Apparatus for controlling an induction motor

[0002] 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.

[0003] 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.

[0004] 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.

[0005] 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, '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.

[0006] 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.

[0007] 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.

[0008] 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.

[0009] FIG. 2 is a schematic diagram showing the calculational function performed by the speed estimator in the speed-control apparatus shown in FIG. 1.

[0010] 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.

[0011] 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.

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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.

[0017] FIG. 10 is a schematic diagram showing the calculational function performed by the slip estimator in the speed-control apparatus shown in FIG. 9.

[0018] 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.

[0019] 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.

[0020] 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.

[0021] 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.

[0022] 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.

[0023] 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.

[0024] 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.

[0025] 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.

[0026] 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.

[0027] Hereafter, details of the embodiments according to the present invention will be explained with reference to the drawings.

[0028] 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 V1*, 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 Ga2 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 ω1{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 ω1* 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 Ga3 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 ω1*. 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 V1* (for three phases) by transforming the coordinates of Vd** and Vq**.

[0029] 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 Ga1 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 Ga2 of the function generator 83. The outputs Ga1 and Ga2 are complementary to each other, which is expressed by the equation (1).

[0030] Ga1+Ga2=1  (1)

[0031] Therefore, the output ωr{circumflex over ( )}{circumflex over ( )} of the switching unit 8 is given by the equation (2).

[0032] ωr{circumflex over ( )}{circumflex over ( )}=ωr{circumflex over ( )}·Gar*·Ga2  (2)

[0033] Further, the output Ga3 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 Ga3 are prepared to smoothly change Id**, and an intermediate value between Id* and Id*+ΔId is output as Id**.

[0034] 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.

[0035] 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.

[0036] 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 ω1*, 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*.

[0037] In the following, the detailed operation of each unit or device will be explained.

[0038] The speed-estimation unit 4 calculates the estimated speed value ωr{circumflex over ( )} based on the equation (3).

[0039] ωr{circumflex over ( )}={1/(1+T0·s)}L2*/(M*−Φd)}{Vq**−ω1*·Lσ*·Id−(Rσ*+Lσ*·s)Iq}  (3)

[0040] where

[0041] T0: a constant of the observer;

[0042] L2*, M*: secondary and exciting inductance values (reference values);

[0043] Φ2d*: a secondary q-axis flux (reference value);

[0044] Rσd*: a sum of primary and secondary resistance values (reference value);

[0045] Lσ*: a sum of primary and secondary leakage inductance values (reference value); and

[0046] ω1*: the output frequency of the power-transformation unit 2 (instruction value).

[0047] 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.

[0048] The estimated value ωr{circumflex over ( )} is used as a feed back signal to the speed-control unit 5, and for the calculation of ω1*. The equation (4) used for the calculation of ω1* is shown below. In the conventional control method, ωr{circumflex over ( )} is directly used as the output frequency reference value ω1* to control the output frequency of the power-conversion unit 2.

[0049] ω1*=ωr{circumflex over ( )}+ωs*  (4)

[0050] 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*, ω1*, and the characteristic parameters of the motor 1. This calculation is performed by the voltage-calculation unit 13.

[0051] Vd=r1·Id−ω1·Lσ·Iq

[0052] Vq=r1·Iq+ω1·Lσ·Id+ω1(M/L2)Φ2d  (5),

[0053] where

[0054] r1: a primary resistance value (actual value);

[0055] Lσ: a sum of primary and secondary leakage inductance values (actual value);

[0056] L2 , M: secondary and exciting inductance values (actual values); and

[0057] Φ2d: a secondary q-axis flux (reference value).

[0058] Vd′=r1*·Id**−ω1*·Lσ*·Iq*

[0059] Vq*=r1*·Iq*+ω1*·Lσ*·Id**+ω1*(M*/L2 *)Φ2d*  (6)

[0060] where * and ** indicate a reference value and an instruction value, respectively.

[0061] 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.

[0062] 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.

[0063] 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.

[0064] 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.

[0065] Specifically, the torque of the motor 1 easily decreases in the speed range near zero due to various kinds of causes.

[0066] 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.

[0067] The decrease of the torque is mainly caused by the error in the estimated speed, and two main causes bring about this error.

[0068] (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.

[0069] (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.

[0070] This embodiment seeks to solve the above problems in accordance with the following control strategies.

[0071] Strategy 1: the output frequency instruction value ω1* is calculated with the speed instruction value ωr* in place of the estimated speed ωr{circumflex over ( )}.

[0072] 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.

