Patent Publication Number: US-6670786-B2

Title: Apparatus for controlling an induction motor

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a divisional of U.S. application Ser. No. 09/550,252, filed in the U.S. Patent and Trademark Office on Apr. 14, 2000, now U.S. Pat. No. 6,344,726, and priority is hereby claimed under 35 USC 119 and 120 based on the aforementioned U.S. patent application and Japanese Patent Application Serial No. 11-115941, filed Apr. 23, 1999. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates in general to an apparatus for controlling the rotational speed (hereafter referred to as the speed) of an induction motor; and, the invention relates especially to a an apparatus using a vector control method which operates without a speed sensor, and is capable of achieving a highly accurate speed control without a speed sensor, and which can obtain high torque from a zero speed range. 
     In the vector control of an induction motor, the output frequency of a power-conversion unit for the induction motor usually corresponds to the sum of the speed and the calculated slip frequency. On the other hand, in the vector control method which operates without a speed sensor, the output frequency of the power-conversion unit is controlled with an estimated value of the speed in place of a detected value of the speed. However, since the estimated value of the speed includes an error, the actual slip frequency shifts from the target reference value. In this situation, the magnetic flux (hereafter referred to as the flux) in the induction motor varies according to the torque, and accordingly the torque generated by the induction motor is not proportional to the torque current, which in turn causes a shortage of torque in an extreme case. 
     Setting-errors in characteristic parameters of the induction motor, which are used for estimating the speed, and changes in the flux in the induction motor, which are caused by the errors, etc., are considered to be the causes of the errors in the estimated speed. A means to effectively correct those changes of the flux has not been devised, and a shortage of torque sometimes occurs in the range near zero speed. A report “Simplified Vector Control System without Speed and Voltage Sensors—Effects of Setting Errors in Control Parameters and their Compensation” by T. Okuyama et al., T. IEE Japan, Vol. 110-D, No. 5, &#39;90, discloses the effects of the setting errors in the parameters and a means to compensate the effects due to the setting errors of the parameters of the induction motor. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a an apparauts using method of accurately and efficiently controlling an induction motor without experiencing the effects of errors in an estimated speed due to changes in constants of the induction motor. 
     To achieve the above object, the present invention provides a speed-control apparatus for an induction motor for controlling the current output from a power-conversion unit so that it is larger than a current value in the ordinary no-load operation, or for controlling the frequency output from the power-conversion unit by calculating a frequency instruction value based on a speed instruction value in place of an estimated speed value if the speed instruction value is less than a predetermined value. By the above control, it is possible to prevent a shortage of torque in the low speed range near zero speed. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of an embodiment according to the present invention. 
     FIG. 2 is a schematic diagram showing the calculational function performed by the speed estimator in the speed-control apparatus shown in FIG.  1 . 
     FIG. 3 is a diagram showing the relationship between the speed and the torque generated in an induction motor controlled by a conventional control method. 
     FIG. 4 is a diagram showing the relationship between the speed and the torque generated in an induction motor controlled by an apparatus using the control method according to the present invention. 
     FIG. 5 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of another embodiment according to the present invention. 
     FIG. 6 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of still another embodiment according to the present invention. 
     FIG. 7 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of yet another embodiment according to the present invention. 
     FIG. 8 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of another embodiment according to the present invention. 
     FIG. 9 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of another embodiment according to the present invention. 
     FIG. 10 is a schematic diagram showing the calculational function performed by the slip estimator in the speed-control apparatus shown in FIG.  9 . 
     FIG. 11 is a diagram showing the relationship between the speed and the torque generated in an induction motor controlled with the slip estimator and the slip frequency-calculator according to the present invention. 
     FIG. 12 is a schematic diagram showing the calculational function performed by the slip frequency-calculation unit in the speed-control apparatus shown in FIG.  9 . 
     FIG. 13 is a schematic diagram showing the calculational function performed by the d-axis flux estimator in the slip frequency-calculation unit shown in FIG.  12 . 
     FIG. 14 is a schematic diagram showing the calculational function performed by the q-axis flux estimator in the slip frequency-calculation unit shown in FIG.  12 . 
     FIG. 15 is a schematic diagram showing the calculational function performed by the slip estimator in the slip frequency-calculation unit shown in FIG.  12 . 
     FIG. 16 is a schematic diagram showing the calculational function performed by another example of the slip frequency-calculation unit in the speed-control apparatus shown in FIG.  9 . 
     FIG. 17 is a schematic diagram showing the calculational function performed by the flux estimator in the slip frequency-calculation unit shown in FIG.  16 . 
     FIG. 18 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of another embodiment according to the present invention. 
     FIG. 19 is a schematic block diagram showing the circuit composition of a speed-control apparatus for an induction motor of another embodiment according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     Hereafter, details of the embodiments according to the present invention will be explained with reference to the drawings. 
     FIG. 1 shows the schematic circuit composition of a speed-control apparatus for an induction motor representing an embodiment according to the present invention. The apparatus includes an induction motor  1 , a power-conversion unit  2  for outputting output voltages proportional to voltage instruction values V 1 *, and a coordinate-transformation unit  3  for transforming the coordinates of output currents iu and iw and calculating d-axis and q-axis currents Id and Iq. A speed-estimation unit  4  is provided for calculating an estimated speed ωr{circumflex over ( )} based on a q-axis voltage instruction value Vq** and the current Iq. A speed-control unit  5  is provided for outputting a q-axis current instruction value Iq* corresponding to a difference between a speed instruction value ωr{circumflex over ( )} and the estimated speed ωr{circumflex over ( )}, which further includes a limiter for limiting the instruction value Iq* corresponding to the value of Id. A q-axis current-control unit  6  is provided *for outputting Δq corresponding to the values Iq* and Iq, and a slip frequency-calculation unit  7  is provided, in which a slip frequency calculator  71  is included for obtaining a calculated slip frequency based on the value Iq*. A switching unit  8  is provided, which includes a multiplier  82  for multiplying ωr{circumflex over ( )} by the output Gal of a function generator  81 , a multiplier  84  for multiplying ωr{circumflex over ( )} by the output Ga 2  of a function generator  83 , and an adder  85  for summing the outputs from both the multipliers  81  and  84 , for switching its output ωr{circumflex over ( )}{circumflex over ( )} between ωr{circumflex over ( )} and ωr* corresponding to the value of the speed. An adder  9  is provided for obtaining a signal ω 1 {circumflex over ( )} by summing the output signal ωr{circumflex over ( )}{circumflex over ( )} of the switching unit  8  and ωs*, and a phase-generation unit  10  is provided for outputting a phase reference value θ by integrating the output frequency instruction value ω 1 * of output from the adder  9 . A d-axis current instruction unit  11  is provided, including a multiplier  112  for multiplying an additional current value ΔId by the output Ga 3  of a function generator  111  and an adder  113  for obtaining a d-axis current instruction value Id** by summing a reference current value Id* and the output of the multiplier  111 . A d-axis current-control unit  12  is provided for outputting a signal Δd corresponding to a difference between Id** and Id and a voltage-calculation unit  13  is provided for calculating d-axis and q-axis reference voltages Vd* and Vq* based on Id**, Iq*, and ω 1 *. Further, adders  14  and  15  are provided for outputting Vd** by summing Vd* and Δd and a coordinate-transformation unit  16  is provided for outputting output-voltage instruction values V 1 * (for three phases) by transforming the coordinates of Vd** and Vq**. 
     In the above units, the units  8  and  11  are specific to this embodiment. The performances of the function generators included in the respective units  8  and  11  are as follows. The output Ga 1  of the function generator  81  is 0 near the input value 0, and 1 in the range of a large input value, and vice versa as to the output Ga 2  of the function generator  83 . The outputs Ga 1  and Ga 2  are complementary to each other, which is expressed by the equation (1). 
     
