JP2008062711A - Motor control device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a motor control device capable of appropriately controlling an electric motor based on a rotation angular velocity by improving rotation angular velocity detection resolution without sacrificing control responsiveness. <P>SOLUTION: The electric motor 3 applying a steering assisting force to a steering mechanism 2 is controlled by the motor control device 5. A resolver 4 attached to the electric motor 3 outputs a sinusoidal signal sinθ and a cosine signal cosθ related to the turning angle θ of the rotor of the electric motor 3. After the output signals are amplified by a resolver amplifier 8, they are sampled in predetermined sampling cycles through an A/D converting port 13, and incorporated into a microcomputer 6. Based on the present values sinθ<SB>i</SB>, COS<SB>i</SB>and the previous values sinθ<SB>i-1</SB>, cosθ<SB>i-1</SB>of the sinusoidal signal and cosine signal thus read, the rotation angular velocity ω of the rotor and the electric motor is determined by an angular velocity calculating section 25. By using the rotation angular velocity, a compensation control part 23 determines a correction value with respect to a target current value. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a motor control device for controlling an electric motor. This motor control device can be applied to, for example, a vehicle steering device that drives an electric motor in accordance with an operation of an operation member such as a steering wheel and applies steering force to a steering wheel using the electric motor as a drive source. . Such a vehicle steering device includes an electric power steering device that applies a steering assist force to the steering mechanism by an electric motor, and an electric pump type power that assists steering by transmitting the generated hydraulic pressure of a pump driven by the electric motor to the steering mechanism. Examples include a steering device, a steer-by-wire system that eliminates the mechanical link between the operation member and the steering mechanism, and steers the steering wheel exclusively by the driving force of the electric motor.

Conventionally, an electric power steering apparatus that assists steering by transmitting torque generated by an electric motor to a steering mechanism of a vehicle has been used. The electric motor is driven and controlled based on a target current value determined in accordance with a steering torque applied to the steering wheel and a vehicle speed.
When a brushless motor is used as the electric motor, the rotation angle information of the rotor is detected, and a control signal for controlling the motor drive circuit is generated based on the detection result. For detecting the rotation angle information, signal output means for generating a sine signal sinθ and a cosine signal cosθ relating to the rotor rotation angle θ is used like a resolver. Based on these signals, a control signal corresponding to the rotor rotation angle θ is generated.

On the other hand, in the electric power steering apparatus, various compensation controls are performed in order to bring the steering feeling (feeling) received by the driver from the steering wheel closer to the hydraulic power steering apparatus. For this compensation control, a rotational angular speed ω that is the rotational speed of the rotor of the electric motor is calculated.
In order to calculate the rotational angular velocity ω, the conventional motor control device calculates the ratio of the sine signal sinθ to the cosine signal cosθ to obtain the tangent signal tanθ and calculates the inverse function Tan ⁻¹ (sinθ / cosθ). Thus, the rotor rotation angle θ is obtained. That is, based on the sine signal sin θ and the cosine signal cos θ sampled every predetermined sampling period, the rotor rotation angle θ is obtained each time. Then, the difference between the current value θ _i and the previous value θ _i-1 of the rotor rotation angle θ is obtained as a control cycle difference dθ (= θ _i −θ _i-1 ), which is used as the rotation angular velocity ω (= dθ). It is done.
JP 2001-187578 A

However, since the resolution (sampling period) when the sine signal sinθ and the cosine signal cosθ are taken into the microcomputer constituting the motor control device is limited, the detection resolution of the rotational angular velocity is also limited accordingly.
Therefore, instead of obtaining the difference between the current value θ _i of the rotor rotation angle and the previous value θ _i−1 , the sampling time interval of the rotor rotation angle θ for obtaining the rotation angular velocity ω is lengthened to obtain the current value θ _i If the difference from the value θ _in before the n sampling period is obtained, the resolution of the rotational angular velocity ω can be increased. That is, since the rotational angular velocity resolution is given by rotor rotational angle resolution / sampling time (for example, 1 deg / 50 msec = 0.02 deg / msec), if the sampling time interval is increased, the sampling period of the rotor rotational angle θ is shortened. Without increasing the resolution of the rotational angular velocity ω.

