Method of controlling induction motor

There is disclosed a method of controlling an induction motor, which controls a primary current of the induction motor on the basis of a magnetic flux component current command i.sub.1d *, a torque component current command i.sub.1q *, and a slip frequency command .omega..sub.s which are orthogonal component command values of the primary current of the induction motor, wherein control parameters R.sub.2 *, l.sub.2 * and M* set in accordance with a secondary resistance R.sub.2, a secondary leakage inductance l.sub.2 and a mutual inductance M of the induction motor are used to calculate the magnetic flux component current command i.sub.1d *, the torque component current command i.sub.1q * and the slip frequency command .omega..sub.s. Even in the case where the mutual inductance M of the induction motor varies, if the coefficient 1/M* is assumed as a magnetic saturation function given by a gap magnetic flux, the influence of the magnetic saturation can be canceled.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to a method of controlling an induction motor 
power-fed by a power converter. 
2. Prior Art 
In recent years, as a method of power-feeding and controlling an induction 
motor by using a power converter, there has been developed a control 
method called a vector control to deal with current and/or magnetic flux, 
etc. of the induction motor as a vector quantity to control them. By such 
vector control, it has become possible to stably control an induction 
motor by a quick response like a d.c. motor. Thus, induction motors have 
been widely used as control motors. 
Meanwhile, although there is a limitation in an output maximum voltage of a 
power converter for feeding a power to an induction motor, since the 
induced voltage becomes high when the rotational speed becomes high, the 
induction motor is brought into an uncontrollable state when the 
rotational speed is above a predetermined value. For this reason, there 
has been carried out a magnetic flux weakening control to weaken magnetic 
flux to thereby lower an induced voltage to permit control up to a higher 
speed rotational region. In order to weaken the magnetic flux, it is 
sufficient to allow the magnetic flux component current of the induction 
motor to be small. However, since the secondary winding of the induction 
motor is generally in a short-circuited state, damper action takes place, 
so a current to cancel a change in the magnetic flux component current 
transiently flows in the secondary winding. For this reason, the magnetic 
flux cannot vary immediately. A method of solving such a problem is 
disclosed in JP-B 57-38116 (the Japanese Patent Publication No. 
38116/1982). In the method disclosed in this literature, it is assumed 
that the inductance of the induction motor is fixed. However, in actual 
induction motors, the inductance may vary by magnetic saturation. In speed 
control of general induction motors, there is not a serious problem in 
practical use although such magnetic saturation is not taken into 
consideration. Meanwhile, in recent years, such uses of induction motors 
to control the torque are increasing. In such cases of controlling the 
torque of the induction motor, if the influence of the magnetic saturation 
is neglected, it is impossible to attain quick-responding, stable and high 
accuracy control. 
SUMMARY OF THE INVENTION 
Accordingly, an object of this invention is to provide a method of 
controlling an induction motor, which can stably carry out vector control 
of an induction motor with high accuracy and quick response by taking into 
consideration the influence of magnetic saturation. 