[0073] 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.

[0074] 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.

[0075] In the case when the strategies 1 and 2 are adopted, the relationship between the torque generated by the motor 1 and the current I1 is shown in the equation (7).

[0076] τm=K(ωs·T2)/(1+(ωs·T2)²)I1²  (7),

[0077] where

[0078] K: a proportional constant;

[0079] ωs: the slip frequency;

[0080] T2: a secondary time constant; and

[0081] I1: the primary current in the motor 1.

[0082] If I1 is constant, the torque Tm generated by the motor 1 is maximum when ωr·T2=±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 ω1(=(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.

[0083] Here, since the maximum torque of the motor 1 is required to be larger than the maximum load-torque, it is necessary to control I1 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.

[0084] 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 I1) such that Id corresponds to the maximum load-torque.

[0085] 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.

[0086] 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.

[0087] 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 ω1*. The gradual increase and decrease characteristics for the outputs Ga1 and Ga2 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 Ga3 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 I1 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).

[0088] IqMAX={square root over (I1*²−Id²))}  (8)

[0089] where I1* is the setting value of current in the motor 1.

[0090] 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 6a. In this figure, the units or devices 1-3, 5, 7-14, and 16 are the same as those in FIG. 1. Reference number 6aindicates 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 6aalso 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.

[0091] 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 ω1* is obtained from the output of the q-axis current-control unit 6b. In this figure, the units or devices 1-3, 5, 7-14, and 16 are the same as those in FIG. 1. Reference number 6aindicates a q-axis current-control unit for outputting ω1* corresponding to the deviation between Iq* and Iq, and reference number 9aindicates a subtracter for obtaining the estimated speed ωr{circumflex over ( )} by subtracting ωr* from ω1* 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 6balso corresponds to ω1*, it is evident that this embodiment functions in the same manner as the above embodiments, and the same effects can be obtained.

[0092] 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.

[0093] 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 Iq0 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 Iq0 by the output Ga4 (0≦Ga4≦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.

[0094] The operation of the q-axis current instruction unit 17 will be explained below. Since Ga4 is “1” in the speed region near zero, and possesses the gradual increase and decrease characteristics (0≦Ga4≦1) in the region other than the speed region near zero, Iq0 is output from the q-axis current instruction unit 17 in the speed region near zero. Therefore, Iq is controlled according to Iq0, and a sufficient torque can be obtained (Iq0 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.

[0095] 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 Iq0, the same effects of the above embodiments can be obtained with this embodiment.

[0096] 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.

[0097] 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 7a1 indicates a slip frequency calculator for obtaining the calculated slip frequency ωs* based on the q-axis current value Iq, and reference number 9bindicates an adder for obtaining the signal ω1* by adding the speed instruction value ωr* to the signal ωr*.

[0098] 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 ω1* (=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 ω1* by the voltage-calculation unit 13.

[0099] 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.

[0100] 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.

[0101] 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 ω1* 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.

[0102] In the above embodiments, since Iq* is controlled to be zero in the speed range near zero, ωs* is zero. Therefore, the output frequency ω1 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.

[0103] 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.

[0104] 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.

[0105] In this figure, the units or devices 1-6, and 8-16 are the same as those in FIG. 1. Reference number 7bindicates 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 7b1 for obtaining ωs* with the current instruction value Iq*; a slip frequency estimator 7b2 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 ω1*; and an adder 7b3 for obtaining the sum of ωs* and ωs{circumflex over ( )}.

[0106] Here, the output of the adder 9 agrees with (ωr*+ωs{circumflex over ( )}) in the speed range near zero, and with (ωs{circumflex over ( )}·Ga1+ωr*·Ga2+ωs{circumflex over ( )})+ωs*) in the range other than the speed range near zero.

[0107] The slip frequency estimator 7b2 will be explained below.

[0108] First, the composition of the estimator 7b2 will be explained with reference to FIG. 10.

[0109] The ω1* input to the estimator 7b2 is multiplied by a coefficient (M*/L2*), and further by a d-axis flux reference value Φ2d*, and the multiplication result is input to an adder 7b22 along with Δq. Furthermore, Δq and the output signal of the adder 7b22 are input to a divider 7b23. The output signal of the divider 7b23 is multiplied by the reciprocal (1/T2*) of the secondary time constant of the motor 1, and the estimated slip frequency ωs{circumflex over ( )} is output from the slip frequency estimator 7b2.

[0110] Next, the effects of this slip frequency estimator 7b2 will be explained.

[0111] 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).