However, if the sampling time interval is lengthened, the update cycle of the rotational angular velocity ω is lengthened accordingly, and as a result, the responsiveness of compensation control is degraded.
Accordingly, an object of the present invention is to provide a motor control device capable of improving the rotational angular velocity detection resolution without sacrificing control responsiveness and thereby appropriately controlling the electric motor based on the rotational angular velocity. is there.

  In order to achieve the above object, the invention according to claim 1 is characterized in that signal output means (4, 8) for outputting a sine signal sinθ and a cosine signal cosθ relating to the rotation angle θ of the rotor of the electric motor (3), and this signal Signal reading means (6, 13) for reading the sine signal sin θ and cosine signal cos θ output by the output means at predetermined intervals, and the current value and the previous value of the sine signal sin θ and cosine signal cos θ read by the signal reading means. Based on the rotation angular velocity calculation means (25) for calculating the rotation angular velocity ω of the rotor of the electric motor, and the control means (23) for controlling the electric motor using the rotation angular velocity ω calculated by the rotation angular velocity calculation means. And a motor control device. The alphanumeric characters in parentheses indicate corresponding components in the embodiments described later. The same applies hereinafter.

  According to this configuration, instead of obtaining the rotor rotation angle θ from the sine signal sin θ and cosine signal cos θ generated by the signal output means, the current value and the previous value of the sine signal sin θ and cosine signal cos θ are used. The rotational angular velocity is calculated. As a result, a high-resolution rotational angular velocity value can be obtained without using a signal obtained with a long time interval, and control responsiveness is not sacrificed. Therefore, by using the rotational angular velocity ω obtained in this way, it is possible to appropriately control the electric motor.

The invention according to claim 2 is the motor control device according to claim 1, wherein the rotational angular velocity calculation means calculates the rotational angular velocity ω based on the following equation (A).
ω = sinθ _i · cosθ _{i -1} -cosθ _i · sinθ _i-1 (A)
However, sinθ _i is the current value of the sine signal, sinθ _i-1 is the previous value of the sine signal, cosθ _i is the current value of the cosine signal, and cosθ _i-1 is the previous value of the cosine signal.

In this configuration, the rotational angular velocity ω is obtained by using the previous value and the current value of the sine signal sinθ and the cosine signal cosθ as they are by calculation using the addition theorem of trigonometric functions. In other words, by utilizing that the _{sin (θ i -θ i-1} ) = sinθ i · cosθ i-1 -cosθ i · sinθ i-1, sin (θ i -θ i-1) ≒ (θ i −θ _i-1 ) and this is the rotational angular velocity ω. By such calculation, the rotational angular velocity ω can be obtained without obtaining the rotor rotational angle θ. In addition, by performing the multiplication operation of the sine signal sinθ and the cosine signal cosθ, the calculation resolution can be improved, and the control accuracy can also be increased.

The rotational angular velocity calculating means, for example, first multiplying means (43) for multiplying the previous value cos [theta] _i-1 of the current value sin [theta _i and cosine signal of the sinusoidal signal, the last current value cos [theta] _i and the sine signal of the cosine signal Second multiplication means (44) for multiplying the value sinθ _i-1 and subtraction means (45) for subtracting the multiplication result of the second multiplication means from the multiplication result of the first multiplication means may be included. .
According to a third aspect of the present invention, the rotational angular velocity calculation means applies the equation (A) in a linear region that can be regarded as sin (θ _i −θ _i−1 ) ≈θ _i −θ _i−1. The motor control device according to claim 2, wherein:

With this configuration, the rotational angular velocity ω can be accurately used by using the formula (A).
In order for the rotational angular velocity calculation means to obtain the rotational angular velocity ω by applying the formula (A) in the linear region, specifically, the period in which the signal reading means reads the sine signal sinθ and the cosine signal cosθ, The amount of change Δθ of the rotor rotation angle θ during the reading cycle may be set sufficiently short so as to satisfy | Δθ | = | θ _i −θ _i-1 | ≦ 60 °.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
FIG. 1 is a block diagram for explaining an electrical configuration of an electric power steering apparatus according to an embodiment of the present invention. The electric power steering apparatus includes a torque sensor 1 that detects a steering torque applied to a steering wheel of a vehicle, an electric motor 3 that applies a steering assist force to a steering mechanism 2 of the vehicle, and a motor control that drives and controls the electric motor 3. A device (ECU: electronic control unit) 5 is provided. The motor control device 5 realizes appropriate steering assistance according to the steering situation by driving the electric motor 3 according to the steering torque detected by the torque sensor 1 and the vehicle speed information given through the in-vehicle LAN (CAN bus). To do. In this embodiment, the electric motor 3 is a three-phase brushless DC motor.

