Control apparatus of three-phase AC motor

Abstract

A position control apparatus detects currents of processing object phases which flow through the three-phase AC motor, applies offset compensation processing to current detected values of the processing object phases based on offset compensation amounts, and controls the three-phase AC motor based on the current detected values of the processing object phases after the offset compensation processing. Processing of obtaining the offset compensation amounts includes processing of obtaining a Fourier coefficient of a frequency component of a torque ripple based on a torque command value signal, processing of obtaining torque amplitude components of the processing object phases, and processing of obtaining the offset compensation amounts with respect to the processing object phases based on the torque amplitude components of the processing object phases.

Claims

1. A control apparatus of a three-phase AC motor, which detects currents of processing object phases being at least two phases among currents of three phases which flow through a three-phase AC motor, applies offset compensation processing with respect to current detected values of the processing object phases based on offset compensation amounts obtained in advance, and controls the three-phase AC motor based on the current detected values of the processing object phases after the offset compensation processing, wherein the processing of obtaining the offset compensation amounts includes: processing of obtaining a Fourier coefficient of a frequency component of a torque ripple with respect to a torque command value signal to the three-phase AC motor; processing of obtaining torque amplitude components of the processing object phases of the three-phase AC motor based on the Fourier coefficient and an electrical angle of the three-phase AC motor at a reference time of the torque command value signal; and processing of obtaining the offset compensation amounts with respect to the processing object phases based on the torque amplitude components of the processing object phases.

2. The control apparatus of a three-phase AC motor according to claim 1, wherein: the processing of obtaining the offset compensation amounts includes: processing of obtaining, based on the torque amplitude components of the processing object phases, offset compensation change amounts with respect to the offset compensation amounts previously obtained with respect to the processing object phases; and obtaining new offset compensation amounts with respect to the processing object phases based on the offset compensation change amounts with respect to the processing object phases and the offset compensation amounts previously obtained with respect to the processing object phases.

3. The control apparatus of a three-phase AC motor according to claim 1, wherein: the torque command value signal indicates a torque command value with respect to the three-phase AC motor rotating at a constant speed.

4. The control apparatus of a three-phase AC motor according to claim 2, wherein: the torque command value signal indicates a torque command value with respect to the three-phase AC motor rotating at a constant speed.

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) An embodiment of the present disclosure will be described based on the following figures, wherein:

(2) FIG. 1 is a block diagram showing a configuration example of a position control apparatus using the three-phase AC motor according to the present disclosure as a drive motor.

(3) FIG. 2 is a block diagram showing an example of a current detection offset compensation value calculator according to the present disclosure.

(4) FIG. 3 is a flow chart for describing an operation sequence of the current detection offset compensation value calculator.

(5) FIG. 4 is a vector diagram of a Fourier coefficient C1 at a torque ripple frequency of a permanent magnet synchronous motor.

(6) FIG. 5 is a vector diagram of the Fourier coefficient C1 at a torque ripple frequency of an induction motor or a synchronous reluctance motor.

(7) FIG. 6 is a block diagram showing a configuration example of a position control apparatus using a conventional three-phase AC motor as a drive motor.

(8) FIG. 7 is a block diagram showing an example of a configuration of a conventional current detection offset compensation value adjuster.

DESCRIPTION OF EMBODIMENT

(9) A best mode for carrying out the present disclosure will be described using examples. FIG. 1 is a block diagram showing an example of an approximate configuration of a position control apparatus 20 of a three-phase AC motor according to the present disclosure. Constituent elements that are the same as the constituent elements shown in FIG. 6 will be denoted by same reference signs and a description thereof will be simplified. The position control apparatus 20 may be constituted by a processor, a digital electronic circuit, or an analog electronic circuit which realizes a function of each constituent element by executing a program.

(10) First, a relationship between a DC offset to be superimposed on current detection of each phase and a torque ripple Trip attributable to the DC offset will be specified. In permanent magnet synchronous motors (SPMSM and IPMSM), a torque can be generated between a permanent magnet field and a q-axis current iq even when a d-axis current command value id*=0. In this case, by denoting current detection DC offsets of the U phase and the V phase as du and dv, the three phase currents iu, iv, and iw when the motor rotates at a constant speed of an electrical angular velocity re are expressed by Formula (1). Note that in the present specification, a sin function will be notated as S and a cos function will be notated as C for the sake of brevity.