[0112] Vd**=r1*·Id**−ω1*·Lσ*·Iq*+Δd

[0113] Vq**=r1*·Iq*+ω1*·Lσ*·Id**+ω1*(M*/L2*)Φ2d*+Δq  (9)

[0114] Vd=r1·Id−ω1·Lσ·Iq−ω1(M/L2 )Φ2q

[0115] Vq=r1·Iq+ω1·Lσ·Id+ω1(M/L2 )Φ2d  (10)

[0116] Here, since the equations (9)=the equations (10), the outputs of the current-control units 12 and 6 are expressed by the equations (11).

[0117] Δd=(r1−r1*)Id−ω1(Lσ−Lσ*)Iq−ω1(M/L2)Φ2q

[0118] Δq=(r1−r1*)Iq+ω1(Lσ−Lσ*)Id+ω1((M/L2 )Φ2d−(M*/L2 *)Φ2d*)  (11),

[0119] provided that ω1*=ω1, Id**=Id, and Iq*=Iq.

[0120] 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).

[0121] Then, Δd and Δq in the equations (11) are expressed by the equations (12).

[0122] Δd≈(r1−r1*)Id−(ω1(M/L2 )Φ2q

[0123] Δq≈ω1{(M/L2 )Φ2d−(M*/L2 *)Φ2d*}  (12)

[0124] Thus, Δd almost agrees with the induced-electromotive force Ed (=ω1(M/L2)Φ2q) related to the q-axis flux Φ2q.

[0125] On the other hand, if the induced-electromotive force reference value ω1(M*/L2*)Φ2d* is added to Δq, the induced-electromotive force Ed (=ω1((M/L2)Φ2d) related to the d-axis flux Φ2d is obtained.

[0126] From the equations (12), the equation (13) is obtained.

[0127] Δq+ω1*(M*/L2 *)Φ2d*=ω1(M/L2 )Φ2d  (13)

[0128] 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 Φ2d and Φ2q, and the slip frequency ωs in the motor 1 is expressed by the equation (14). $\begin{array}{cc}\begin{array}{c}\omega s=\left(1/\mathrm{T2}\right)\left(-\varphi 2q/\varphi 2q\right)\\ =\left(1/\mathrm{T2}\right)\left(\mathrm{ed}/\mathrm{eq}\right)\end{array}& \left(14\right)\end{array}$

[0129] Further, by performing the calculation indicated by the equation (15), the estimated slip frequency ωs{circumflex over ( )} can be obtained.

[0130] ωs{circumflex over ( )}=(1/T2*){Δd/(Δq+ω1*(M*/L2 *)Φ2d*)}  (15)

[0131] 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).

[0132] ωs{circumflex over ( )}=Iq*·M/(T2*·Φ2d)  (16)

[0133] Here, the output frequency instruction value ω1* 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.

[0134] ω1*=ωr{circumflex over ( )}{circumflex over ( )}+ωs*+ωs{circumflex over ( )}  (17)

[0135] 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.

[0136] 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**.

[0137] By subtracting the resistance voltage-decrease r1·Id and the leakage inductance voltage-decrease ω1·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. $\begin{array}{cc}\begin{array}{c}{\mathrm{ed}}^{^}={\mathrm{Vq}}^{**}-{\mathrm{r1}}^{*}·{\mathrm{Id}}^{*}+-\omega 1^{*}\left(m^{*}/{\mathrm{L2}}^{*}\right)\varphi 2q^{^}\\ {\mathrm{ed}}^{^}={\mathrm{Vd}}^{**}-{\omega 1}^{*}·L{\sigma }^{*}·{\mathrm{Id}}^{**}\\ ={\omega 1}^{*}\left(M^{*}/{\mathrm{L2}}^{*}\right)\varphi 2d^{^}\end{array}& \left(18\right)\end{array}$

[0138] Since as is obtained by the equation (14), ωs{circumflex over ( )} can be calculated by the equation (19) using Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )}, or ed{circumflex over ( )} and ed{circumflex over ( )}. $\begin{array}{cc}\begin{array}{c}\omega s^{^}=\left(1/{\mathrm{T2}}^{*}\right)\left(-\varphi 2q^{^}/\varphi 2q^{^}\right)\\ =\left(1/{\mathrm{T2}}^{*}\right)\left({\mathrm{ed}}^{^}/{\mathrm{eq}}^{^}\right)\end{array}& \left(19\right)\end{array}$

[0139] By controlling the speed according to ω1 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.

[0140] 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.

[0141] 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).