The motor control device 5 includes a microcomputer 6 including a CPU, a RAM, and a ROM, motor current detection circuits 7U and 7V for detecting a U-phase current i _ua and a V-phase current i _va flowing in the electric motor 3, respectively, And a resolver amplifier 8 for amplifying the output signal of the resolver 4 attached to the motor, and a motor driver 9 for supplying electric power to the electric motor 3. The resolver amplifier 8 constitutes signal output means together with the resolver 4, and outputs a sine signal sinθ and a cosine signal cosθ relating to the rotor rotation angle θ of the electric motor 3. The rotor rotation angle θ is an angle of the rotor (field) based on the position of the U-phase armature winding of the electric motor 3.

  The microcomputer 6 captures the output signal of the torque sensor 1 as a steering torque represented by digital data via the A / D conversion port 11 and captures vehicle speed information from the in-vehicle LAN via the communication port 12. The microcomputer 6 sets the current command value of the electric motor 3 based on the steering torque and the vehicle speed, and further determines the voltage command value based on the current command value and the output signals of the motor current detection circuits 7U and 7V. The voltage command value is set and given to the motor driver 9. As a result, an appropriate voltage is applied from the motor driver 9 to the electric motor 3, and a necessary and sufficient torque for assisting steering is generated from the electric motor 3.

The microcomputer 6 includes a plurality of function processing means realized by executing a predetermined program. The plurality of function processing means includes a target current calculation unit 21 that calculates a target current value based on the steering torque and the vehicle speed. The target current value output by the target current calculation unit 21 is input to the addition unit 22. The addition unit 22 is given a correction value from the compensation control unit 23 that performs various compensation controls, and the correction value is added to the target current value to obtain a corrected target current value. Yes. The corrected target current value is a current command value I _a ^* representing the amplitude of a current (sine wave current) to be applied to the U phase, V phase, and W phase of the electric motor 3.

The compensation control unit 23 includes, for example, a convergence correction unit that calculates a convergence correction value for improving the convergence of the steering wheel, and adjusts the vehicle speed from the communication port 12 and the rotational angular velocity ω of the rotor of the electric motor 3. Based on this, a correction value for correcting the target current value is calculated.
The microcomputer 6 includes an angular velocity calculation unit 25 for calculating the rotational angular velocity ω of the rotor of the electric motor 3. The angular velocity calculation unit 25 is supplied with data from the A / D conversion port 13 which converts the output signal of the resolver amplifier 8 into digital data and takes it in. The A / D conversion port 13 samples the output signal of the resolver amplifier 8 at a predetermined sampling period and converts it into digital data, and generates a digitized sine signal sinθ and cosine signal cosθ.

Angular velocity calculating unit 25, in accordance with the following formula (A), and is configured to determine a rotational angular velocity ω ω = Δθ ≒ sinΔθ = sinθ i cosθ i-1 -cosθ i sinθ i-1 ...... (A)
Where θ _i is the rotor rotation angle at the sampling period,
θ _i-1 is the rotor rotation angle in the previous sampling period
Δθ = θ _i −θ _i−1 .

The microcomputer 6 further includes a dq axis current command value calculation unit 26. The dq-axis current command value calculator 26 obtains _a d-axis current command value i _da ^* and a q-axis current command value i _qa ^* in the dq coordinate system based on the current command value I _a ^* . The dq coordinate system is a rotation orthogonal coordinate system including a d axis and a q axis that rotate in synchronization with the rotor of the electric motor 3. The d axis is an axis along the direction of the magnetic flux formed by the rotor, and the q axis is an axis along the direction of the torque generated by the electric motor 3.

  Here, the conversion matrix [c] for converting the three-phase alternating current coordinates into the dq coordinates is as follows.