       
         Ga 1 +Ga 2 =1  (1) 
       
     
     Therefore, the output ωr{circumflex over ( )}{circumflex over ( )} of the switching unit  8  is given by the equation (2). 
     
       
         ω r{circumflex over ( )}{circumflex over ( )}=ωr{circumflex over ( )}·Ga 1 +ω   r *·Ga 2   (2) 
       
     
     Further, the output Ga 3  of the function generator  111  is 0 if ωr* is near 0, and 1 if ωr* is in the range of a large value. Accordingly, Id** and Id are increased from the reference value Id* by ΔId. The gradual increase and decrease regions of Ga 3  are prepared to smoothly change Id**, and an intermediate value between Id* and Id*+ΔId is output as Id**. 
     The operation of the induction motor control system according to this embodiment will be explained below. The operations of the units or devices  1 - 7 ,  9 ,  10 , and  12 - 16  are the same as those in the conventional vector control system without a speed sensor. First, the outline of the conventional vector control system without a speed sensor will be explained. 
     In the conventional vector control system without a speed sensor, the speed is estimated based on the output voltage and current of the power-conversion unit  2 , and the speed is controlled by feeding-back the estimated speed ωr{circumflex over ( )} to the speed-control unit  5 . Further, the output frequency of the power-conversion unit  2  is controlled based on the sum of the estimated speed ωr{circumflex over ( )} and the calculated slip frequency ωs*. The difference between the vector control without a speed sensor and the well-known vector control with a speed sensor is that, in the vector control system without a speed sensor, the estimated speed is used in place of the speed detected by a speed sensor mounted on the induction motor  1 . However, the fundamental operation is common to both the controls. 
     To control the current flows Id and Iq in the induction motor  1  according to the d-axis current instruction value and the q-axis current instruction value output from the speed-control unit  5 , it is necessary to feed the required voltage to the induction motor  1  from the power-conversion unit  2 . Therefore, the voltage-calculation unit  13  calculates the d and q-axis voltage reference values Vd* and Vq* based on the current instruction values Id** and Iq*, and the output frequency instruction value ω 1 *, and the output voltage of the power-conversion unit  2  is controlled according to the calculated voltage reference values Vd* and Vq*. However, since the current flows Id and Iq agree with their instruction values due to control errors by performing only the above control, the reference voltage values Vd* and Vq* are corrected with the Δd and Δq output from the d and q-axis current-control units  12  and  6  so that the current flows Id and Iq agree with their instruction values. In this way, the slip frequency-control-type vector control is performed, and the torque of the induction motor  1  is controlled in proportion to Iq*. 
     In the following, the detailed operation of each unit or device will be explained. 
     The speed-estimation unit  4  calculates the estimated speed value ωr{circumflex over ( )} based on the equation (3). 
     
       
         ω r{circumflex over ( )}={ 1/(1+ T   0 · s )} L   2 */( M*−Φ 2     d )}{ Vq **−ω 1   *·Lσ*·Id −( Rσ*+Lσ*·s ) Iq}   (3) 
       
     
     where 
     T 0 : a constant of the observer; 
     L 2 *, M*: secondary and exciting inductance values (reference values); 
     Φ 2 d*: a secondary q-axis flux (reference value); 
     Rσd*: a sum of primary and secondary resistance values (reference value); 
     Lσ*: a sum of primary and secondary leakage inductance values (reference value); and 
     ω 1 *: the output frequency of the power-transformation unit  2  (instruction value). 
     FIG. 2 shows the calculational function performed based on the equation (3) by the speed estimator  4 . Reference number  41  indicates the model of the inductance motor  1 , which shows the relationship among the q-axis current Vq (=Vq**) of the motor  1 , the induced-electromotive force Eq, and the current Iq. In the method of estimating ωr{circumflex over ( )}, Eq is estimated with the inverse model of the motor  1 , and ωr{circumflex over ( )} obtained by dividing the estimated Eq by the reference flux. 
     The estimated value ωr{circumflex over ( )} is used as a feed back signal to the speed-control unit  5 , and for the calculation of ω 1 *. The equation (4) used for the calculation of ω 1 * is shown below. In the conventional control method, ωr{circumflex over ( )} is directly used as the output frequency reference value ω 1 * to control the output frequency of the power-conversion unit  2 . 
     
       
         ω 1 *=ω r{circumflex over ( )}+ωs*   (4) 
       
     
     In the speed-control unit  5 , the q-axis current instruction value Iq* is calculated corresponding to the speed deviation (ωr*−ωr*). Since the torque of the motor  1  is basically proportional to Iq*, the speed is controlled such that ωr* agrees with ωr{circumflex over ( )}. In order that the torque of the motor  1  is precisely proportional to Iq*, it is required that the current value Iq of the motor  1  agrees with Iq*, and the flux in the motor  1  is kept at the reference value. To attain the above conditions, it is necessary to control the current values Id and Iq of the motor  1  so as to agree with the respective instruction values Id** and Iq*. To implement the above control, the d and q-axis current-control units  12  and  6  are equipped. Although the voltage values Vd and Vq of the motor  1  under various operational conditions are expressed by the equations (5), the reference voltage values Vd* and Vq* corresponding to Vd and Vq can be calculated in advance with the equations (6) using Id**, Iq*, ω 1 *, and the characteristic parameters of the motor  1 . This calculation is performed by the voltage-calculation unit  13 . 
     