[0142] Vq*≈ω1(M/L2 )Φ2d  (20)

[0143] Further, since Δd is obtained by the equations (12), ωs{circumflex over ( )} can be calculated by the equation (21) using Δd and Vq*.

[0144] ωs{circumflex over ( )}=(1/T2*)(Δd/Vq*)  (21)

[0145] By controlling the speed according to ω1 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.

[0146] Although the slip frequency-calculation unit 7bshown 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 7cshown in FIG. 12.

[0147] The unit 7cis the slip frequency-calculation unit for calculating the sum ωs** of ωs* and ωs{circumflex over ( )}, which includes a slip frequency calculator 7c1 for obtaining ωs* using Id and Φ2d{circumflex over ( )}; a slip frequency estimator 7c2 for obtaining ωs{circumflex over ( )} using Φ2d and Φ2q{circumflex over ( )}; an adder 7c3 for adding Φs{circumflex over ( )} to ωs*; a d-axis flux estimator 7c4 for calculating Φ2d{circumflex over ( )} using Δq and ω1*; and a q-axis flux estimator 7c5 for calculating Φ2q{circumflex over ( )} using Δd and ω1*.

[0148] First, the d-axis flux estimator 7c4, which is one of the elements composing the slip frequency-calculation unit 7c, will be explained below with reference to FIG. 13.

[0149] The ω1* input to the estimator 7c4 is multiplied by the coefficient (M*/L2*), and further by the d-axis flux reference value Φ2d*, and the multiplication result is input to the adder 7c42 along with Δq. Further, the output of the adder 7c42 and the value ω1* (M*/L2*) are input to a divider 7c43, and the divider 7c43 outputs the estimated flux Φ2d.

[0150] Next, the q-axis flux estimator 7c5 will be explained below with reference to FIG. 14.

[0151] The ω1* input to the estimator 7c5 is multiplied by the coefficient (M*/L2*), and the multiplication result is input to the divider 7c52 along with Δd. Further, the divider 7c52 outputs the estimated flux Φ2q{circumflex over ( )}.

[0152] The composition of the slip frequency estimator 7c2 for calculating ωs{circumflex over ( )} using the calculated Φ2d and Φ2q is shown in FIG. 15.

[0153] The estimated values Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )} input to the slip frequency estimator 7c2 are input to a divider 7c21.

[0154] The output signal of the divider 7c21 is multiplied by the reciprocal (I/T2*) of the secondary time constant of the motor 1, and the estimator 7c2 outputs the estimated slip frequency ωs{circumflex over ( )}. Further, the frequency instruction value is corrected with the obtained ωs{circumflex over ( )} and ωs*.

[0155] In this control method, the estimated fluxes Φ2d and Φ2q 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 Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )} as shown by the equations (23). Thus, the speed is controlled according to ω1* which is calculated based on the equations (17) using the obtained values ωs{circumflex over ( )} and ωs*.

[0156] Φ2d=[{Δq+ω1*(M*/L2 *)Φ2d*}/(ω1*M*/L2 *)]

[0157] Φ2q={Δq/(ω1*M*/L2 *)}  (22)

[0158] ωs=(1/T2*)(−Φ2q/Φ2q{circumflex over ( )})

[0159] ωs*=Iq*·M*/(T2*·Φ2d{circumflex over ( )})  (23)

[0160] 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.

[0161] Further, by using a slip frequency-calculation unit 7d shown in FIG. 16 in place of the slip frequency-calculation unit 7bshown in FIG. 9, the same effects can also be obtained.

[0162] The unit 7dis a slip frequency-calculation unit for obtaining the sum ωs** of ωs* and ωs{circumflex over ( )}, which includes a slip frequency calculator 7d1 for obtaining ωs* using Iq* and Φ2d{circumflex over ( )}; a slip frequency estimator 7d2 for obtaining (s using Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )}; an adder 7d3 for adding ωs{circumflex over ( )} to ωs*; and a flux estimator 7d4 for calculating Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )} using Vd** and Vq**, and ω1*.

[0163] The composition of the flux estimator 7d4, which is one of elements composing the unit 7d, is shown in FIG. 17.

[0164] Vd**, the calculated resistance voltage-decrease value (r1*·Id*), and the calculated leakage inductance voltage-decrease value (−ω1*·Lσ*·Iq*) are input to a subtracter 7d41. Further, by multiplying ω1* by the coefficient (M*/L2*), and further by Φ2q, the estimated d-axis induced-electromotive force ed{circumflex over ( )} is obtained. The obtained value ed{circumflex over ( )} is input to a subtracter 7d43 along with the output signal of the subtracter 7d41. Furthermore, the output signal of the subtracter 7d43 is input to an integrator 7d44, and the estimated flux Φ2d{circumflex over ( )} is output from the integrator 7d44.