(11) $\left[\mathrm{Expression}1\right]$$\begin{array}{cc}\{\begin{array}{cc}{i}_u& =\mathrm{Is}.Math.C_{\mathrm{re}}+d_u\\ i_v& =\mathrm{Is}.Math.C_{\left(\mathrm{re}-2/3\right)}+d_v\\ i_w& =\mathrm{Is}.Math.C_{\left(\mathrm{re}+2/3\right)}-\left(d_u+d_v\right)\end{array}& \left(1\right)\end{array}$ where Is denotes a phase current amplitude.

(12) According to the three phase-to-dq transformer 62, the q-axis current iq is expressed as Formula (2).

(13) $\left[\mathrm{Expression}2\right]$$\begin{array}{cc}\begin{array}{cc}{i}_q& =\sqrt{\frac{2}{3}}\left\{i_u.Math.C_{\mathrm{re}}+i_v.Math.C_{\left(\mathrm{re}-2/3\right)}+i_w.Math.C_{\left(\mathrm{re}+2/3\right)}\right\}\\ & =\sqrt{\frac{2}{3}}\left\{\frac{3}{2}\mathrm{Is}+d_u\left(C_{\mathrm{re}}-C_{\left(\mathrm{re}+2/3\right)}\right)+d_v\left(C_{\left(\mathrm{re}-2/3\right)}-C_{\left(\mathrm{re}+2/3\right)}\right)\right\}\\ & =\sqrt{\frac{2}{3}}\left\{\frac{3}{2}\mathrm{Is}+\sqrt{}3.Math.d_u{S}_{\left(\mathrm{re}+/3\right)}+\sqrt{}3.Math.d_v{S}_{\left(\mathrm{re}\right)}\right\}\end{array}& \left(2\right)\end{array}$

(14) In the case of an SPMSM, a generated torque is a magnetic torque proportional to the q-axis current iq (iq). In particular, a torque ripple rip attributable to current detection DC offsets du and dv can be expressed by Formula (3).
[Expression 3]
rip=A{d.sub.uS.sub.(re+/3)+d.sub.vS.sub.(re)}(3)
where A denotes a constant (A>0) for matching units between rip and du, dv.
In other words, the current detection DC offsets du and dv are converted to the torque ripple rip having an angular frequency of an electrical angular velocity re (=p.Math.m).

(15) On the other hand, according to the three phase-to-dq transformer 62, the d-axis current id is expressed as Formula (4).

(16) $\left[\mathrm{Expression}4\right]$$\begin{array}{cc}\begin{array}{cc}{i}_d& =\sqrt{\frac{2}{3}}\left\{i_u.Math.S_{\mathrm{re}}+i_v.Math.S_{\left(\mathrm{re}-2/3\right)}+i_w.Math.S_{\left(\mathrm{re}+2/3\right)}\right\}\\ & =\sqrt{\frac{2}{3}}\left\{d_u{S}_{\mathrm{re}}+d_v{S}_{\left(\mathrm{re}-2/3\right)}-\left(d_u+d_v\right)S_{\left(\mathrm{re}+2/3\right)}\right\}\end{array}& \left(4\right)\end{array}$

(17) A reluctance torque r of an IPMSM is proportional to iq.Math.id (riq.Math.id). Since a squared term of a current detection DC offset is small, by ignoring the squared term, we obtain Formula (5).

(18) $\left[\mathrm{Expression}5\right]$$\begin{array}{cc}\begin{array}{cc}r{i}_q.Math.i_d& \underset{.}{\stackrel{.}{=}}\mathrm{Is}\left\{d_u{S}_{\mathrm{re}}+d_v{S}_{\left(\mathrm{re}-2/3\right)}-\left(d_u+d_v\right)S_{\left(\mathrm{re}+2/3\right)}\right\}\\ & =\mathrm{Is}\left\{d_u{S}_{\left(\mathrm{re}+/3\right)}+d_v{S}_{\left(\mathrm{re}\right)}\right\}\end{array}& \left(5\right)\end{array}$
This is a constant multiple of the magnet torque ripple rip of Formula (3). In other words, a torque ripple of a total torque (=magnet torque+reluctance torque) of an IPMSM can also be expressed by Formula (3) in a similar manner to an SPMSM.