To achieve this object, in accordance with this invention, there is 
provided a method of controlling an induction motor, which controls a 
primary current of the induction motor on the basis of a magnetic flux 
component current command (i.sub.1d *), a torque component current command 
(i.sub.1q *), and a slip frequency command (.omega..sub.s) which are 
orthogonal component command values of the primary current of the 
induction motor calculated from a secondary magnetic flux command 
(.PHI..sub.2 *) and a torque command (T*) of the induction motor, 
characterized in that control parameters R.sub.2 *, l.sub.2 * and M* set 
in accordance with a secondary resistance R.sub.2, a secondary leakage 
inductance l.sub.2 and a mutual inductance M of the induction motor are 
used to calculate the magnetic flux component current command (i.sub.1d 
*), the torque component current command (.sub.1q *) and a slip frequency 
command (.omega..sub.s) by the following equations: 
EQU i.sub.1d *=(d.PHI..sub.2 */dt)/R.sub.2 *+(.PHI..sub.2 *+(d.PHI..sub.2 
*/dt)/R.sub.2 *.times.l.sub.2 *)/M* 
EQU i.sub.1q *=T*/.PHI..sub.2 *+(T*/.PHI..sub.2 *.times.l.sub.2)/M* 
EQU .omega..sub.s =T*/.PHI..sub.2.sup.*2 .times.R.sub.2 * 
Further, in accordance with this invention, there is provided a method of 
controlling an induction motor. The method controls a primary current of 
the induction motor on the basis of a magnetic flux component current 
command (i.sub.1d *) and a torque component current command (i.sub.1q *) 
which are orthogonal component command values of the primary current of 
the induction motor calculated from a secondary magnetic flux command 
(.omega..sub.2 *) and a slip frequency command (.omega..sub.s) of the 
induction motor, characterized in that control parameters R.sub.2 *, 
l.sub.2 * and M* set in accordance with a secondary resistance R.sub.2, a 
secondary leakage inductance I.sub.2 and a mutual inductance M of the 
induction motor are used to calculate the magnetic flux component current 
command (i.sub.1d *) and the torque component current command (i.sub.1q *) 
by the following equations: 
EQU i.sub.1d *=(d.PHI..sub.2 */dt)/R.sub.2 *+(.PHI..sub.2 *+(d.PHI..sub.2 
*/dt)/R.sub.2 *.times.l.sub.2 *)/M* 
In accordance with this invention, even if the inductance of the induction 
motor varies, a primary current command is calculated in accordance with 
such a control operational expression capable of canceling that change to 
control a primary current of the induction motor on the basis of the 
primary current command by using a power converter. 
For an analysis of the transient characteristic, etc. of the induction 
motor, a voltage/current differential equation of the induction motor is 
used. A voltage/current differential equation using complex variables of a 
squirrel-cage motor can be expressed by the following equation (1), and 
the torque thereof can be expressed by the following equation (2). It is 
to be noted that the the number of pairs of poles is set to 1. 
##EQU1## 
where v.sub.1s is a primary voltage, 0(v.sub.2S) is a secondary voltage, 
R.sub.1 is a primary resistance, R.sub.2 is a secondary resistance, 
.omega..sub.r is a rotor angular velocity, T is a torque, j is an 
imaginary unit, a.sub.s is a conjugate complex number of a.sub.s, i.sub.1S 
is a primary current, i.sub.2S is a secondary current, L.sub.1 is a 
primary inductance, L.sub.2 is a secondary inductance, M is a mutual 
inductance, s is a differential operator d/dt, and Im(a.sub.s) is an 
imaginary part nary part of a.sub.s. 
It is to be noted that, in the above-mentioned equation (1), for example, 
voltage v and current i, etc. expressed by bold face are complex 
variables. 
The complex variable a.sub.s can be expressed by combination of the real 
part a.sub.ds and the imaginary part a.sub.q (a.sub.s =a.sub.ds 
+ja.sub.qs). Namely, the above-mentioned equation (1) is equivalent to the 
equation of four rows by four columns in general orthogonal (rectangular) 
coordinates in the case where the real part and the imaginary part are 
respectively caused to be in correspondence with the d.sub.s axis and the 
q.sub.s axis, and the rotational direction of .omega..sub.r, etc. is set 
so that the counterclockwise direction from the d.sub.s axis to the 
q.sub.s axis is positive. Since the differential term of the equation (1) 
is originally a term showing a voltage by magnetic flux change, the 
position of the differential operator s is before L.sub.1, L.sub.2, M. 
Namely, this differentiation is not a differentiation of a current, but is 
a differentiation of inductance x current (e.g., L.sub.1 i.sub.1s) which 
is the dimension of magnetic flux. Here, v.sub.1S, i.sub.1S and i.sub.2S 
are replaced as follows: 
##EQU2## 
In the above equation, .theta. is an arbitrary angle. 
v.sub.1, i.sub.1, i.sub.2 can be interpreted as values on the d-q 
coordinates (orthogonal coordinates) obtained by rotating the d.sub.s 
q.sub.s axis by .theta..sub.0. This substitution is equivalent to the 
rotational coordinate transform. In order to rewrite the equation (1) into 
the relationship of values on the coordinates rotating at an angular 
velocity .omega..sub.0 =d.theta..sub.0 /dt, it is sufficient that 
s+j.omega..sub.0 is substituted for s. 