       
           Vd=r   1   ·Id −ω 1   ·Lσ·Iq   
       
     
     
       
           Vq=r   1   ·Iq +ω 1   ·Lσ·Id +ω 1 ( M/L   2 )Φ 2   d   (5), 
       
     
     where 
     r 1 : a primary resistance value (actual value); 
     Lσ: a sum of primary and secondary leakage inductance values (actual value); 
     L 2  , M: secondary and exciting inductance values (actual values); and 
     Φ 2 d: a secondary q-axis flux (reference value). 
     
       
           Vd′=r   1 *· Id **−ω1*· Lσ*·Iq*   
       
     
     
       
           Vq*=r   1 *· Iq *+ω 1 *· Lσ*·Id **+ω 1 *( M*/L   2  *)Φ 2   d*   (6) 
       
     
     where * and ** indicate a reference value and an instruction value, respectively. 
     The output voltage of the power-conversion unit  2  (the voltage in the motor  1 ) is basically controlled according to Vd* and Vq*. If a control error exists, the actual current values Id and Iq do not agree with the respective instruction values by performing only the above control. Therefore, the adjustment signals Δd and Δq corresponding to the respective current deviations are obtained by the d and q-axis current-control units  12  and  6 , and the output voltage of the power-conversion unit  2  is corrected based on the adjustment signals Δd and Δq so that Id and Iq agree with the respective instruction values. The operations which are explained up to here are common to the conventional control method. 
     FIG. 3 shows the relationship between the speed ωr and the torque τm generated in an induction motor controlled by a conventional control method in the speed range near zero. The shadowed region in this figure indicates an unstable region in which the decrease of the torque easily happens. 
     In the shadowed region, the range 0.5-1 Hz of speed for corresponds to an unstable area in the motoring region in which the signs of τm and ωr are the same, and the range less than several Hz of speed cor corresponds to an unstable area in the regeneration region in which the sign of τm is different from the sign of ωr. Also, if the estimation error in ωr{circumflex over ( )} obtained by the speed-estimation unit  4  increases, the shadowed region is extended, which in turn sometimes makes the on-load operation of the motor  1  at a low speed impossible. 
     The estimation error in ωr{circumflex over ( )} is caused by changes in the temperature of the primary and secondary resistance values; changes in the leakage-inductance values due to the flux saturation in the iron core of the motor  1 ; etc. 
     Specifically, the torque of the motor  1  easily decreases in the speed range near zero due to various kinds of causes. 
     The control method of this embodiment, which is aimed at preventing the decrease of the torque, controls the motor  1  in the speed range near zero with a control principle different from the above conventional control method. This control principle is mentioned below. 
     The decrease of the torque is mainly caused by the error in the estimated speed, and two main causes bring about this error. 
     (1) since the frequency is controlled based on the estimated speed, the actual slip frequency is deviated from the proper value due to the estimation error. 
     (2) Since the speed is controlled based on the estimated speed, the estimation error makes it impossible to control the torque current at the proper value. 
     This embodiment seeks to solve the above problems in accordance with the following control strategies. 
     Strategy 1: the output frequency instruction value ω 1 * is calculated with the speed instruction value ωr* in place of the estimated speed ωr{circumflex over ( )}. 
     That is, the output frequency of the power-conversion unit  2  is controlled according to the speed instruction value ωr* in the speed region near zero by outputting ωr* from the switching unit  8  in place ωr{circumflex over ( )} used in the ordinary speed region. 
     Strategy 2: the output current of the power-conversion unit  2  is controlled at a predetermined value larger than that in the ordinary no-load operation. 
     For example, the q-axis current is set to zero, and the d-axis current is controlled at a predetermined value larger than that in the ordinary no-load operation. In this control, ΔId is added to the reference value by the d-axis current instruction unit  11  so as to control the current Id at a larger value. 
     In the case when the strategies 1 and 2 are adopted, the relationship between the torque generated by the motor  1  and the current I 1  is shown in the equation (7). 
     
       
         τ m=K (ω s·T   2 )/(1+(ω s·T   2 ) 2 ) I   1   2   (7), 
       
     
     where 
     K: a proportional constant; 
     ωs: the slip frequency; 
     T 2 : a secondary time constant; and 
     I 1 : the primary current in the motor  1 . 
     If I 1  is constant, the torque Tm generated by the motor  1  is maximum when ωr·T 2 =±1, and τm changes corresponding to the value of ωs between 0 and ±1. The slip frequency ωr changes corresponding to changes in the actual speed ωr in response to the output frequency ω 1 (=(ωr*). That is, since ωr increases or decreases corresponding to the increase or decrease of a load torque, the torque is generated following a load torque. Consequently, the speed ωr of the motor  1  is kept near ωr* (deviates by a slip). Thus, the speed is controlled according to the speed instruction value. 
     Here, since the maximum torque of the motor  1  is required to be larger than the maximum load-torque, it is necessary to control I 1  so as to be a value larger than that corresponding to the maximum load-torque. Therefore, Id or Iq is controlled to attain such a value. 
     Although Id or Iq can be set to the predetermined value independent of the speed deviation, since detecting the direction of the load torque based on the estimated speed ωr{circumflex over ( )} is difficult because of the bad estimation accuracy of speed ωr{circumflex over ( )} in the speed range near zero, the polarity of Iq* cannot be set. Therefore, a method of setting Id** to the predetermined value, for which setting of the polarity is not necessary, is used in the embodiment shown in FIG.  1 . In this method, as mentioned in Strategy 2, Iq* is set to 0, and Id** is set to the sum of the reference value Id* in the ordinary speed region and ΔId to control Id (corresponds to I 1 ) such that Id corresponds to the maximum load-torque. 
     In the speed range near zero, since the output frequency and current of the power-conversion unit  2  are controlled as mentioned above, the above problems (1) and (2) are solved, which in turn solves the problem of the shortage in torque. 
     FIG. 4 shows the relationship between the speed and the torque generated by the induction motor  1  in this embodiment. The unstable region (shadowed region) shown in FIG. 3 disappears in FIG.  4 . Although the speed changes by a slip frequency, a high torque value can be achieved even in the speed region including and near zero. 
     In the regions corresponding to frequency values less than negative several Hz and more than positive several Hz, the output or the switching unit  8  shown in FIG. 1 is switched from ωr* to ωr{circumflex over ( )},and the frequency is controlled using the estimated speed by the same method as that in the conventional control. Moreover, to smoothly switch the output of the switching unit  8 , the switching between ωr* and ωr{circumflex over ( )} is gradually performed so as to prevent a rapid change due to the switching ω 1 *. The gradual increase and decrease characteristics for the outputs Ga 1  and Ga 2  of the function generators  81  and  82  are prepared to implement the above objective. Also, in the d-axis current-instruction unit, The gradual increase and decrease characteristics for the output Ga 3  are prepared to prevent a rapid change in Id*. Further, in the operational state in which Id should be enhanced (the speed region near zero), since it is necessary to restrict Id* such that the current I 1  in the motor  1  does not exceed the rated value, and Iq* deviates from the proper value due to the degradation in accuracy in the estimated speed ωr{circumflex over ( )}, Iq* is required to be set to a predetermined value or almost zero. In this embodiment, the limit value IqMax of Iq* is changed corresponding to Id based on the equation (8). 
     