(19) FIG. 2 is a block diagram showing an example of a configuration of a current detection offset compensation value calculator 1 according to the present disclosure shown in FIG. 1. Hereinafter, an operation of the current detection offset compensation value calculator 1 will be described. FIG. 3 is a flow chart for describing each step of an operation sequence of the current detection offset compensation value calculator 1.

(20) (Step 1). An electrical angular velocity re and the total number of sampling points N that satisfy Formula (6) are selected among a velocity range where a large torque ripple attributable to a current detection DC offset is generated, and the motor is operated at a constant velocity re under id*=0.
[Expression 6]
.sub.reTs.Math.N=2(6)
where Ts denotes a sampling period.

(21) (Step 2). A torque command value c* [n] of N-number of points is collected at the sampling period Ts.

(22) An electrical angle re at c* [0] is saved as 0.

(23) (Step 3). A Fourier coefficient C1 of a fundamental wave component of a known discrete Fourier transform (DFT) is calculated from Formula (7).

(24) $\begin{array}{cc}{C}_1=\frac{I}{N}\underset{n=0}{\overset{N-1}{.Math.}}{}_c^{*}\left[n\right]e^{-j\left(2/N\right).Math.n}& \left(7\right)\end{array}$
(Step 2) and (Step 3) become operations of a Fourier coefficient calculating unit 2 shown in FIG. 2.

(25) From Formula (3), the torque ripple rip of the electrical angular velocity re is a combination of a torque amplitude component u attributable to du and a torque amplitude component v attributable to dv and has a relationship with the Fourier coefficient C1 as shown in FIG. 4.

(26) The torque ripple rip of Formula (3) can be notated by Formula (8) using the torque amplitude components u and v described above.
[Expression 8]
rip=B{.sub.uS.sub.(re+/3)+.sub.vS.sub.(re)}(8)
where B denotes a constant (B>0) for matching units between rip and u, v.

(27) (Step 5). u and v shown in FIG. 4 have a relationship with the Fourier coefficient C1 that is represented by Formula (9.1) and Formula (9.2).

(28) $\left[\mathrm{Expression}9\right]$$\{\begin{array}{cc}\mathrm{Re}\left(C_1\right)=u.Math.C_{\left(/3+\right)}+v.Math.C_{}& \left(9.1\right)\\ \mathrm{Im}\left(C_1\right)=u.Math.S_{\left(/3+\right)}+v.Math.S_{}& \left(9.2\right)\\ \mathrm{where}={}_0-\frac{}{2}& \end{array}$

(29) Solving these simultaneous equations enable u and v shown in FIG. 4 to be expressed by Formula (10).

(30) $\left[\mathrm{Expression}10\right]$$\begin{array}{cc}\{\begin{array}{cc}u& =-\frac{\mathrm{Re}\left(C_1\right)S_{}-\mathrm{Im}\left(C_1\right)C_{}}{\left(\sqrt{}3/2\right)}\\ v& =\frac{\mathrm{Re}\left(C_1\right)S\left(/3+\right)-\mathrm{Im}\left(C_1\right)C\left(/3+\right)}{\left(\sqrt{}3/2\right)}\end{array}& \left(10\right)\end{array}$

(31) (Step 5) becomes an operation of a per-phase torque amplitude component calculating unit 3 shown in FIG. 2.

(32) (Step 6). Current detection offset compensation increments duc and dvc are calculated from the derived u and v by Formula (11).

(33) $\left[\mathrm{Expression}11\right]$$\begin{array}{cc}\{\begin{array}{c}\mathrm{duc}=-G.Math.u\\ \mathrm{dvc}=-G.Math.v\end{array}& \left(11\right)\end{array}$
where a gain G is a constant within a range of 0<GB/A.

(34) The current detection offset compensation amounts duc [m] and dvc [m] of the present cycle (m-th cycle) are represented by the current detection offset compensation amounts duc [m1] and dvc [m1] of the previous cycle (m1-th cycle) and the current detection offset compensation increments duc and dvc. In other words, the current detection offset compensation amounts duc [m] and dvc [m] of the present cycle (m-th cycle) operate to cause the torque ripple to gradually converge to 0 according to Formula (12).