Accordingly, the voltage/current differential equation on the coordinates 
rotating at an angular velocity .omega..sub.0 is expressed by the 
following equation (4) or (5), and the torque is expressed by the 
following equation (6). 
##EQU3## 
In the case of solving the differential equation of the above-mentioned 
equation (5) by simulation, etc., differential terms are put together at 
the left side as indicated by the following equation (7): 
EQU s[L][i]=[v]-([R]+j[.omega.][L])[i] (7) 
[L].sup.-1 is multiplied from the left side: 
EQU [L].sup.-1 s[L][i]=[L].sup.-1 [v]-([L].sup.-1 [R]+j[.omega.][i](8) 
If [L] is constant, [L].sup.-1 s[L] is equal to s. Accordingly, 
EQU s[i]=[L].sup.-1 [v]-([L].sup.-1 [R]+j[.omega.])[i] (9) 
This differential equation is dealt as an equation of state with the 
current [i] being as a state parameter. However, in the case where [L] 
cannot be regarded as a constant by magnetic saturation, etc., [L].sup.-1 
s[L] is not equal to s. Therefore, the equation (9) does not hold, failing 
to obtain a correct solution. The control method disclosed in the 
reference JP-B 57-38116 (the Japanese Patent Publication No. 38116/1982) 
is based on such an analysis technique. 
In the case where [L] cannot be regarded as a constant by magnetic 
saturation, etc.,[L] [i] at the left side of the equation (7) is replaced 
by [.PHI.]. This parameter is selected as a state parameter. 
##EQU4## 
Accordingly, the following relationship holds. 
EQU [i]=[L].sup.-1 [.PHI.] (11) 
.PHI..sub.1 is a magnetic flux interlinking with the primary winding, which 
is called a primary magnetic flux, and .PHI..sub.2 is a magnetic flux 
interlinking with the secondary winding, which is called a secondary 
magnetic flux. Replacement of [L] [i] of the equation (7) by [.PHI.] gives 
the following equation (12). Further, substitution of the equation (11) 
into the equation (12) gives the following equation (13). 
EQU s[.PHI.]=[v]-[R][i]-j[.omega.][.PHI.] (12) 
EQU s[.PHI.]=[v]-([R][L].sup.-1 +j[.omega.])[.PHI.] (13) 
Even in the case where the motor parameters vary, [.PHI.] can be correctly 
solved, and [i] is indirectly calculated by the equation (11) from 
[.PHI.]. Accordingly, if a control method is determined on the basis of 
the above analysis method, it is possible to cope with a change of the 
inductance by magnetic saturation. 
A block diagram of an induction motor in accordance with the above analysis 
method in the case of controlling a primary current by a power converter 
will now be determined. In the case of controlling a primary current, the 
equations related to the primary side are unnecessary, and the equations 
of the portion relating to the secondary side in the equations (12) and 
(10) are the following equations (14) and (15), respectively. 
EQU s.PHI..sub.2 =-R.sub.2 i.sub.2 -j.omega..sub.s .PHI..sub.2 ( 14) 
EQU .PHI..sub.2 =Mi.sub.1 +L.sub.2 i.sub.2 ( 15) 
On the basis of the idea that the mutual inductance M varies by magnetic 
saturation in an induction motor, the secondary inductance L.sub.2 is 
decomposed into the secondary leakage inductance l.sub.2 and the mutual 
inductance M. 