       
           Iq MAX={square root over (I 1 * 2 − Id   2 ))}  (8) 
       
     
     where I 1 * is the setting value of current in the motor  1 . 
     FIG. 5 shows a schematic block diagram of the circuit composition of a speed-control apparatus for the induction motor  1  representing another embodiment according to the present invention. This embodiment is an application example of a vector control apparatus without a speed sensor, in which the estimated speed ωr{circumflex over ( )} is obtained from the output of the q-axis current-control unit  6   a . In this figure, the units or devices  1 - 3 ,  5 ,  7 - 14 , and  16  are the same as those in FIG.  1 . Reference number  6   a  indicates a q-axis current-control unit for outputting ωr{circumflex over ( )} corresponding to the deviation between Iq* and Iq, and the switching unit  8  selects and outputs one of ωr* and ωr{circumflex over ( )} depending on the value of ωr* as well as that in the previous embodiment. In the ordinary speed range, as well as in the conventional control, since ωr{circumflex over ( )} is output from the switching unit  8 , and the output of the current-control unit  6   a  also corresponds to ωr{circumflex over ( )}, it is evident that this embodiment functions in the same manner as the previous embodiment, and the same effects can be obtained. 
     Further, FIG. 6 shows a schematic block diagram of the circuit composition of a speed-control apparatus for the induction motor  1  of another embodiment according to the present invention. This embodiment is an application example of a vector control apparatus without a speed sensor, in which the estimated speed ω 1 * is obtained from the output of the q-axis current-control unit  6   b . In this figure, the units or devices  1 - 3 ,  5 ,  7 - 14 , and  16  are the same as those in FIG.  1 . Reference number  6   a  indicates a q-axis current-control unit for outputting ω 1 * corresponding to the deviation between Iq* and Iq, and reference number  9   a  indicates a subtracter for obtaining the estimated speed ωr{circumflex over ( )} by subtracting ωr* from ω 1 * and for feeding back ωr{circumflex over ( )} to the speed-control unit  5 . The switching unit  8  selects and outputs one of ωr* and ωr{circumflex over ( )} depending on the value of ωr* as well as that in the previous embodiment. In the ordinary speed range, as well as in the conventional control, since ωr{circumflex over ( )} is output from the switching unit  8 , and the output of the current-control unit  6   b  also corresponds to ω 1 *, it is evident that this embodiment functions in the same manner as the above embodiments, and the same effects can be obtained. 
     Although Id is controlled to attain the predetermined enhanced value in the speed range near zero, if both the positive and negative directions of the torque possibly exist in the speed range near zero, and the direction is not fixed, the control method of this embodiment, in which Iq* is set to zero, and Id is enhanced, is suitable for this case. On the other hand, if there is only one direction of the torque, since the polarity of Iq* can be set corresponding to the direction of the torque, it is possible to set Iq* to a predetermined value (corresponds to the maximum load-torque) in place of setting Id to a predetermined value as performed in the previous embodiment in the speed range near zero. 
     Furthermore, FIG. 7 shows a schematic block diagram of the circuit composition of a speed-control apparatus for the induction motor  1  representing another embodiment according to the present invention. In this figure, the compositions and operations of the units or devices  1 - 10 , and  12 - 16  are the same as those in FIG.  1 . Reference number  17  indicates a q-axis current instruction unit for outputting the sum of the set current value Iq 0  which is modified depending on the value of ωr* and the output Iq* of the speed-control unit  5 , and this q-axis current instruction unit  17  includes a multiplier  172  for multiplying Iq 0  by the output Ga 4  (0≦Ga 4 ≦1) of a function generator  171  with the gradual increase and decrease characteristics, and an adder  173  for outputting Iq** by adding Iq* to the output of the multiplier  172 . 
     The operation of the q-axis current instruction unit  17  will be explained below. Since Ga 4  is “1” in the speed region near zero, and possesses the gradual increase and decrease characteristics (0≦Ga 4 ≦1) in the region other than the speed region near zero, Iq 0  is output from the q-axis current instruction unit  17  in the speed region near zero. Therefore, Iq is controlled according to Iq 0 , and a sufficient torque can be obtained (Iq 0  is set to a value which corresponds to the maximum load-torque.) On the other hand, in the region other than the speed region near zero, Iq is controlled based on Iq, which is the same as the conventional control. 
     In this way, in the speed range near zero, since the output frequency of the power-conversion unit  2  is controlled according to ωr*, and the current in the motor  1  is controlled based on the predetermined value Iq 0 , the same effects of the above embodiments can be obtained with this embodiment. 
     In the above embodiments, although the speed-control unit  5  is provided, and the control methods in those embodiments are applied to a speed-control method in which the torque is controlled based on Iq* or Iq** output from the speed-control unit  5 , the present invention can be applied to a control method which operates without the speed-control unit  5 . 
     FIG. 8 shows a schematic block diagram of the circuit composition of a speed-control apparatus for the induction motor  1  representing another embodiment without the speed-control unit  5 . In this figure, the units or devices  1 - 3 ,  10 - 14 , and  16  are the same as those in FIG.  1 . Reference number  7   a   1  indicates a slip frequency calculator for obtaining the calculated slip frequency ωs* based on the q-axis current value Iq, and reference number  9   b  indicates an adder for obtaining the signal ω 1 * by adding the speed instruction value ωr* to the signal ωr*. 
     The operation of the control system shown in FIG. 8 will be explained below. In the region other than the speed region near zero, the frequency instruction value ω 1 * (=ωr*+ωs*) is output, and the d-axis current instruction value Id** is output from the d-axis current instruction unit  11 . Thus, the operation of this system is the same as that of the conventional vector control without a sensor. That is, the output frequency of the power-conversion unit  2  is controlled mostly according to ωr*, and the output voltage of the power-conversion unit  2  is also controlled based on the necessary voltage of the motor  1  which is calculated based on Id**, Iq, and ω 1 * by the voltage-calculation unit  13 . 
     Since the output voltage and frequency of the power-conversion unit  2  are controlled as explained above, an operation similar to that of a V/f control is performed. 
     However, since the induced-electromotive-force (the magnetic flux in the motor  1 ) is controlled so as to attain a predetermined value by compensating the internal voltage decrease in the motor  1  with the voltage-calculation unit  13  in this embodiment, a sufficient quantity of torque can be obtained to the speed range near zero. 
     In the speed range near zero, the d-axis current instruction unit  11  outputs the instruction value Id** obtained by adding ΔId to Id* in order to enhance Id. By this control, in this embodiment as well as the previous embodiment, the frequency instruction value ω 1 * is controlled according to the speed reference value ωr*, and the d-axis current is controlled so as to have a higher value than that in the ordinary speed range. Accordingly, the shortage of the torque can be eliminated. 
     In the above embodiments, since Iq* is controlled to be zero in the speed range near zero, ωs* is zero. Therefore, the output frequency ω 1  agrees with the speed instruction value ωr*. Thus, if a load torque is applied to the motor  1 , the speed ωr of the motor  1  deviates from ωr* by the slip frequency ωs. This deviation can be compensated by estimating the slip frequency using the voltage instruction values Vd** and Vq** in the embodiment shown in FIG. 1, or the outputs Δd and Δq of the current-control units  12  and  6 , which are obtained based on the output voltage values of the power-conversion unit  2 , and by adding the estimated slip frequency ωr{circumflex over ( )} to the frequency instruction value. 
     Further, the estimated slip frequency obtained based on the output voltage values is added to the calculated slip frequency obtained using the current instruction value Iq. Furthermore, this sum is used as a new calculated slip frequency to correct the frequency instruction value, and this makes it possible to compensate the deviation of the speed due to the load torque in the whole speed range from zero. 
     FIG. 9 shows a schematic block diagram of the circuit composition of a speed control apparatus for the induction motor  1  representing another embodiment which implements the above-mentioned control. This embodiment applies the above control to the vector control apparatus without a speed sensor shown in FIG.  1 . 
     In this figure, the units or devices  1 - 6 , and  8 - 16  are the same as those in FIG.  1 . Reference number  7   b  indicates a slip frequency-calculation unit for calculating the slip frequency ωs* and the estimated slip frequency ωs{circumflex over ( )} and obtaining the sum ωs** of ωs* and ωs{circumflex over ( )}. Further, there is provided a slip frequency calculator  7   b   1  for obtaining ωs* with the current instruction value Iq*; a slip frequency estimator  7   b   2  for obtaining ωs{circumflex over ( )} with the outputs Δd and Δq of the current-control units  12  and  6 , and the output frequency instruction value ω 1 *; and an adder  7   b   3  for obtaining the sum of ωs* and ωs{circumflex over ( )}. 
     Here, the output of the adder  9  agrees with (ωr*+ωs{circumflex over ( )}) in the speed range near zero, and with (ωs{circumflex over ( )}·Ga 1 +ωr*·Ga 2 +ωs{circumflex over ( )})+ωs*) in the range other than the speed range near zero. 
     The slip frequency estimator  7   b   2  will be explained below. 
     First, the composition of the estimator  7   b   2  will be explained with reference to FIG.  10 . 
     The ω 1 * input to the estimator  7   b   2  is multiplied by a coefficient (M*/L 2 *), and further by a d-axis flux reference value Φ 2 d*, and the multiplication result is input to an adder  7   b   22  along with Δq. Furthermore, Δq and the output signal of the adder  7   b   22  are input to a divider  7   b   23 . The output signal of the divider  7   b   23  is multiplied by the reciprocal (1/T 2 *) of the secondary time constant of the motor  1 , and the estimated slip frequency ωs{circumflex over ( )} is output from the slip frequency estimator  7   b   2 . 
     Next, the effects of this slip frequency estimator  7   b   2  will be explained. 
     The voltage instruction values Vd** and Vq**, and the voltage values Vd and Vq in the motor  1  are expressed by the equations (9) and (10). 
     