したがって、電流指令値Ｉ_a ^*を三相分相処理して得られるＵ相電流指令値をｉ_ua ^*とし、Ｖ相電流指令値をｉ_va ^*とし、Ｗ相電流指令値をｉ_wa ^*とすると、ｄ−ｑ座標系のｄ軸電流指令値ｉ_da ^*およびｑ軸電流指令値ｉ_qa ^*は、下記第(2)式で表される。

Therefore, the U-phase current command value obtained by subjecting the current command value I _a ^* to the three-phase phase separation process is i _ua ^* , the V-phase current command value is i _va ^* , and the W-phase current command value is i _wa ^* . Then, the d-axis current command value i _da ^* and the q-axis current command value i _qa ^* in the dq coordinate system are expressed by the following equation (2).

また、Ｕ相電流指令値ｉ_ua ^*、Ｖ相電流指令値ｉ_va ^*およびＷ相電流指令値ｉ_wa ^*は、それぞれ下記第(3)，(4)，(5)式で表される。

The U-phase current command value i _ua ^* , the V-phase current command value i _va ^*, and the W-phase current command value i _wa ^* are expressed by the following equations (3), (4), and (5), respectively.

そして、これらの第(3)，(4)，(5)式を上記第(2)式に代入して整理すると、ｄ軸電流指令値ｉ_da ^*およびｑ軸電流指令値ｉ_qa ^*は、下記第(6)式のように表すことができる。

When these equations (3), (4), (5) are substituted into the above equation (2) and rearranged, the d-axis current command value i _da ^* and the q-axis current command value i _qa ^* are It can be expressed as the following formula (6).

したがって、ｄ−ｑ軸電流指令値演算部２６は、ｄ軸電流指令値ｉ_da ^*＝０と設定する一方で、次の第(7)式に従ってｑ軸電流指令値ｉ_qa ^*を算出する。

Therefore, the dq-axis current command value calculation unit 26 sets the d-axis current command value i _da ^* = 0, and calculates the q-axis current command value i _qa ^* according to the following equation (7).

ｄ−ｑ軸電流指令値演算部２６によって算出されたｑ軸電流指令値ｉ_qa ^*は、減算部２７ｑに入力されるようになっている。この減算部２７ｑには、Ｕ相モータ電流検出回路７ＵおよびＶ相モータ電流検出回路７Ｖがそれぞれ検出するＵ相電流ｉ_uaおよびＶ相電流ｉ_vaを三相交流／ｄ−ｑ座標変換して求められるｑ軸電流ｉ_qaが入力されている。Ｕ相モータ電流検出回路７ＵおよびＶ相モータ電流検出回路７Ｖの出力信号は、Ａ／Ｄ変換ポート１４，１５によってディジタルデータに変換されてマイクロコンピュータ６に取り込まれ、電流検波部１６，１７で検波された後、三相交流／ｄ−ｑ座標変換部２８に入力されるようになっている。三相交流／ｄ−ｑ座標変換部２８は、下記第(8)式に従って、Ｕ相電流ｉ_uaおよびＶ相電流ｉ_vaをｄ−ｑ座標系の値に変換する。

The q-axis current command value i _qa ^* calculated by the dq-axis current command value calculation unit 26 is input to the subtraction unit 27q. The subtracting unit 27q obtains the U-phase current i _ua and the V-phase current i _va detected by the U-phase motor current detection circuit 7U and the V-phase motor current detection circuit 7V, respectively, by three-phase AC / dq coordinate conversion. Q-axis current i _qa is inputted. The output signals of the U-phase motor current detection circuit 7U and the V-phase motor current detection circuit 7V are converted into digital data by the A / D conversion ports 14 and 15 and taken into the microcomputer 6, and detected by the current detection units 16 and 17. After that, the three-phase AC / dq coordinate conversion unit 28 is inputted. The three-phase AC / dq coordinate converter 28 converts the U-phase current i _ua and the V-phase current i _va into values in the dq coordinate system according to the following equation (8).

三相交流／ｄ−ｑ座標変換部２８には、Ａ／Ｄ変換ポート１３からの正弦信号sinθおよび余弦信号θが与えられており、これらを用いて前記式(8)に従う演算が行われるようになっている。

The three-phase AC / dq coordinate conversion unit 28 is provided with the sine signal sin θ and the cosine signal θ from the A / D conversion port 13, and the calculation according to the above equation (8) is performed using these signals. It has become.

