu*, V-phase voltage command value Vv* and W-phase voltage command value Vw* corresponding to the calculated d-axis voltage command value Vd* and q-axis voltage command value Vq* are calculated (step S8). The PWM control signals corresponding to the calculated voltage command values Vu*, Vv*, Vw* of the respective phases are generated, and the motor 1 is driven by switching on and off the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 by the PWM control signals (step S9), whether the control is to be ended is judged based on, for example, ON/OFF state of the ignition switch (step S10), and the processing flow returns to step S1 in a state where the control is not to be ended.

According to the above-mentioned embodiment, the d-axis equivalent resistance value Rd and q-axis equivalent resistance value Rq corresponding to the power loss generated by switching on and off the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 are predetermined and stored, the d-axis voltage command value Vd* is determined by adding the d-axis voltage drop value Vd determined from the d-axis equivalent resistance value Rd and d-axis current value Id to the d-axis target applied voltage value Vd, the q-axis voltage command value Vq* is determined by adding the q-axis voltage drop value Vq determined from the q-axis equivalent resistance value Rq and q-axis current value Iq to the q-axis target applied voltage value Vq, and the output of the motor 1 is controlled by the control signals corresponding to the voltage command values Vd* and Vq*. Therefore, the voltage drops due to the power loss generated by switching on and off the FET 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 is compensated, and the difference between the target output and the actual output of the three-phase brushless the motor 1 open-loop controlled via the inverter circuit can be reduced. Furthermore, by making the equivalent resistance values Rd, Rq used for determining the voltage command values Vd*, Vq* correspond to the current values flowing in the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 and the voltage values applied to the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2, the difference between the target output, and the actual output of the motor 1 can be further reduced. Therefore, the motor 1 can be sufficiently performed and the capability of the electric power steering apparatus can be improved. FIG. 5 shows relations between the angular velocity and the output torque of the motor 1, in which the relation in the above-mentioned embodiment where the voltage drop values Vd, Vq are added to the target applied voltage values Vd, Vq is expressed by a solid line, and the relation in the prior art where the voltage drop values Vd, Vq are not added to the target applied voltage values Vd, Vq is expressed by a broken line, and it can be confirmed that the reduction of the output torque is prevented in the above-mentioned embodiment in comparison with the prior art.

FIG. 6 shows a function block diagram of a controller 10 of the second embodiment. The difference in the second embodiment from the first embodiment is that the motor 1 is feedback controlled. The parts that are the same as the first embodiment are indicated by the same reference symbols, and the differences are explained.

The signal processing part 12 has a voltage drop calculation part 56, a d-axis difference calculation part 57d, a q-axis difference calculation part 57q, a d-axis PI calculation part 58d, a q-axis PI calculation part 58q, a d-axis addition part 59d and a q-axis addition part 59q instead of the dq-axes voltage command value calculation part 52 of the first embodiment.

The voltage drop calculation part 56 determines a d-axis voltage drop value Vd and a q-axis voltage drop value Vq as the voltage drop values from the d-axis current value Id, q-axis current value Iq and above-mentioned formulas (3) and (4). Here, the d-axis equivalent resistance value Rd and q-axis equivalent resistance value Rq are read from the storage part 55 based on the voltage value VE determined by the voltage determination part 53 and the d-axis current value Id and q-axis current value Iq determined by the phase current coordinate conversion part 51.

The d-axis difference calculation part 57d determines the difference between the d-axis current command value Id* and the d-axis current value Id determined by the phase current coordinate conversion part 51, the d-axis target applied voltage value Vd is determined by carrying out the PI calculation of the difference in the d-axis PI calculation part 58d. The q-axis difference calculation part 57q determines the difference between the q-axis current command value Iq* and the q-axis current value Iq determined by the phase current coordinate conversion part 51, the q-axis target applied voltage value Vq is determined by carrying out the PI calculation of the difference in the q-axis PI calculation part 58q. As a result, the d-axis difference calculation part 57d, the q-axis difference calculation part 57q, the d-axis PI calculation part 58d and the q-axis PI calculation part 58q serve as the calculation part for determining the target applied voltage values to the motor 1 corresponding to the current command values.