       
           Vd**=r   1 *· Id **−ω 1   *·Lσ*·Iq*+Δd   
       
     
     
       
           Vq**=r   1 *· Iq *+ω 1   *·Lσ*·Id **+ω 1 *( M*/L   2 *)Φ 2   d*+Δq   (9) 
       
     
     
       
           Vd=r   1   ·Id −ω 1 · Lσ·Iq −ω 1 ( M/L   2  )Φ 2   q   
       
     
     
       
           Vq=r   1   ·Iq +ω 1   ·Lσ·Id +ω 1 ( M/L   2  )Φ 2   d   (10) 
       
     
     Here, since the equations (9)=the equations (10), the outputs of the current-control units  12  and  6  are expressed by the equations (11). 
     
       
         Δ d =( r   1   −r   1 *) Id −ω 1 ( Lσ−L σ*) Iq −ω 1 ( M/L   2 )Φ 2   q   
       
     
     
       
         Δ q =( r   1   −r   1 *) Iq +ω 1 ( Lσ−L σ*) Id +ω 1 (( M/L   2  )Φ 2   d −( M*/L   2  *)Φ 2   d *)  (11), 
       
     
     provided that ω 1 *=ω 1 , Id**=Id, and Iq*=Iq. 
     Since the q-axis current Iq is controlled to be zero in the speed range near zero, if Iq=0, or Lσ≈Lσ*, the second term is sufficiently small to be neglected in comparison with the third term in the equations (11). 
     Then, Δd and Δq in the equations (11) are expressed by the equations (12). 
     