(35) $\left[\mathrm{Expression}12\right]$$\begin{array}{cc}\{\begin{array}{c}\mathrm{duc}\left[m\right]=\mathrm{duc}+\mathrm{duc}\left[m-1\right]\\ \mathrm{dvc}\left[m\right]=\mathrm{dvc}+\mathrm{dvc}\left[m-1\right]\end{array}& \left(12\right)\end{array}$
(Step 6) becomes an operation of a per-phase current detection offset compensation value setting unit 4 shown in FIG. 2.

(36) As described above, the position control apparatus 20 according to the embodiment of the present disclosure detects currents of two phases (the U phase and the V phase) among the currents of three phases which flow through the three-phase AC motor, applies offset compensation processing to the current detected values of the two phases based on offset compensation amounts obtained in advance, and controls the three-phase AC motor based on the current detected values of the two phases after the offset compensation processing.

(37) The processing of obtaining the offset compensation amounts includes processing of obtaining a Fourier coefficient C1 of a frequency component of a torque ripple with respect to a torque command value signal (the torque command value signal c* [n]) to the three-phase AC motor. The torque command value signal may be a signal indicating a torque command value with respect to the three-phase AC motor rotating at a constant speed. In addition, the processing of obtaining the offset compensation amounts duc [m] and dvc [m] includes processing of obtaining torque amplitude components (u and v) of the two phases of the three-phase AC motor. The processing of obtaining the torque amplitude components of the two phases includes processing of obtaining the torque amplitude components (u and v) of the two phases based on the Fourier coefficient C1 and an electrical angle 0 of the three-phase AC motor at a reference time (n=0) of the torque command value signal c* [n]. Furthermore, the processing of obtaining the offset compensation amounts includes processing of obtaining the offset compensation amounts duc [m] and dvc [m] with respect to the two phases based on the torque amplitude components (u and v) of the two phases.

(38) In addition, the processing of obtaining the offset compensation amounts duc [m] and dvc [m] includes: processing of obtaining, based on the torque amplitude components (u and v) of the two phases, offset compensation change amounts (offset compensation increments duc and dvc) with respect to offset compensation amounts duc [m1] and dvc [m1] previously obtained with respect to the two phases, and obtaining new offset compensation amounts duc [m] and dvc [m] with respect to the two phases based on the offset compensation change amounts with respect to the two phases and the offset compensation amounts duc [m1] and dvc [m1] previously obtained with respect to the two phases. While an example in which the U phase and the V phase are direct processing objects and processing of the W phase is executed based on calculation results of the U phase and the V phase has been demonstrated, all three phases being the U phase, the V phase, and the W phase may be phases that are direct processing objects (processing object phases).

(39) While this concludes the description of operations of the current detection offset compensation value calculator 1, as shown in (Step 4) in FIG. 3, after calculating the Fourier coefficient C1 in (Step 3), a magnitude |C1| of the Fourier coefficient and a convergence reference value ref of the torque ripple amplitude are compared with each other, the operation sequence from (Step 2) to (Step 6) is executed until |C1|ref is satisfied, and the calculation of the current detection offset compensation values duc and dvc is repeated. Once |C1|ref is satisfied, the calculation of the current detection offset compensation values duc and dvc is completed and the constant-speed operation of the motor is ended.

(40) The description of the series of operations thus far concerns a case of permanent magnet synchronous motors (SPMSM and IPMSM). Next, operations of the current detection offset compensation value calculator 1 in the cases of an induction motor (IM) or a synchronous reluctance motor (SynRM) will be described with a focus on differences from the case of permanent magnet synchronous motors (SPMSM and IPMSM). In the case of an IM or a SynRM, since torque is generated between the q-axis current iq and the d-axis current id (iq.Math.id), d-axis current command value id*0 becomes a prerequisite.

(41) In consideration thereof, in a current vector control calculating unit 10 shown in FIG. 1, after calculating the q-axis current command value iq* and the d-axis current command value id*, a vector synthesis current I of iq* and id* is obtained and an angle formed between I and id* is calculated.

(42) In the case of an IM or a SynRM, the relationship between the current detection DC offsets du and dv and the three-phase currents iu, iv, and iw when the motor rotates at a constant speed of the current angular velocity (the electrical angular velocity re in the case of a SynRM) can be represented by Formula (13) using the angle formed between I and id*.