The d-axis addition part 59d determines the d-axis voltage command value Vd* by adding the d-axis voltage drop value Vd to the d-axis target applied voltage value Vd as expressed by the formula (5), and the q-axis addition part 59q determines the q-axis voltage command value Vq* by adding the q-axis voltage drop value Vq to the q-axis target applied voltage value Vq as expressed by the formula (6). As a result, the voltage drop calculation part 56, the d-axis addition part 59d and the q-axis addition part 59q constitute the calculation part for determining the voltage command values.

The flowchart of FIG. 7 shows a control procedure with the controller 10 of the second embodiment for the motor 1.

First, the detected values by the resolver 2, the torque sensor 7, the vehicle velocity sensor 8, the current detectors 11u, 11v, 11w, and the voltage determination part 53 are read (step S101), and the basic target current value I* is calculated based on the detected torque and vehicle velocity (step S102). The d-axis current command value Id* and q-axis current command value Iq* corresponding to the basic target current value I* are calculated (step S103), the d-axis current value Id and q-axis current value Iq corresponding to the detected phase current values Iu, Iv, Iw and rotation positions of the rotor 1b are calculated (step S104), the d-axis target applied voltage value Vd is calculated by the PI calculation of the difference between the calculated d-axis current command value Id* and the calculated d-axis current value Id, and the q-axis target applied voltage value Vq is calculated by the PI calculation of the difference between the calculated q-axis current command value Iq* and the calculated q-axis current value Iq (step S105). The d-axis equivalent resistance value Rd and q-axis equivalent resistance value Rq corresponding to the calculated d-axis current value Id, calculated q-axis current value Iq and detected voltage value VE are read from the storage part 55 (step S106). Next, the d-axis voltage drop value Vd and q-axis voltage drop value Vq are calculated from the calculated d-axis current value Id, calculated q-axis current value Iq, read equivalent resistance values Rd, Rq and relation expressed by the formulas (3) and (4) (step S107), the d-axis voltage command value Vd* is calculated by adding the calculated d-axis target applied voltage value Vd and the calculated d-axis voltage drop value Vd, and the q-axis voltage command value Vq* is calculated by adding the calculated q-axis target applied voltage value Vq and the calculated q-axis voltage drop value Vq (step S108). The U-phase voltage command value Vu*, V-phase voltage command value Vv* and W-phase voltage command value Vw* corresponding to the calculated d-axis voltage command value Vd* and calculated q-axis voltage command value Vq* are calculated (step S109). The PWM control signals corresponding to the calculated voltage command values Vu*, Vv*, Vw* of the respective phases are generated, and the motor 1 is driven by switching on and off the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 by the PWM control signals (step S110), whether the control is to be ended is judged based on, for example, ON/OFF state of the ignition switch (step S111), and the processing flow returns to step S101 in a state where the control is not to be ended. Other features are similar to those of the first embodiment.

FIG. 8 shows a function block diagram of a controller 10 of the third embodiment. The difference in the third embodiment from the first embodiment is that the basic target current I* is determined from the respective phase voltage command values Vu*, Vv*, Vw* without carrying out the calculation in the dq coordinate system. The parts that are the same as the first embodiment are indicated by the same reference symbols, and the differences are explained.

The signal processing part 12 has a three-phase current command value calculation part 60 and a three-phase voltage command value calculation part 61 instead of the dq-axes current command value calculation part 50, the phase current coordinate conversion part 51, the dq-axes voltage command value calculation part 52 and the voltage coordinate conversion part 54 of the first embodiment.

The three-phase current command value calculation part 60 calculates the respective U-phase current command value Iu*, V-phase current command value Iv* and W-phase current command value Iw* of the three-phase coils as the current command values based on the basic target current value I*. The calculation in the three-phase current command value calculation part 60 can be performed by a known method. Therefore, in the present embodiment, the basic target current calculation part 15 and the three-phase current command value calculation part 60 serve as the current command value determination part for determining the current command values corresponding to the target output of the motor 1.

The storage part 55 stores a U-phase equivalent resistance value Ru, a V-phase equivalent resistance value Rv and a W-phase equivalent resistance value Rw as the equivalent resistance values. To be more precise, a relation between the U-phase current value Iu determined by the current determination part 11, the voltage value VE determined by the voltage determination part 53 and the U-phase equivalent resistance value Ru is predetermined and stored as a form of table or calculation formula or the like, a relation between the V-phase current value Iv determined by the current determination part 11, the voltage value VE determined by the voltage determination part 53 and the V-phase equivalent resistance value Rv is predetermined and stored as a form of table or calculation formula or the like, and a relation between the W-phase current value Iw determined by the current determination part 11, the voltage value VE determined by the voltage determination part 53 and the W-phase equivalent resistance value Rw is predetermined and stored as a form of table or calculation formula or the like.