       
         Δ d ≈( r   1   −r   1 *) Id− (ω 1 ( M/L   2  )Φ 2   q   
       
     
     
       
         Δ q ≈ω 1 {( M/L   2  )Φ 2   d −( M*/L   2  *)Φ 2   d*}   (12) 
       
     
     Thus, Δd almost agrees with the induced-electromotive force Ed (=ω 1 (M/L 2 )Φ 2 q) related to the q-axis flux Φ 2 q. 
     On the other hand, if the induced-electromotive force reference value ω 1 (M*/L 2 *)Φ 2 d* is added to Δq, the induced-electromotive force Ed (=ω 1 ((M/L 2 )Φ 2 d) related to the d-axis flux Φ 2 d is obtained. 
     From the equations (12), the equation (13) is obtained. 
     
       
         Δ q +ω 1 *( M*/L   2  *)Φ 2   d *=ω 1 ( M/L   2  )Φ 2   d   (13) 
       
     
     Here, if Id and Iq are controlled such that Id is a predetermined value, and Iq=0, in the above method, the relationship among the fluxes Φ 2 d and Φ 2 q, and the slip frequency ωs in the motor  1  is expressed by the equation (14).                      ω                 s     =                  (     1   /   T2     )                     (       -   ϕ                   2                   q   /   ϕ                   2                 q     )                   =                  (     1   /   T2     )                     (     ed   /   eq     )                     (   14   )                         
     Further, by performing the calculation indicated by the equation (15), the estimated slip frequency ωs{circumflex over ( )} can be obtained. 
     
       
         ω s {circumflex over ( )}=(1 /T   2 *){Δ d /(Δ q +ω 1 *( M*/L   2  *)Φ 2   d *)}  (15) 
       
     
     On the other hand, in the range other than the speed range near zero, the current instruction value Iq* is generated by the speed-control unit  5 . In this region, the estimated slip frequency ωs{circumflex over ( )} is obtained using Iq* as shown by the equation (16). 
     
       
         ω s{circumflex over ( )}=Iq*·M /( T   2 *·Φ 2   d )  (16) 
       
     
     Here, the output frequency instruction value ω 1 * is obtained by adding the sum ωs** of ωs{circumflex over ( )} obtained by the equation (15) and ωs* obtained by the equation (16) to the output ωs{circumflex over ( )}{circumflex over ( )} of the switching unit  8 . 
     
       
         ω 1 *=ω r{circumflex over ( )}{circumflex over ( )}+ωs*+ωs{circumflex over ( )}   (17) 
       
     
     FIG. 11 shows the relationship between the speed and the torque generated in an induction motor controlled using the above slip frequency-compensation method according to the present invention. By means of this slip frequency-compensation method, the deviation of the speed can be corrected corresponding to the torque from the speed range near zero (ωr≈0), which in turn makes it possible to achieve a highly accurate speed control of the motor  1 . 
     Moreover, although ωs{circumflex over ( )} is calculated using Δd and Δq in this embodiment shown in FIG. 9, ωs{circumflex over ( )} can also be obtained using the induced-electromotive force values ed{circumflex over ( )} and eq{circumflex over ( )} calculated from the voltage instruction values Vd** and Vq**. 
     By subtracting the resistance voltage-decrease r 1 ·Id and the leakage inductance voltage-decrease ω 1 ·Lσ·Id from Vd and Vq, respectively, the respective values ed{circumflex over ( )} and eq{circumflex over ( )} can be obtained as shown by the equations (18). ed{circumflex over ( )}. Here, in the speed range near zero, Iq=0.                      ed             ^       =                  Vq   **     -       r1   *     ·     Id   *       +       -   ω                     1   *          (       m   *     /     L2   *       )        ϕ                 2          q                ^                       ed             ^       =                  Vd   **     -           ω      1     *     ·   L                       σ   *     ·     Id   **                       =                      ω      1     *          (       M   *     /     L2   *       )          ϕ                 2          d                ^                     (   18   )                         
     Since as is obtained by the equation (14), ωs{circumflex over ( )} can be calculated by the equation (19) using Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )}, or ed{circumflex over ( )} and ed{circumflex over ( )}.                      ω                   s   ^       =                  (     1   /     T2   *       )                     (       -   ϕ                   2                     q   ^     /   ϕ                   2                   q   ^       )                   =                  (     1   /     T2   *       )                     (       ed             ^       /     eq   ^       )                     (   19   )                         
     By controlling the speed according to ω 1  calculated by the equation (17) using the obtained ωs{circumflex over ( )} and ωs*, the same effects as those of the speed control performed based on the equation (15) can be achieved. 
     Although this control method is applied to the control apparatus shown in FIG. 1 in the above embodiment shown in FIG. 9, if this invention is applied to the control apparatuses shown in FIGS. 5,  6 , and  8 , ωs{circumflex over ( )} is calculated p based on the voltage instruction value Vq* and the output Δd of the current-control unit  12 . 
     That is, since Vq*=Vq (the second one of the equations (6) the second one of the equations (10)), Iq=0, and the effect of leakage inductance voltage-decrease is small enough to be neglected (even if Lσ≈Lσ*), Vq* is expressed by the equation (20). 
     
       
           Vq *≈ω 1 ( M/L   2  )Φ 2   d   (20) 
       
     
     Further, since Δd is obtained by the equations (12), ωs{circumflex over ( )} can be calculated by the equation (21) using Δd and Vq*. 
     
       
         ω s {circumflex over ( )}=(1 /T   2 *)(Δ d/Vq *)  (21) 
       