EQU L.sub.2 =l.sub.2 +M (16) 
Substitution of the above-mentioned relationship into the equation (15) 
gives: 
EQU .PHI..sub.2 =M(i.sub.1 +i.sub.2)+l.sub.2 i.sub.2 ( 17) 
Accordingly, 
##EQU5## 
When a block diagram of the induction motor with respect to the primary 
current i.sub.1 is depicted from the equations (14) and (18), FIG. 1 is 
obtained. Inputs/outputs of respective blocks shown in the figure have the 
following relationships in connection with the physical quantity: 
##EQU6## 
Namely, a difference between the primary current i.sub.1 and the excitation 
current i.sub.0 is a secondary current -i.sub.2 of a negative sign. Since 
the secondary winding of the squirrel-cage motor is in a short-circuited 
state, the sum of the voltage drop R.sub.2 i.sub.2 by the secondary 
resistance, speed electromotive voltage j .omega..sub.s .PHI..sub.2 by the 
secondary magnetic flux, and voltage s.PHI..sub.2 by a change in the 
secondary magnetic flux is equal to zero. Integration of -R.sub.2 i.sub.2 
-j.omega..sub.s .PHI..sub.2 gives a secondary magnetic flux .PHI..sub.2. A 
difference between the secondary magnetic flux and the secondary leakage 
magnetic flux is a gap magnetic flux .PHI..sub.0. A current obtained by 
dividing the gap magnetic flux .PHI..sub.0 by the mutual inductance is an 
excitation current i.sub.0. 
In the case where it can be considered that the primary current (actual 
value) i.sub.1 is controlled so that it is equal to a primary current 
command i.sub.1 * and the induction motor is controlled by a current 
source, if the inverse block of the block diagram from the primary current 
i.sub.1 up to the secondary magnetic flux .PHI..sub.2 is assumed as a 
controller as shown in FIG. 2, the transfer function from the secondary 
magnetic flux command .PHI..sub.2 * up to the secondary magnetic flux 
.PHI..sub.2 is caused to be a constant. In this case, .omega..sub.s may 
take an arbitrary value. In FIG. 2, asterisk (*) is attached to motor 
parameters used in the controller. 
The torque T is expressed as the following equation (19) by using the 
secondary magnetic flux .PHI..sub.2 : 
##EQU7## 
For simplifying the controller, the secondary magnetic flux command 
.PHI..sub.2 * is considered to be comprised of only the real part 
.PHI..sub.2 *. If the parameters of the controller are equal to motor 
parameters, the secondary magnetic flux is equal to the command value 
.PHI..sub.2 *, and only the real part is controlled. In this case, the 
relationship expressed as .PHI..sub.2 =.PHI..sub.2 *=.PHI..sub.2 * holds. 
The torque T is expressed by the following equation (20). 
##EQU8## 
Accordingly, if a selection is made such that .omega..sub.s (=.omega..sub.0 
-.omega..sub.r) is expressed as the following equation (21), the torque 
transfer function is also caused to be a constant. 
##EQU9## 
From these relationships, the controller of the vector control for allowing 
the transfer functions of the secondary magnetic flux and the torque of 
the induction motor to be a constant is as shown by the block diagram of 
FIG. 4. The induction motor is controlled in accordance with a primary 
current calculated in accordance with this block diagram. 
While an explanation has been given by using equations as mentioned above, 
the key point is as follows. Namely, the fact that differentiation of the 
differential equation of an induction motor is not differentiation of a 
current, but differentiation of magnetic flux, is taken into consideration 
to determine a block diagram of the induction motor which holds even when 
the inductance varies by magnetic saturation to allow a block diagram 
which has the reversed relationship with respect to the above-mentioned 
block to serve as a controller. Accordingly, even when there is any 
magnetic saturation, if control parameters used in the control operation 
are adjusted in correspondence with parameters of the induction motor, it 
is possible to precisely control the induction motor by a quick response 
both transiently and steadily. It is sufficient that 1/M* is caused to be 
a saturation function with respect to the magnetic saturation of the 
mutual inductance M. In addition, it is sufficient that, also with respect 
to other induction motor parameters, control parameters corresponding 
thereto are caused to be in a suitable function form.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Preferred embodiments of this invention will now be described with 
reference to the attached drawings. 