(43) 0$\left[\mathrm{Expression}13\right]$$\begin{array}{cc}\{\begin{array}{c}{i}_u=\mathrm{Is}.Math.S_{\left(+\right)}+d_u\\ i_v=\mathrm{Is}.Math.S_{\left(-2/3+\right)}+d_v\\ i_w=\mathrm{Is}.Math.S_{\left(+2/3+\right)}-\left(d_u+d_v\right)\end{array}& \left(13\right)\end{array}$
Hereinafter, a SynRM will be described as an example. (Since the SynRM is a synchronous motor, current angular velocity .fwdarw.electrical angular velocity re is satisfied).

(44) According to the three phase-to-dq transformer 62, the q-axis current iq is expressed as Formula (14) and the d-axis current id is expressed as Formula (15).

(45) $\left[\mathrm{Expression}14\right]$$\begin{array}{cc}\begin{array}{cc}{i}_q& =\sqrt{\frac{2}{3}}\left\{i_u.Math.C_{\mathrm{re}}+i_v.Math.C_{\left(\mathrm{re}-2/3\right)}+i_w.Math.C_{\left(\mathrm{re}+2/3\right)}\right\}\\ & =\sqrt{\frac{2}{3}}\left\{\frac{3}{2}\mathrm{Is}.Math.S_{}+d_u{C}_{\mathrm{re}}+d_v{C}_{\left(\mathrm{re}-2/3\right)}-\left(d_u+d_v\right)C_{\left(\mathrm{re}+2/3\right)}\right\}\end{array}& \left(14\right)\end{array}$$\left[\mathrm{Expression}15\right]$$\begin{array}{cc}\begin{array}{cc}{i}_d& =\sqrt{\frac{2}{3}}\left\{i_u.Math.S_{\mathrm{re}}+i_v.Math.S_{\left(\mathrm{re}-2/3\right)}+i_w.Math.S_{\left(\mathrm{re}+2/3\right)}\right\}\\ & =\sqrt{\frac{2}{3}}\left\{\frac{3}{2}\mathrm{Is}.Math.C_{}+d_u{S}_{\mathrm{re}}+d_v{S}_{\left(\mathrm{re}-2/3\right)}-\left(d_u+d_v\right)S_{\left(\mathrm{re}+2/3\right)}\right\}\end{array}& \left(15\right)\end{array}$

(46) At this point, by ignoring a minute square term of the current detection DC offset and calculating a generated torque , we obtain Formula (16).

(47) $\left[\mathrm{Expression}16\right]$$\begin{array}{cc}\mathrm{iq}.Math.\mathrm{id}\underset{.}{\stackrel{.}{=}}\frac{3}{2}{\mathrm{Is}}^2.Math.S_{}{C}_{}+\mathrm{Is}.Math.d_u\left\{S_{}{S}_{\mathrm{re}}+C_{}{C}_{\mathrm{re}}-S_{}{S}_{\left(\mathrm{re}+2/3\right)}-C_{}{C}_{\left(\mathrm{re}+2/3\right)}\right\}+\mathrm{Is}.Math.d_v\left\{S_{}{S}_{\left(\mathrm{re}-2/3\right)}+C_{}{C}_{\left(\mathrm{re}-2/3\right)}-S_{}{S}_{\left(\mathrm{re}+2/3\right)}-C_{}{C}_{\left(\mathrm{re}+2/3\right)}\right\}=\frac{3}{2}{\mathrm{Is}}^2.Math.S_{}{C}_{}+\sqrt{3}.Math.\mathrm{Is}.Math.d_u{S}_{\left(\mathrm{re}+/3-\right)}+\sqrt{3}.Math.\mathrm{Is}.Math.d_v{S}_{\left(\mathrm{re}-\right)}& \left(16\right)\end{array}$

(48) In particular, a torque ripple Trip attributable to current detection DC offsets du and dv can be expressed by Formula (17).
[Expression 17]
ripA(d.sub.uS.sub.(re+/3)+d.sub.vS.sub.(re)(7)
where A denotes a constant (A>0) for matching units between rip and du, dv in the case of a SynRM, and although A differs from A in Formula (3), the expression A will be used for the sake of convenience. In other words, even in the case of a SynRM, the current detection DC offsets are converted to the torque ripple rip having an angular frequency of an electrical angular velocity re.