     
     By controlling the speed according to ω 1  calculated by the equation (17) using the obtained ωs{circumflex over ( )} and ωs*, the same operation and effects as those of the embodiment shown in FIG. 9 which is controlled based on the equation (15) can be achieved. 
     Although the slip frequency-calculation unit  7   b  shown in FIG. 9 is used in the above embodiments, the same effects as those of the above embodiment can be obtained using a slip frequency-calculation unit  7   c  shown in FIG.  12 . 
     The unit  7   c  is the slip frequency-calculation unit for calculating the sum ωs** of ωs* and ωs{circumflex over ( )}, which includes a slip frequency calculator  7   c   1  for obtaining ωs* using Id and Φ 2 d{circumflex over ( )}; a slip frequency estimator  7   c   2  for obtaining ωs{circumflex over ( )} using Φ 2 d and Φ 2 q{circumflex over ( )}; an adder  7   c   3  for adding Φs{circumflex over ( )} to ωs*; a d-axis flux estimator  7   c   4  for calculating Φ 2 d{circumflex over ( )} using Δq and ω 1 *; and a q-axis flux estimator  7   c   5  for calculating Φ 2 q{circumflex over ( )} using Δd and ω 1 *. 
     First, the d-axis flux estimator  7   c   4 , which is one of the elements composing the slip frequency-calculation unit  7   c , will be explained below with reference to FIG.  13 . 
     The ω 1 * input to the estimator  7   c   4  is multiplied by the coefficient (M*/L 2 *), and further by the d-axis flux reference value Φ 2 d*, and the multiplication result is input to the adder  7   c   42  along with Δq. Further, the output of the adder  7   c   42  and the value ω 1 * (M*/L 2 *) are input to a divider  7   c   43 , and the divider  7   c   43  outputs the estimated flux Φ 2 d. 
     Next, the q-axis flux estimator  7   c   5  will be explained below with reference to FIG.  14 . 
     The ω 1 * input to the estimator  7   c   5  is multiplied by the coefficient (M*/L 2 *), and the multiplication result is input to the divider  7   c   52  along with Δd. Further, the divider  7   c   52  outputs the estimated flux Φ 2 q{circumflex over ( )}. 
     The composition of the slip frequency estimator  7   c   2  for calculating ωs{circumflex over ( )} using the calculated Φ 2 d and Φ 2 q is shown in FIG.  15 . 
     The estimated values Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )} input to the slip frequency estimator  7   c   2  are input to a divider  7   c   21 . 
     The output signal of the divider  7   c   21  is multiplied by the reciprocal (I/T 2 *) of the secondary time constant of the motor  1 , and the estimator  7   c   2  outputs the estimated slip frequency ωs{circumflex over ( )}. Further, the frequency instruction value is corrected with the obtained ωs{circumflex over ( )} and ωs*. 
     In this control method, the estimated fluxes Φ 2 d and Φ 2 q are obtained by the equations (22) based on the output voltage values, and ωs{circumflex over ( )} and ωs* are further calculated using the estimated fluxes Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )} as shown by the equations (23). Thus, the speed is controlled according to ω 1 * which is calculated based on the equations (17) using the obtained values ωs{circumflex over ( )} and ωs*. 
      Φ 2   d=[{Δq +ω 1 *( M*/L   2  *)Φ 2   d *}/(ω 1 * M*/L   2  *)] 
     
       
         Φ 2   q={Δq /(ω 1 * M*/L   2  *)}  (22) 
       
     
     
       
         ω s =( 1 / T   2 *)(−Φ 2   q /Φ 2   q {circumflex over ( )}) 
       
     
     
       
         ω s*=Iq*·M */( T   2 *·Φ 2   d {circumflex over ( )})  (23) 
       
     
     In this control method also, the same operation and effects as those of the embodiment shown in FIG. 9 which is controlled based on the equation (14) can be achieved. 
     Further, by using a slip frequency-calculation unit  7 d shown in FIG. 16 in place of the slip frequency-calculation unit  7   b  shown in FIG. 9, the same effects can also be obtained. 
     The unit  7   d  is a slip frequency-calculation unit for obtaining the sum ωs** of ωs* and ωs{circumflex over ( )}, which includes a slip frequency calculator  7   d   1  for obtaining ωs* using Iq* and Φ 2 d{circumflex over ( )}; a slip frequency estimator  7   d   2  for obtaining (s using Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )}; an adder  7   d   3  for adding ωs{circumflex over ( )} to ωs*; and a flux estimator  7   d   4  for calculating Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )} using Vd** and Vq**, and ω 1 *. 
     The composition of the flux estimator  7   d   4 , which is one of elements composing the unit  7   d , is shown in FIG.  17 . 
     Vd**, the calculated resistance voltage-decrease value (r 1 *·Id*), and the calculated leakage inductance voltage-decrease value (−ω 1 *·Lσ*·Iq*) are input to a subtracter  7   d   41 . Further, by multiplying ω 1 * by the coefficient (M*/L 2 *), and further by Φ 2 q, the estimated d-axis induced-electromotive force ed{circumflex over ( )} is obtained. The obtained value ed{circumflex over ( )} is input to a subtracter  7   d   43  along with the output signal of the subtracter  7   d   41 . Furthermore, the output signal of the subtracter  7   d   43  is input to an integrator  7   d   44 , and the estimated flux Φ 2 d{circumflex over ( )} is output from the integrator  7   d   44 . 
     Also, Vq**, the calculated resistance voltage-decrease value (r 1 *·Iq*), and the calculated leakage inductance voltage-decrease value (−ω 1 *·Lσ*·Id**) are input to a subtracter  7   d   45 . 
     Further, by multiplying ω 1 * by the coefficient (M*/L 2 *), and further by ω 2 d{circumflex over ( )}, the estimated q-axis induced-electromotive force eq{circumflex over ( )} is obtained. The obtained value eq{circumflex over ( )} is input to a subtracter  7   d   46  along with the output signal of the subtracter  7   d   45 . Furthermore, the output signal of the subtracter  7   d   46  is input to an integrator  7   d   47 , and the estimated flux Φ 2 q is output from the integrator  7   d   47 . 
     In this speed control method, Φ 2 d and Φ 2 q are obtained by the equations (24) based on the output voltage, and ωs{circumflex over ( )} is then calculated. 
     
       
         Φ 2   d{circumflex over ( )}=∫[Vd**−r   1   ·Id **+ω 1   *·Lσ*·Iq *−ω 1 *( M*/L   2  *)Φ 2   q{circumflex over ( )}]dt   
       
     
     
       
         Φ 2   q{circumflex over ( )}=≠[Vq**−r   1   ·Iq *+ω 1   *·Lσ*·Id *+ω 1 *( M*/L   2  *)Φ 2   d{circumflex over ( )}]dt   (24) 
       