The three-phase voltage command value calculation part 61 determines the U-phase target applied voltage value Vu, V-phase target applied voltage value Vv and W-phase target applied voltage value Vw, which are the target applied voltage values, from the respective phase current command values Iu*, Iv*, Iw* determined by the three-phase current command value calculation part 60 and the following formulas (7) through (9), so that it serves as a calculation part for determining the target applied voltage values to the motor 1 corresponding to the current command values.


Vu=(R+PL)Iu*PM(Iv*+Iw*)/2+Eu(7)


Vv=(R+PL)Iv*PM(Iu*+Iw*)/2+Ev(8)


Vw=(R+PL)Iw*PM(Iu*+Iv*)/2+Ew(9)

Here, in the formulas (7) through (9), R is resistance of the three-phase coils, L is the self-inductance of the respective three-phase coils, and M is mutual inductance between the three phase coils, which are predetermined and stored in the storage part 55 respectively. Furthermore, Eu, Ev and Ew are speed electromotive forces induced in the respective three-phase coils, which are determined by multiplying a predetermined counter electromotive force constant that is particular to the motor 1 by an angular velocity calculated based on the rotation positions of the rotor 1b inputted in time series from the resolver 2. P stands for a differential operator.

Furthermore, the three-phase voltage command value calculation part 61 determines the U-phase voltage drop value Vu, V-phase voltage drop value Vv and W-phase voltage drop value Vw as the voltage drop values from the respective phase current values Iu, Iv, Iw determined by the current determination part 11 and the following formulas (10) through (12). Here, the respective phase equivalent resistance values Ru, Rv, Rw are read from the storage part 55 based on the respective phase current values Iu, Iv, Iw determined by the current determination part 11 and the voltage value VE determined by the voltage determination part 53.


Vu=RuIu(10)


Vv=RvIv(11)


Vw=RwIw(12)

Furthermore, the three-phase voltage command value calculation part 61 determines the U-phase voltage command value Vu*, V-phase voltage command value Vv* and W-phase voltage command value Vw* as the voltage command values, by adding the respective phase voltage drop values Vu, Vv, Vw to the respective phase target applied voltage values Vu, Vv, Vw as shown by the following formulas (13) through (15).


Vu*=Vu+Vu(13)


Vv*=Vv+Vv(14)


Vw*=Vw+Vw(15)

In the third embodiment, the PWM control parts 18u, 18v, 18w serve as the signal generating part for generating the PWM control signals according to the respective phase voltage command values Vu*, Vv*, Vw*.

The flowchart of FIG. 9 shows a control procedure with the controller 10 of the third embodiment for the motor 1. First, the detected values by the resolver 2, the torque sensor 7, the vehicle velocity sensor 8, the current detectors 11u, 11v, 11w and the voltage determination part 53 are read (step S301), and the basic target current value I* is calculated based on the detected torque and vehicle velocity (step S302). The respective phase current command values Iu*, Iv*, Iw* corresponding to the basic target current value I* are calculated (step S303), the speed electromotive forces Eu, Ev, Ew, which are determined based on the rotation positions of the rotor 1b detected in time series, are calculated (step S304), the respective phase equivalent resistance values Ru, Rv, Rw corresponding to the respective phase current values Iu, Iv, Iw determined by the current determination part 11 and the detected voltage value VE is read from the storage part 55 (step S305), and the respective phase voltage command values Vu*, Vv*, Vw* are calculated from the calculated current command values Iu*, Iv*, Iw*, calculated speed electromotive forces Eu, Ev, Ew of the respective phases, determined respective phase current values Iu, Iv, Iw, read respective phase equivalent resistance values Ru, Rv, Rw, and relation expressed by the formulas (7) through (15) (step S306). The PWM control signals corresponding to the calculated voltage command values Vu*, Vv*, Vw* of the respective phases are generated, and the motor 1 is driven by switching on and off the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 by the PWM control signals (step S307), whether the control is to be ended is judged based on, for example, ON/OFF state of the ignition switch (step S308), and the processing flow returns to step S301 in a state where the control is not to be ended. Other features are similar to those of the first embodiment.