FIG. 4 shows the example where the control block indicated by using complex 
variables in FIG. 3 is embodied. This control apparatus comprises dividers 
1 and 2, coefficient elements 3, 5, 6, and 9, a differentiator 4, 
adding/subtracting elements 8, 10, 12, 13, 19 and 20, a two-phase sine 
wave generator 14, multipliers 7, 11, 15, 16, 17 and 18, function 
generators 31 and 32, a two-phase/three-phase converter 21, a power 
converter 22, and a speed detector 24. By this control apparatus, the 
primary current of an induction motor 23 is controlled. A magnetic flux 
command .PHI..sub.2 and a torque command T* are given to the control 
apparatus. At the circuit sections indicated by reference numerals 1-12, a 
slip frequency command .omega..sub.s, a magnetic flux component current 
command i.sub.1d * and a torque component current command i.sub.1q * are 
calculated. In accordance with these calculated command .omega..sub.s, 
i.sub.1d * and i.sub.1q *, the induction motor 23 is controlled at the 
circuit sections indicated by reference numerals 13-22. 
At the divider 1, the torque command T* is divided by the secondary 
magnetic flux command .PHI..sub.2 *. As a result, -i.sub.2q * is 
determined by calculation. This -.sub.2q * is further divided by the 
secondary magnetic flux command .PHI..sub.2 * at the divider 2, and an 
output from the divider 2 is multiplied by a coefficient R.sub.2 * 
corresponding to the secondary resistance of the induction motor at the 
coefficient element 3. Thus, slip frequency command .omega..sub.s is 
determined by calculation. Accordingly, the slip frequency command 
.omega..sub.s has the relationship expressed by the following equation 
(22): 
EQU .omega..sub.s =T*/.PHI..sub.2.sup.*2 .times.R.sub.2 * (22) 
On the other hand, output -i.sub.2q * of the divider 1 is multiplied by a 
coefficient l.sub.2 * corresponding to the secondary leakage inductance of 
the induction motor at the coefficient element 6, and an output from the 
coefficient element 6 is multiplied by a coefficient 1/M* corresponding to 
the inverse number of the mutual inductance of the induction motor at the 
multiplier 7. Thus, i.sub.0q * is determined by calculation. The 
coefficient 1/M* is obtained by the function generator 31 on the basis of 
gap magnetic flux .PHI..sub.0 *. Further, -i.sub.2q * and i.sub.0q * are 
added by the adding/subtracting element 8. Thus, a torque component 
current command i.sub.1q * is determined by calculation. Accordingly, the 
torque component current command i.sub.1q * has the relationship expressed 
by the following equation (23): 
EQU i.sub.1q *=T*/.PHI..sub.2 +(T*/.PHI..sub.2 *.times.l.sub.2 *)/M*(23) 
The magnetic flux component current command i.sub.1d * is calculated from 
the secondary magnetic flux command .PHI..sub.2. The secondary magnetic 
flux command .PHI..sub.2 is differentiated at the differentiator 4. An 
output from the differentiator 4 is multiplied by a coefficient 1/R.sub.2 
* corresponding to the inverse number of the secondary resistance of the 
induction motor at the coefficient element 5. Thus, -i.sub.2d * is 
determined by calculation. Then, -i.sub.2d * is multiplied by a 
coefficient l.sub.2 * corresponding to the secondary leakage inductance of 
the induction motor at the coefficient element 9. The secondary magnetic 
flux command .PHI..sub.2 * is further added to the above operation result 
(an output from the coefficient element 9) at the adding/subtracting 
element 10. Thus, .PHI..sub.0d * is obtained. The value .PHI..sub.0d * 
thus obtained is multiplied by a coefficient 1/M* corresponding to the 
inverse number of the mutual inductance of the induction motor at the 
coefficient element 11. Thus, i.sub.0d * is determined by calculation. The 
coefficient 1/M* is obtained by the function generator 32 on the basis of 
gap magnetic flux .PHI..sub.0 * in the same manner as in the case of the 
above-mentioned gap magnetic flux .PHI..sub.0 *. At the adding/subtracting 
element 12, -i.sub.2d * and i.sub.0d * are added. Thus, a magnetic flux 
component current command i.sub.1d * is determined by calculation. 