     
     That is, Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )} are obtained with the flux estimator  7   d   4  using the voltage instruction values Vd** and, and Vq**, and the calculator  7   d   1  and the estimator  7   d   2  shown in FIG. 16 calculate ωs* and ωs{circumflex over ( )}, respectively, according to the equations (23). Further, the adder  7   d   3  adds ωs* to ωs{circumflex over ( )}, and the frequency instruction value ω 1 * is corrected with the sum ωs{circumflex over ( )}{circumflex over ( )}. 
     In this control method also, the same operation and effects as those of the embodiment shown in FIG. 9 can be achieved. 
     Meanwhile, the respective calculational functions of the calculator  7   d   1  and the estimator  7   d   2  are the same as those of the calculator  7   c   1  and the estimator  7   c   2 . 
     In the above embodiments, the d-axis current Id is controlled to be constant independent of the load torque, but the operational efficiency deteriorates in an operation with light load-torque. Here, the operational efficiency in the operation with light load-torque can be improved by correcting the current instruction value Id**, corresponding to an estimated torque τm{circumflex over ( )}. 
     FIG. 18 shows the circuit composition of a speed-control apparatus for an induction motor of an embodiment in which this speed control method is used. In this embodiment, the above q-axis current-correction method according to this control method is applied to the control apparatus shown in FIG.  1 . 
     In this figure, the units or devices  1 - 10 , and  12 - 16  are the same as those in FIG.  1 . Reference number  18  indicates a torque estimator for calculating the output torque of the motor  1  based on the voltage instruction values Vd** and Vq**, the detected current values Id and Iq, and the frequency instruction value ω 1 *. 
     The output signal τm{circumflex over ( )} is input to a function generator  11   a   1  in the d-axis current instruction unit  11   a . The function generator  11   a   1  calculates a correction gain Ga 5  (0≦Ga 5 .≦1) based on the output signal τm{circumflex over ( )}. 
     In a multiplier  11   a   1 , the increment ΔId* of the current instruction value is multiplied by the above Ga 5 . Further, Id** is obtained by adding Id* to the result of the multiplication, and the sum is output from the d-axis current instruction unit  11   a . Next, a torque estimator  18  will be explained. The estimator  18  performs the calculation shown by the equation (25) based on Vd** and Vq**, Id and Iq, and ω 1 *. 
     
       
         τ m {circumflex over ( )}=( Vd**·Id+Vq**·Iq )/ω 1 *  (25) 
       
     
     Id** which corresponds to the load torque is calculated according to the equation (26) using τm{circumflex over ( )} obtained by the above equation (25). 
     
       
           Id**=Id*+F (τ m{circumflex over ( )} )·Δ Id*   (26), 
       
     
     provided that the output Ga 5  of F(τm{circumflex over ( )}) is as follows: 
     that is; 
     if |τm{circumflex over ( )}|=0, then Ga 5  0, and 
     if |τm{circumflex over ( )}|≈0, then 0&lt;Ga 5 ≦1. 
     The value of Id according to the equation (26) is as follows: 
     without a load (|τm{circumflex over ( )}|=0), Id**=Id*, and 
     with a load (|τm{circumflex over ( )}|&gt;0), Id**&gt;Id*. 
     Thus, since Id** is corrected corresponding to the load torque, the operational efficiency in an operation with a light load can be increased. 
     Although this control method is applied to the control apparatus shown in FIG. 1, if it is applied to the respective control apparatuses shown in FIGS. 5,  6 , and  8 , τm{circumflex over ( )} is calculated by the equation (27) using the voltage instruction reference value Vq* in place of the voltage instruction value Vq** . 
     
       
         τ m {circumflex over ( )}=( Vd**·Id+Vq*·Iq )/ω 1 *  (27) 
       
     
     By calculating Id** which changes corresponding to the load torque with the τm{circumflex over ( )} calculated according to the above equation, the same operation and effects as those of the above embodiments can be achieved. 
     Moreover, although the estimated torque τm{circumflex over ( )} is calculated by using vd** and Vq**, and Id and Iq in this embodiment, it is possible to obtain τm{circumflex over ( )} according to the equation (28) using the estimated fluxes Φ 2 d{circumflex over ( )} and Φ 2 q{circumflex over ( )}. 
     
       
         τ m{circumflex over ( )}=K   1 (Φ 2   d{circumflex over ( )}·Iq −Φ 2   q{circumflex over ( )}Id )  (28), 
       
     
     where K: a torque constant. 
     By calculating Id** which changes corresponding to the load torque with τm{circumflex over ( )} calculated according to the above equation, the same operation and effects as those of the above embodiments can be achieved. 
     Further, although the operational efficiency in an operation with a light load is improved by correcting Id, corresponding to τm{circumflex over ( )}, the same effects can be obtained using the calculated slip frequency ωs** in place of τm{circumflex over ( )}. 
     FIG. 19 shows a schematic block diagram of the circuit composition of a speed-control apparatus for an induction motor of this embodiment. This embodiment is an example of a control method for correcting Id** by using ωs**, which is applied to the apparatus shown in FIG.  1 . 
     In this figure, the units or devices  1 - 10 , and  12 - 16  are the same as those in FIG.  7 . Reference number  11   b  indicates a d-axis current instruction unit for calculating the gain Ga 6  corrected with ωs**. 
     The calculated slip frequency ωs** is input to a function generator  11   b   1  in the instruction unit  11   b . The function generator  11   b   1  calculates the gain Ga 6  (0≦Ga 6 ≦1) to be corrected. 
     A multiplier  11   b   2  multiplies the gain Ga 6  by the increment ΔId**. Further, Id** is obtained by adding the result of the multiplication to Id*, and the sum is output from the current instruction unit  11   b.    
     Next, the effects of the d-axis current instruction unit  11   b  which is one of the main features of the present invention will be explained below. The calculated slip frequency is proportional to the torque. 
     Accordingly, if Id is controlled using ωs** in accordance with the equation (29), the same effects as those of the above embodiments can be obtained. 
     
       
           Id**=Id*+F (ωs**)·Δ Id*   (29) 
       
     
     provided that the output Ga 6  of F(ωs**) is as follows: 
     that is; 
     if |ωs**|=0, then Ga 6  0, and 
     if |ωs**|&gt;0, then 0&lt;Ga 6 ≦1. 
     If Id obtained by the equation (29) is used, 
     without a load (|ωs**|=0), Id**=Id*, and 
     with a load (|ωs**|&gt;0), Id**&gt;Id*. 
     Thus, since Id is corrected corresponding to the load torque (ωs**), it is apparent that the same operations and effects as the above embodiments can be obtained. 
     Although this control method is applied to the control apparatus shown in FIG. 1, if it is applied to the respective control apparatuses shown in FIGS. 5,  6 , and  8 , ωs{circumflex over ( )} is obtained by the equation (21) using the ratio of Δd to Vq*, and by correcting Id** corresponding to the sum ωs** of ωs{circumflex over ( )} and ωs*, the same operations and effects as the above embodiments can be obtained. 
     In accordance with the present invention, it is possible to provide an apparatus using a speed-control method for an induction motor, which does not cause a shortage in the torque in the speed range near zero.