(49) Next, an operation sequence (Steps) of the current detection offset compensation value calculator 1 in the case of a SynRM will be described. The sequence up to (Step 3) is the same as in the case of permanent magnet synchronous motors (SPMSM and IPMSM). In the case of a SynRM, the relationship between the torque amplitude components u and v and the Fourier coefficient C1 is a relationship shown in FIG. 5.

(50) Therefore, the torque ripple Trip of Formula (17) can be notated by Formula (18) using the torque amplitude components u and v.
[Expression 18]
ripB{.sub.uS.sub.(re+/3)+.sub.vS.sub.(re)}(18)
where B denotes a constant (B>0) for matching units between rip and u, v in the case of a SynRM, and although B differs from B in Formula (8), the expression B will be used for the sake of convenience.

(51) Since the relationship between u and v and the Fourier coefficient C1 is shown in FIG. 5, a relationship expressed by Formula (19.1) and Formula (19.2) is satisfied.

(52) $\left[\mathrm{Expression}19\right]$$\{\begin{array}{cc}\mathrm{Re}\left(C_1\right)=u.Math.C_{\left(/3+-\right)}+v.Math.C_{\left(-\right)}& \left(19.1\right)\\ \mathrm{Im}\left(C_1\right)=u.Math.S_{\left(/3+-\right)}+v.Math.S_{\left(-\right)}& \left(19.2\right)\\ \mathrm{where}={}_0-\frac{}{2}& \end{array}$

(53) Solving these simultaneous equations enable u and v shown in FIG. 5 to be expressed by Formula (20).

(54) $\left[\mathrm{Expression}20\right]$$\begin{array}{cc}\{\begin{array}{cc}u& =-\frac{\mathrm{Re}\left(C_1\right)S_{\left(-\right)}-\mathrm{Im}\left(C_1\right)C_{\left(-\right)}}{\left(\sqrt{}3/2\right)}\\ v& =\frac{\mathrm{Re}\left(C_1\right)S\left(/3+-\right)-\mathrm{Im}\left(C_1\right)C\left(/3+-\right)}{\left(\sqrt{}3/2\right)}\end{array}& \left(20\right)\end{array}$
In other words, in a SynRM, the sequence of (Step 5) which is an operation of the per-phase torque amplitude component calculating unit 3 shown in FIG. 2 is executed based on Formula (20). Thereafter, the sequence of (Step 6) and (Step 4) is the same as in the case of permanent magnet synchronous motors (SPMSM and IPMSM) described earlier.

(55) Next, a case of an IM will be described. The relationship between the current detection DC offsets du and dv and the three-phase currents iu, iv, and iw when the motor rotates at a constant speed of the current angular velocity can be represented by Formula (13) described earlier using the angle formed between I and id*. According to the three phase-to-dq transformer 62, the q-axis current iq is expressed as Formula (21).

(56) $\left[\mathrm{Expression}21\right]$$\begin{array}{cc}\begin{array}{c}{i}_q=\sqrt{\frac{2}{3}}\left\{i_u.Math.C_{}+i_v.Math.C_{\left(-2/3\right)}+i_w.Math.C_{\left(+2/3\right)}\right\}\\ \sqrt{\frac{3}{2}}\mathrm{Is}.Math.S_{}+\sqrt{2}\left(d_u{S}_{\left(+/3\right)}+d_v{S}_{\left(\right)}\right)\end{array}& \left(21\right)\end{array}$

(57) Note that under a constant speed in the case of an IM, id* is set to a constant value, and even when a current detection DC offset is present, the d-axis current id is controlled to id*=id. Therefore, the torque ripple Trip is proportional to a ripple component of the q-axis current iq in a similar manner to a case of an SPMSM and can be expressed by Formula (22).
[Expression 22]
ripA{d.sub.uS.sub.(+/3)+d.sub.vS.sub.()}(22)
where A denotes a constant (A>0) for matching units between rip and du, dv in the case of an IM, and in the case of an IM, the current detection DC offsets are converted to the torque ripple rip having an angular frequency of a current angular velocity .