Accordingly, the magnetic component current command i.sub.1d * has the 
relationship expressed by the following equation (24): 
EQU i.sub.1d *=(d.PHI..sub.2 */dt)/R.sub.2 *+(.PHI..sub.2 *+(d.PHI..sub.2 
*/dt)/R.sub.2 *.times.l.sub.2 *)/M* (24) 
At the adding/subtracting element 13, the slip frequency command 
.omega..sub.s and a speed frequency .omega..sub.r detected by a speed 
detector 24 are added. Thus, a synchronous frequency .omega..sub.0 is 
obtained. A two-phase sine wave of the synchronous frequency .omega..sub.0 
is generated by the two-phase sine wave generator 14. On the basis of the 
two-phase sine wave, by using multipliers 15-18, and adding/subtracting 
elements 19, 20, the magnetic component current command i.sub.1d * and the 
torque component current command i.sub.1q * are converted to two-phase 
a.c. current commands i.sub.d * and i.sub.q *. Further, these two-phase 
a.c. current commands i.sub.d * and i.sub.q * are converted to three-phase 
a.c. current commands i.sub.u *, i.sub.v *, i.sub.w * by the 
two-phase/three-phase converter 21. In accordance with the three-phase 
a.c. current commands, three-phase a.c. primary currents of the induction 
motor 23 are controlled by the power converter 22. 
In the case where, in the apparatus of FIG. 4, the mutual inductance M of 
the induction motor can be considered to be fixed and a corresponding 
controller coefficient M* can be considered to be fixed, it is possible to 
stably control the induction motor by a quick response while controlling 
the secondary magnetic flux with the magnetic flux component current 
command i.sub.1d * and the secondary magnetic flux command .PHI..sub.2 * 
having a fixed relationship therebetween. 
In the case where, in the previously described embodiment, the mutual 
inductance M of the induction motor varies by magnetic saturation, a 
corresponding controller coefficient 1/M* set at the multiplier 7, 11 is 
caused to be a saturation function f(.PHI..sub.0 *) which varies in 
correspondence with saturation of gap magnetic flux .PHI..sub.0 * of the 
induction motor. It is to be noted that the magnitude of the gap magnetic 
flux .PHI..sub.0 is the square root of the sum of the squares of an output 
.PHI..sub.0q * of the coefficient element 6 and an output .PHI..sub.0d * 
of the adding/subtracting element 10. 
##EQU10## 
FIG. 5 shows an example of the configuration of the function generator for 
calculating gap magnetic flux .PHI..sub.0 * and saturation function 
f(.PHI..sub.0). .PHI..sub.0q.sup.*2 obtained by squaring an output 
.PHI..sub.0q * of the coefficient element 6 by using a multiplier 33 and 
.PHI..sub.0d.sup.*2 obtained by squaring an output .PHI..sub.0d * of the 
adder 10 by using a multiplier 34 are added by an adding/subtracting 
element 35. Thus, .PHI..sub.0q.sup.*2 +.PHI..sub.0d.sup.*2 is obtained. By 
calculating square root of .PHI..sub.0q.sup.*2 and .PHI..sub.0d.sup.*2 by 
using an element 36 for extraction of the square root, gap magnetic flux 
.PHI..sub.0 * is determined. By inputting this gap magnetic flux 
.PHI..sub.0 * to a function generator 37, a coefficient 1/M*, i.e., a 
saturation function f(.PHI..sub.0 *)=1/M* is determined. By multiplying 
output .PHI..sub.0q * of the coefficient element 6 and output .PHI..sub.0d 
* of the adding/subtracting element 10 by the coefficient 1/M* determined 
by the function generator 37 (corresponding to function generators 31, 32 
of FIG. 4) by using multipliers 7, 11 i.sub.0q * and i.sub.0d * in which 
magnetic saturation is taken into consideration are obtained. The function 
generator 37 varies in such a manner that when the gap magnetic flux 
.PHI..sub.0 * is small, the coefficient M* is fixed, i.e., the coefficient 
1/M* is fixed, while when the gap magnetic flux .PHI..sub.0 * becomes 
large, the coefficient M* is saturated so that it rapidly becomes small, 
i.e., the coefficient 1/M* rapidly becomes large. This function is set on 
the basis of the result obtained by actually measuring the relationship 
between the gap magnetic flux .PHI..sub.0 * and the mutual inductance M of 
the induction motor. 