FIG. 10 shows a function block diagram of a controller 10 of the fourth embodiment. The difference in the fourth embodiment from the first embodiment is that the motor 1 is feedback controlled and the basic target current I* is determined from the respective phase voltage command values Vu*, Vv*, Vw* without carrying out the calculation in the dq coordinate system. The parts that are the same as the first embodiment are indicated by the same reference symbols, and the differences are explained.

The signal processing part 12 has a three-phase current command value calculation part 60, a voltage drop calculation part 56, a U-phase difference calculation part 57u, a V-phase difference calculation part 57v, a W-phase difference calculation part 57w, a U-phase PI calculation part 58u, a V-phase PI calculation part 58v, a W-phase PI calculation part 58w, a U-phase addition part 59u, a V-phase addition part 59v and a W-phase addition part 59w instead of the dq-axes current command value calculation part 50, the phase current coordinate conversion part 51, the dq-axes voltage command value calculation part 52 and the voltage coordinate conversion part 54 of the first embodiment.

The three-phase current command value calculation part 60 calculates the respective phase current command values Iu*, Iv*, Iw* as the current command values like in the third embodiment. Therefore, in the present embodiment, the basic target current calculation part 15 and the three-phase current command value calculation part 60 serve as the current command value determination part for determining the current command values corresponding to the target output of the motor 1.

The storage part 55 stores the respective phase equivalent resistance values Ru, Rv, Rw as the equivalent resistance values like in the third embodiment.

The voltage drop calculation part 56 reads the respective phase equivalent resistance values Ru, Rv, Rw from the storage part 55 based on the respective phase current values Iu, Iv, Iw determined by the current determination part 11 and the voltage value VE determined by the voltage determination part 53, and determines the respective phase voltage drop values Vu, Vv, Vw as the voltage drop values from the respective phase equivalent resistance values Ru, Rv, Rw, respective phase current values Iu, Iv, Iw and formulas (10) through (12), like the three-phase voltage command value calculation part 61 in the third embodiment.

The U-phase difference calculation part 57u determines the difference between the U-phase current command value Iu* and the U-phase current value Iu, and the U-phase target applied voltage value Vu is determined by carrying out the PI calculation of the difference in the U-phase PI calculation part 58u. The V-phase difference calculation part 57v determines the difference between the V-phase current command value Iv* and the V-phase current value Iv, and the V-phase target applied voltage value Vv is determined by carrying out the PI calculation of the difference in the V-phase PI calculation part 58v. The W-phase difference calculation part 57w determines the difference between the W-phase current command value Iw* and the W-phase current value Iw, and the W-phase target applied voltage value Vw is determined by carrying out the PI calculation of the difference in the W-phase PI calculation part 58w. As a result, the respective phase difference calculation parts 57u, 57v, 57w and the respective phase PI calculation part 58u, 58v, 58w serve as the calculation part for determining the target applied voltage values to the motor 1 corresponding to the current command values.

The U-phase addition part 59u determines the U-phase voltage command value Vu* by adding the U-phase target applied voltage value Vu and the U-phase voltage drop value Vu as expressed by the formula (13), the V-phase addition part 59v determines the V-phase voltage command value Vv* by adding the V-phase target applied voltage value Vv and the V-phase voltage drop value Vv as expressed by the formula (14), the W-phase addition part 59w determines the W-phase voltage command value Vw* by adding the W-phase target applied voltage value Vw and the W-phase voltage drop value Vw as expressed by the formula (15).

In the fourth embodiment, the PWM control parts 18u, 18v, 18w serve as the signal generating part for generating the PWM control signals according to the respective phase voltage command values Vu*, Vv*, Vw*.