(58) Next, an operation sequence (Steps) of the current detection offset compensation value calculator 1 in the case of an IM will be described. The sequence up to (Step 3) represents the same operations, provided that the electrical angular velocity re are replaced with the current angular velocity . However, in the case of an IM, since there is a difference in slip angular velocity s between the current angular velocity and the electrical angular velocity re, when a load is heavy, the motor must be operated at a constant speed at the electrical angular velocity re that produces the current angular velocity in consideration of the slip angular velocity s.

(59) In the case of an IM, the relationship between the torque amplitude components u and v and the Fourier coefficient C1 is a relationship shown in FIG. 4 in a similar manner to permanent magnet synchronous motors (SPMSM and IPMSM). Therefore, the torque ripple rip of Formula (22) can be notated by Formula (23) using the torque amplitude components u and v.
[Expression 23]
ripB{.sub.uS.sub.(+/3)+.sub.vS.sub.()}(23)
where B denotes a constant (B>0) for matching units between rip and u, v in the case of an IM.

(60) Since the relationship between u and v and the Fourier coefficient C1 is shown in FIG. 4, the relationship expressed by Formula (9.1) and Formula (9.2) is satisfied, and solving these simultaneous equations enable u and v to be expressed by Formula (10). In other words, in an IM, the sequence of (Step 5) which is an operation of the per-phase torque amplitude component calculating unit 3 shown in FIG. 2 is executed based on Formula (10). Thereafter, the sequence of (Step 6) and (Step 4) is also the same as in the case of permanent magnet synchronous motors (SPMSM and IPMSM) described earlier.

(61) When the three-phase AC motor is a permanent magnet synchronous motor (SPMSM and IPMSM), the position control apparatus 20 similarly detects currents of two phases (the U phase and the V phase) among the currents of three phases which flow through the three-phase AC motor, applies offset compensation processing to the current detected values of the two phases based on offset compensation amounts duc [m] and dvc [m] obtained in advance, and controls the three-phase AC motor based on the current detected values of the two phases after the offset compensation processing.

(62) The processing of obtaining the offset compensation amounts includes processing of obtaining a Fourier coefficient C1 of a frequency component of a torque ripple with respect to a torque command value signal (the torque command value signal c* [n]) to the three-phase AC motor. The torque command value signal may be a signal indicating a torque command value with respect to the three-phase AC motor rotating at a constant speed. In addition, the processing of obtaining the offset compensation amounts duc [m] and dvc [m] includes processing of obtaining torque amplitude components (u and v) of the two phases of the three-phase AC motor. The processing of obtaining the torque amplitude components of the two phases includes processing of obtaining the torque amplitude components (u and v) of the two phases based on the Fourier coefficient C1 and an electrical angle 0 of the three-phase AC motor at a reference time (n=0) of the torque command value signal c* [n]. Furthermore, the processing of obtaining the offset compensation amounts includes processing of obtaining the offset compensation amounts duc [m] and dvc [m] with respect to the two phases based on the torque amplitude components (u and v) of the two phases.

(63) In addition, the processing of obtaining the offset compensation amounts duc [m] and dvc [m] includes: processing of obtaining, based on the torque amplitude components (u and v) of the two phases, offset compensation change amounts (offset compensation increments duc and dvc) with respect to offset compensation amounts duc [m1] and dvc [m1] previously obtained with respect to the two phases, and obtaining new offset compensation amounts duc [m] and dvc [m] with respect to the two phases based on the offset compensation change amounts with respect to the two phases and the offset compensation amounts duc [m1] and dvc [m1] previously obtained with respect to the two phases. In this case, the U phase and the V phase (the V phase and the W phase) may be direct processing objects and processing of the W phase (U phase) may be executed based on calculation results of the U phase and the V phase (the V phase and the W phase).

(64) As described above, with the position control apparatus 20 of a three-phase AC motor according to the present disclosure shown in FIG. 1, an appropriate per-phase offset compensation amount can be calculated and output and a magnitude of a torque ripple attributable to a current detection DC offset can be minimized both when a drive motor is a permanent magnet synchronous motor (SPMSM and IPMSM) and when the drive motor is an induction motor (IM) or a synchronous reluctance motor (SynRM) for which d-axis current command value id*0 is a prerequisite.