In accordance with the above-described embodiment, the influence of 
magnetic saturation can be canceled. Even if there is any magnetic 
saturation, it is possible to stably control the induction motor by a 
quick response while precisely controlling the secondary magnetic flux. 
A second embodiment of this invention will now be described. FIG. 6 shows 
the example where the control block using complex variables of FIG. 2 is 
embodied. This embodiment shows an example of the configuration in the 
case where a slip frequency command .omega..sub.s and a secondary magnetic 
flux command .PHI..sub.2 * are given. In this embodiment, dividers 1 and 2 
and coefficient element 3 for calculating slip frequency command 
.omega..sub.s from the torque command T* and secondary magnetic flux 
command .PHI..sub.2 * are omitted, and a multiplier 25 and a coefficient 
element 26 for calculating a torque component current command i.sub.1q * 
by using slip frequency command .omega..sub.s are newly provided in place 
of the above-mentioned circuit components. 
In the embodiment of FIG. 6, calculation of the magnetic flux component 
current command i.sub.1d * is carried out in the same manner as in the 
embodiment of FIG. 4. The torque component current command i.sub.1q * is 
calculated as follows. Namely, slip frequency command .omega..sub.s and 
the secondary magnetic flux command .PHI..sub.2 * are multiplied at the 
multiplier 25, and an output from the multiplier 25 is multiplied by a 
coefficient 1/R.sub.2 * corresponding to the inverse number of the 
secondary resistance of the induction motor at the coefficient element 26. 
Thus, -i.sub.2q * is determined by calculation Thereafter, -1.sub.2q * is 
multiplied by a coefficient l.sub.2 * corresponding to the secondary 
leakage inductance of the induction motor at the coefficient element 6, 
and an output from the coefficient element 6 is multiplied by a 
coefficient 1/M* corresponding to the inverse number of the mutual 
inductance of the induction motor at the multiplier 7. Thus, i.sub.0q * is 
determined by calculation. Further, -i.sub.2q * and i.sub.0q * are added 
at the adding/subtracting element 8. Thus, a torque component current 
command i.sub.1q * is determined by calculation. Accordingly, the torque 
component current command i.sub.1q * has the relationship expressed by the 
following equation (25): 
EQU i.sub.1q *=.omega..sub.s .times..PHI..sub.2 */R.sub.2 *+(.omega..sub.s 
.times..PHI..sub.2 */R.sub.2 *.times.l.sub.2 *)/M* (25) 
In accordance with this embodiment, in the case where the slip frequency 
command .omega..sub.s and the secondary magnetic flux command .PHI..sub.2 
* are given, the coefficient 1/M* of the coefficient elements 7 and 11 is 
caused to be varied as a function of the magnitude of the gap magnetic 
flux .PHI..sub.0 * in correspondence with the magnetic saturation of the 
induction motor in the same manner as in the embodiment of FIG. 4, thereby 
making it possible to cancel the influence of the magnetic saturation. 
Accordingly, even if there is any magnetic saturation, it is possible to 
stably control the induction motor by a quick response while precisely 
controlling the secondary magnetic flux. 
It is to be noted that since there are various known arts as the circuit 
sections (reference numerals 13-22) for controlling the primary current of 
the induction motor on the basis of the magnetic flux component current 
command i.sub.1d *, the torque component current command i.sub.1q *, the 
slip frequency command .omega..sub.s and the rotational frequency 
.omega..sub.r, they may be suitably used.