The flowchart of FIG. 11 shows a control procedure with the controller 10 of the fourth embodiment for the motor 1. First, the detected values by the resolver 2, the torque sensor 7, the vehicle velocity sensor 8, the current detectors 11u, 11v, 11w and the voltage determination part 53 are read (step S401), and the basic target current value I* is calculated based on the detected torque and vehicle velocity (step S402). The respective phase current command values Iu*, Iv*, Iw* corresponding to the basic target current value I* are calculated (step S403), the U-phase target applied voltage value Vu is calculated by carrying out the PI calculation of the difference between the calculated U-phase current command value Iu* and the determined U-phase current value Iu, the V-phase target applied voltage value Vv is calculated by carrying out the PI calculation of the difference between the calculated V-phase current command value Iv* and the determined V-phase current value Iv, and the W-phase target applied voltage value Vw is calculated by carrying out the PI calculation of the difference between the calculated W-phase current command value Iw* and the determined W-phase current value Iw (step S404). Further, the respective phase equivalent resistance values Ru, Rv, Rw corresponding to the determined respective phase current values Iu, Iv, Iw and voltage value VE are read from the storage part (step S405), the respective phase voltage drop values Vu, Vv, Vw are then calculated from the read respective phase equivalent resistance values Ru, Rv, Rw, determined respective phase current values Iu, Iv, Iw and relation expressed by the formulas (10) through (12) (step S406), the U-phase voltage command value Vu* is calculated by adding the calculated U-phase target applied voltage value Vu and the calculated U-phase voltage drop value Vu, the V-phase voltage command value Vv* is calculated by adding the calculated V-phase target applied voltage value Vv and the calculated V-phase voltage drop value Vv, and the W-phase voltage command value Vw* is calculated by adding the calculated W-phase target applied voltage value Vw and the calculated W-phase voltage drop value Vw (step S407). The PWM control signals corresponding to the calculated voltage command values Vu*, Vv*, Vw* of the respective phases are generated, and the motor 1 is driven by switching on and off the FETs 13u1, 13u2, 13v1, 13v2, 13w1, 13w2 by the PWM control signals (step S408), whether the control is to be ended is judged based on, for example, ON/OFF state of the ignition switch (step S409), and the processing flow returns to step S401 in a state where the control is not to be ended. Other features are similar to those of the first embodiment.

The present invention is not limited to the above-described embodiments. For example, the application of the motor controlled by the controller of the present invention is not particularly limited. Further, the number of phases and type of the motor is not limited, and the present invention can be applied to a brush motor. Furthermore, each value corresponding to the equivalent resistance stored in the storage part is not limited to the equivalent resistance value itself, for example, the equivalent resistance value can be substantially stored by storing the voltage value, which is obtained by multiplying the equivalent resistance value by a current value, with related to the current value. In this case, the voltage value related to the current value that is determined by the current determination part can be read from the storage part as the voltage drop value. Furthermore, when the output of the motor is controlled under a condition where the fluctuation of the equivalent resistance value is small, the value corresponding to the equivalent resistance stored in the storage part can be constant.

Claims

1. A motor controller for controlling output of a motor by switching on and off switching elements arranged in a power supply line to said motor by control signals, comprising
a current command value determination part for determining current command values corresponding to a target output of said motor;
a calculation part for determining target applied voltage values to said motor corresponding to said current command values;
a storage part for storing values corresponding to predetermined equivalent resistance which corresponds to power loss generated by switching on and off said switching elements;
a current determination part for determining values of current flowing in said switching elements;
a calculation part for determining voltage command values by adding voltage drop values determined from the values corresponding to said equivalent resistance and the values of current flowing in said switching elements to said target applied voltage values; and
a signal generating part for generating said control signals according to said voltage command values.
a current command value determination part for determining current command values corresponding to a target output of said motor;
a calculation part for determining target applied voltage values to said motor corresponding to said current command values;
a storage part for storing values corresponding to predetermined equivalent resistance which corresponds to power loss generated by switching on and off said switching elements;
a current determination part for determining values of current flowing in said switching elements;
a calculation part for determining voltage command values by adding voltage drop values determined from the values corresponding to said equivalent resistance and the values of current flowing in said switching elements to said target applied voltage values; and
a signal generating part for generating said control signals according to said voltage command values.
2. The motor controller according to claim 1, further comprising
a voltage determination part for determining values of voltage applied to said switching elements, wherein
values which correspond to the values of current flowing in said switching elements determined by said current determination part and the values of voltage applied to said switching elements determined by said voltage determination part are stored as the values corresponding to said equivalent resistance.
a voltage determination part for determining values of voltage applied to said switching elements, wherein
values which correspond to the values of current flowing in said switching elements determined by said current determination part and the values of voltage applied to said switching elements determined by said voltage determination part are stored as the values corresponding to said equivalent resistance.
3. The motor controller according to claim 1, wherein
an output of a three-phase brushless motor is open-loop controlled as the output of said motor via an inverter circuit constituted of said switching elements,
U-phase current value, V-phase current value and W-phase current value which are values of current flowing in the respective three-phase coils constituting an armature winding of said motor are determined as values of current flowing in said switching elements,
said motor controller further comprises
a rotation position determination part for determining rotation positions of a rotor of said motor,
a calculation part for calculating an angular velocity of said rotor based on said rotation positions, and
a phase current coordinate conversion part for calculating a d-axis current value and a q-axis current value based on said U-phase current value, said V-phase current value, said W-phase current value and said rotation positions, in which an axis along the magnetic flux direction of field system of the rotor is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor is taken as the q-axis,
said current command value determination part has dq-axes current command value calculation part for determining a d-axis current command value and a q-axis current command value as said current command values based on the target output of said motor,
a d-axis equivalent resistance value and a q-axis equivalent resistance value are stored as the values corresponding to said equivalent resistance,
a d-axis target applied voltage value Vd and a q-axis target applied voltage value Vq are determined as said target applied voltage values from the following formulas (1) and (2),