The three-phase AC / dq coordinate conversion unit 28 gives the q-axis current i _qa obtained by the three-phase AC / dq coordinate conversion to the subtraction unit 27q. Accordingly, the subtraction unit 27q outputs a deviation of the q-axis current i _{qa from} the q-axis current command value i _qa ^* .
On the other hand, it can be understood from the equation (6) that the d-axis current command value i _da ^* is preferably set to zero regardless of the current command value I _a ^* . Therefore, this d-axis current command value i _da ^* is always set to zero, and this “d-axis current command value i _da ^* = 0” is input to the subtraction unit 27 d. The subtractor 27d performs three-phase AC / dq coordinate conversion on the U-phase current i _ua and the V-phase current i _va in the three-phase AC / dq coordinate conversion unit 28 according to the above equation (8). The d-axis current i _da obtained in this way is input. Thereby, the subtraction unit 27d outputs a deviation of the d-axis current i _{da from} the d-axis current command value i _da ^* .

Deviations output from the subtracting units 27d and 27q are given to a d-axis current PI (proportional integration) control unit 29d and a q-axis current PI control unit 29q, respectively. The PI control units 29d and 29q perform the PI calculation based on the deviations input from the subtraction units 27d and 27q, respectively, thereby obtaining the d-axis voltage command value V _da ^* and the q-axis voltage command value V _qa ^* .
The d-axis voltage command value V _da ^* and the q-axis voltage command value V _qa ^* are input to the dq / three-phase AC coordinate conversion unit 31. The dq / three-phase AC coordinate conversion unit 31 also receives a sine signal sinθ and a cosine signal cosθ that are input from the resolver amplifier 8 via the A / D conversion port 13. The dq / three-phase alternating current coordinate conversion unit 31 uses these and outputs the d-axis voltage command value V _da ^* and the q-axis voltage command value V _qa ^* according to the following equation (9): Converted to values V _ua ^* , V _va ^* , and V _wa ^* . Then, the obtained U-phase voltage command value V _ua ^* , V-phase voltage command value V _va ^*, and W-phase voltage command value V _wa ^* are input to the three-phase PWM forming unit 32.

なお、Ｗ相電圧指令値Ｖ_wa ^*は、上記第(9)式の演算によるのではなく、零からＵ相電圧指令値Ｖ_ua ^*およびＶ相電圧指令値Ｖ_va ^*を減算することにより求めることができる。このようにすれば、ＣＰＵへの負担を軽減できる。むろん、ＣＰＵの演算速度が十分である場合には、上記第(9)式に従う演算によってＷ相電圧指令値Ｖ_wa ^*を算出するようにしてもよい。

The W-phase voltage command value V _wa ^* is obtained by subtracting the U-phase voltage command value V _ua ^* and the V-phase voltage command value V _va ^* from zero, not by the calculation of the above equation (9). be able to. In this way, the burden on the CPU can be reduced. Of course, if the calculation speed of the CPU is sufficient, the W-phase voltage command value V _wa ^* may be calculated by calculation according to the above equation (9).

The three-phase PWM forming unit 32 generates PWM signals S _u , S _v , and S _w corresponding to the U-phase voltage command value V _ua ^* , the V-phase voltage command value V _va ^*, and the W-phase voltage command value V _wa ^* , respectively. Then, the generated PWM signals S _u , S _v , S _w are output to the motor driver 9. As a result, voltages V _ua , V _va , V _wa corresponding to the PWM signals S _u , S _v , S _w are applied from the motor driver 9 to the U phase, V phase, and W phase of the electric motor 3, respectively. Torque necessary for assisting steering is generated from the motor 3.

FIG. 2 is a block diagram for explaining a configuration example of the angular velocity calculation unit 25. The angular velocity calculation unit 25 stores a sine signal memory 41 that stores a sine signal sin θ _i-1 before one sampling period in the A / D conversion port 13 and a cosine signal memory that stores a cosine signal cos θ _i-1 before one sampling period. 42, two multipliers 43 and 44, and a subtractor 45. One multiplier 43 is supplied with the sine signal sinθ _i of the current sampling period and the cosine signal cosθ _{i−1 of} the previous sampling period read from the cosine signal memory 42, and these are multiplied to sinθ _i cosθ. _i-1 is required. The other multiplier 44 is supplied with the cosine signal cosθ _i of the current sampling period and the sine signal sinθ _{i−1 of} the previous sampling period read from the sine signal memory 41, and these are multiplied to give cosθ _i sinθ. _i-1 is required. The subtracter 45, the output of the multiplier 44 from the output of the multiplier 43 is subtracted, as a _{result, sinθ i cosθ i-1 -cosθ} i sinθ i-1 = sin (θ i -θ i-1) is determined . This is output as the rotational angular velocity ω.