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)
a d-axis voltage drop value Vd and a q-axis voltage drop value Vq are determined as said voltage drop values from the following formulas (3) and (4),

Vd=RdId(3)

Vq=RqIq(4), and
a d-axis voltage command value Vd* and a q-axis voltage command value Vq* are determined as said voltage command values from the following formulas (5) and (6),

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),
in formulas (1) through (6), Rd stands for a d-axis equivalent resistance value, Rq stands for a q-axis equivalent resistance value, Id stands for a d-axis current value, Iq stands for a q-axis current value, R stands for a predetermined resistance value of said three-phase coils, P stands for a differential operator, Ld stands for a predetermined d-axis self-inductance of said three-phase coils, Lq stands for a predetermined q-axis self-inductance of said three-phase coils, Id* stands for a d-axis current command value, Iq* stands for a q-axis current command value, stands for an angular velocity of said rotor, is a value predetermined by multiplying a maximum value of magnetic flux linkage of said three-phase coils by (3/2)1/2.
an output of a three-phase brushless motor is open-loop controlled as the output of said motor via an inverter circuit constituted of said switching elements,
U-phase current value, V-phase current value and W-phase current value which are values of current flowing in the respective three-phase coils constituting an armature winding of said motor are determined as values of current flowing in said switching elements,
said motor controller further comprises
a rotation position determination part for determining rotation positions of a rotor of said motor,
a calculation part for calculating an angular velocity of said rotor based on said rotation positions, and
a phase current coordinate conversion part for calculating a d-axis current value and a q-axis current value based on said U-phase current value, said V-phase current value, said W-phase current value and said rotation positions, in which an axis along the magnetic flux direction of field system of the rotor is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor is taken as the q-axis,
said current command value determination part has dq-axes current command value calculation part for determining a d-axis current command value and a q-axis current command value as said current command values based on the target output of said motor,
a d-axis equivalent resistance value and a q-axis equivalent resistance value are stored as the values corresponding to said equivalent resistance,
a d-axis target applied voltage value Vd and a q-axis target applied voltage value Vq are determined as said target applied voltage values from the following formulas (1) and (2),

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)
a d-axis voltage drop value Vd and a q-axis voltage drop value Vq are determined as said voltage drop values from the following formulas (3) and (4),

Vd=RdId(3)

Vq=RqIq(4), and
a d-axis voltage command value Vd* and a q-axis voltage command value Vq* are determined as said voltage command values from the following formulas (5) and (6),

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),
in formulas (1) through (6), Rd stands for a d-axis equivalent resistance value, Rq stands for a q-axis equivalent resistance value, Id stands for a d-axis current value, Iq stands for a q-axis current value, R stands for a predetermined resistance value of said three-phase coils, P stands for a differential operator, Ld stands for a predetermined d-axis self-inductance of said three-phase coils, Lq stands for a predetermined q-axis self-inductance of said three-phase coils, Id* stands for a d-axis current command value, Iq* stands for a q-axis current command value, stands for an angular velocity of said rotor, is a value predetermined by multiplying a maximum value of magnetic flux linkage of said three-phase coils by (3/2)1/2.

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)

Vd=RdId(3)

Vq=RqIq(4), and

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),
4. The motor controller according to claim 2, wherein
an output of a three-phase brushless motor is open-loop controlled as the output of said motor via an inverter circuit constituted of said switching elements,
U-phase current value, V-phase current value and W-phase current value which are values of current flowing in the respective three-phase coils constituting an armature winding of said motor are determined as values of current flowing in said switching elements,
said motor controller further comprises
a rotation position determination part for determining rotation positions of a rotor of said motor,
a calculation part for calculating an angular velocity of said rotor based on said rotation positions, and
a phase current coordinate conversion part for calculating a d-axis current value and a q-axis current value based on said U-phase current value, said V-phase current value, said W-phase current value and said rotation positions, in which an axis along the magnetic flux direction of field system of the rotor is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor is taken as the q-axis,
said current command value determination part has dq-axes current command value calculation part for determining a d-axis current command value and a q-axis current command value as said current command values based on the target output of said motor,
a d-axis equivalent resistance value and a q-axis equivalent resistance value are stored as the values corresponding to said equivalent resistance,
a d-axis target applied voltage value Vd and a q-axis target applied voltage value Vq are determined as said target applied voltage values from the following formulas (1) and (2),

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)
a d-axis voltage drop value Vd and a q-axis voltage drop value Vq are determined as said voltage drop values from the following formulas (3) and (4),

Vd=RdId(3)

Vq=RqIq(4), and
a d-axis voltage command value Vd* and a q-axis voltage command value Vq* are determined as said voltage command values from the following formulas (5) and (6),

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),
in formulas (1) through (6), Rd stands for a d-axis equivalent resistance value, Rq stands for a q-axis equivalent resistance value, Id stands for a d-axis current value, Iq stands for a q-axis current value, R stands for a predetermined resistance value of said three-phase coils, P stands for a differential operator, Ld stands for a predetermined d-axis self-inductance of said three-phase coils, Lq stands for a predetermined q-axis self-inductance of said three-phase coils, Id* stands for a d-axis current command value, Iq* stands for a q-axis current command value, stands for an angular velocity of said rotor, is a value predetermined by multiplying a maximum value of magnetic flux linkage of said three-phase coils by (3/2)1/2.
an output of a three-phase brushless motor is open-loop controlled as the output of said motor via an inverter circuit constituted of said switching elements,
U-phase current value, V-phase current value and W-phase current value which are values of current flowing in the respective three-phase coils constituting an armature winding of said motor are determined as values of current flowing in said switching elements,
said motor controller further comprises
a rotation position determination part for determining rotation positions of a rotor of said motor,
a calculation part for calculating an angular velocity of said rotor based on said rotation positions, and
a phase current coordinate conversion part for calculating a d-axis current value and a q-axis current value based on said U-phase current value, said V-phase current value, said W-phase current value and said rotation positions, in which an axis along the magnetic flux direction of field system of the rotor is taken as the d-axis, and an axis perpendicular to the d-axis and the rotation axis of the rotor is taken as the q-axis,
said current command value determination part has dq-axes current command value calculation part for determining a d-axis current command value and a q-axis current command value as said current command values based on the target output of said motor,
a d-axis equivalent resistance value and a q-axis equivalent resistance value are stored as the values corresponding to said equivalent resistance,
a d-axis target applied voltage value Vd and a q-axis target applied voltage value Vq are determined as said target applied voltage values from the following formulas (1) and (2),

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)
a d-axis voltage drop value Vd and a q-axis voltage drop value Vq are determined as said voltage drop values from the following formulas (3) and (4),

Vd=RdId(3)

Vq=RqIq(4), and
a d-axis voltage command value Vd* and a q-axis voltage command value Vq* are determined as said voltage command values from the following formulas (5) and (6),

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),
in formulas (1) through (6), Rd stands for a d-axis equivalent resistance value, Rq stands for a q-axis equivalent resistance value, Id stands for a d-axis current value, Iq stands for a q-axis current value, R stands for a predetermined resistance value of said three-phase coils, P stands for a differential operator, Ld stands for a predetermined d-axis self-inductance of said three-phase coils, Lq stands for a predetermined q-axis self-inductance of said three-phase coils, Id* stands for a d-axis current command value, Iq* stands for a q-axis current command value, stands for an angular velocity of said rotor, is a value predetermined by multiplying a maximum value of magnetic flux linkage of said three-phase coils by (3/2)1/2.

Vd=(R+PLd)Id*LqIq*(1)

Vq=(R+PLq)Iq*LdId*+(2)

Vd=RdId(3)

Vq=RqIq(4), and

Vd*=Vd+Vd(5)

Vq*=Vq+Vq(6),