However, as shown in FIG. 3, the rotational angular velocity ω (= Δθ = θ _i −θ _i-1 ) can be obtained by the above formula, in a region that can be regarded as sin Δθ≈Δθ, that is, linearity in sin Δθ. It is within the linear region 40 where (linearity) is recognized. Therefore, it is preferable to determine the sampling period of the A / D conversion port 13 so that the change amount Δθ of the rotor rotation angle θ between the sampling periods is within the range of the linear region 40. More specifically, the sampling period of the A / D conversion port 13 may be determined so that Δθ is within a range of ± 60 °.

  On the other hand, for example, if the A / D conversion port 13 digitizes the sine signal sinθ and the cosine signal cosθ with a resolution of 16 bits, the multiplication operation of the sine signal sinθ and the cosine signal cosθ is performed to obtain the rotational angular velocity ω. The obtained angular velocity calculation unit 25 obtains the rotational angular velocity ω with a resolution of 32 bits. By obtaining the rotational angular velocity ω with high resolution in this way, it is possible to increase the accuracy of the control in the compensation control unit 23 performed using the rotational angular velocity ω, and to improve the steering feeling accordingly. . Specifically, motor control sound and vibration can be reduced. In addition, the resolution is not improved by increasing the sampling time interval, and the rotational angular velocity ω updated at every sampling period of the A / D conversion port 13 can be obtained. It won't get worse. Therefore, the compensation control in the compensation control unit 23 can be performed with sufficient responsiveness.

As mentioned above, although one Embodiment of this invention was described, this invention can also be implemented with another form. For example, the angular velocity calculation unit 25 may further include an averaging processing unit that performs an averaging process on the output of the subtracter 45. Thereby, the dispersion | variation resulting from a multiplication calculation can be reduced and the value of rotation angular velocity (omega) can be stabilized.
In the above-described embodiment, the case where PI control is applied has been described as an example. However, PID (proportional integral derivative) control may be applied instead of PI control.

  In addition, various design changes can be made within the scope of matters described in the claims.

It is a block diagram for demonstrating the electrical constitution of the electric power steering device which concerns on one Embodiment of this invention. It is a block diagram for demonstrating the structural example of an angular velocity calculating part. It is a figure for demonstrating the linear area | region which can calculate rotation angular velocity.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 3 ... Electric motor, 4 ... Resolver, 5 ... Motor controller, 6 ... Microcomputer, 40 ... Linear region, 41 ... Sine signal memory, 42 ... Cosine signal memory, 43, 44 ... Multiplier, 45 ... Subtractor

Claims (3)

A signal output means for outputting a sine signal sinθ and a cosine signal cosθ relating to the rotation angle θ of the rotor of the electric motor;
Signal reading means for reading the sine signal sinθ and cosine signal cosθ output by the signal output means at predetermined intervals;
Based on the current value and the previous value of the sine signal sinθ and the cosine signal cosθ read by the signal reading means, a rotational angular speed calculating means for calculating the rotational angular speed ω of the rotor of the electric motor;
And a control unit that controls the electric motor using the rotation angular velocity ω calculated by the rotation angular velocity calculation unit. The motor control device according to claim 1, wherein the rotation angular velocity calculation means calculates a rotation angular velocity ω based on the following equation (A).
ω = sinθ _i · cosθ _{i -1} -cosθ _i · sinθ _i-1 (A)
However, sinθ _i is the current value of the sine signal, sinθ _i-1 is the previous value of the sine signal, cosθ _i is the current value of the cosine signal, and cosθ _i-1 is the previous value of the cosine signal. The rotational angular velocity calculation means obtains the rotational angular velocity ω by applying the formula (A) in a linear region that can be regarded as sin (θ _i −θ _i−1 ) ≈θ _i −θ _i−1. 2. The motor control device according to 2.

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