[0165] Also, Vq**, the calculated resistance voltage-decrease value (r1*·Iq*), and the calculated leakage inductance voltage-decrease value (−ω1*·Lσ*·Id**) are input to a subtracter 7d45.

[0166] Further, by multiplying ω1* by the coefficient (M*/L2*), and further by ω2d{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 7d46 along with the output signal of the subtracter 7d45. Furthermore, the output signal of the subtracter 7d46 is input to an integrator 7d47, and the estimated flux Φ2q is output from the integrator 7d47.

[0167] In this speed control method, Φ2d and Φ2q are obtained by the equations (24) based on the output voltage, and ωs{circumflex over ( )} is then calculated.

[0168] Φ2d{circumflex over ( )}=∫[Vd**−r1·Id**+ω1*·Lσ*·Iq*−ω1*(M*/L2 *)Φ2q{circumflex over ( )}]dt

[0169] Φ2q{circumflex over ( )}=≠[Vq**−r1·Iq*+ω1*·Lσ*·Id*+ω1*(M*/L2 *)Φ2d{circumflex over ( )}]dt  (24)

[0170] That is, Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )} are obtained with the flux estimator 7d4 using the voltage instruction values Vd** and, and Vq**, and the calculator 7d1 and the estimator 7d2 shown in FIG. 16 calculate ωs* and ωs{circumflex over ( )}, respectively, according to the equations (23). Further, the adder 7d3 adds ωs* to ωs{circumflex over ( )}, and the frequency instruction value ω1* is corrected with the sum ωs{circumflex over ( )}{circumflex over ( )}.

[0171] In this control method also, the same operation and effects as those of the embodiment shown in FIG. 9 can be achieved.

[0172] Meanwhile, the respective calculational functions of the calculator 7d1 and the estimator 7d2 are the same as those of the calculator 7c1 and the estimator 7c2.

[0173] 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 ( )}.

[0174] 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.

[0175] 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 ω1*.

[0176] The output signal τm{circumflex over ( )} is input to a function generator 11a1 in the d-axis current instruction unit 11a. The function generator 11a1 calculates a correction gain Ga5 (0≦Ga5.≦1) based on the output signal τm{circumflex over ( )}.

[0177] In a multiplier 11a1, the increment ΔId* of the current instruction value is multiplied by the above Ga5. 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 11a. 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 ω1*.

[0178] τm{circumflex over ( )}=(Vd**·Id+Vq**·Iq)/ω1*  (25)

[0179] Id** which corresponds to the load torque is calculated according to the equation (26) using τm{circumflex over ( )} obtained by the above equation (25).

[0180] Id**=Id*+F(τm{circumflex over ( )})·ΔId*  (26),

[0181] provided that the output Ga5 of F(τm{circumflex over ( )}) is as follows:

[0182] that is;

[0183] if |τm{circumflex over ( )}|=0, then Ga5 0, and

[0184] if |τm{circumflex over ( )}|≈0, then 0<Ga5≦1.

[0185] The value of Id according to the equation (26) is as follows:

[0186] without a load (|τm{circumflex over ( )}|=0), Id**=Id*, and

[0187] with a load (|τm{circumflex over ( )}|>0), Id**>Id*.

[0188] Thus, since Id** is corrected corresponding to the load torque, the operational efficiency in an operation with a light load can be increased.

[0189] 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** .

[0190] τm{circumflex over ( )}=(Vd**·Id+Vq*·Iq)/ω1*  (27)

[0191] 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.

[0192] 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 Φ2d{circumflex over ( )} and Φ2q{circumflex over ( )}.

[0193] τm{circumflex over ( )}=K1(Φ2d{circumflex over ( )}·Iq−Φ2q{circumflex over ( )}Id)  (28),

[0194] where K: a torque constant.

[0195] 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.

[0196] 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 ( )}.

[0197] 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.

[0198] In this figure, the units or devices 1-10, and 12-16 are the same as those in FIG. 7. Reference number 11bindicates a d-axis current instruction unit for calculating the gain Ga6 corrected with ωs**.

[0199] The calculated slip frequency ωs** is input to a function generator 11b1 in the instruction unit 11b. The function generator 11b1 calculates the gain Ga6 (0≦Ga6≦1) to be corrected.

[0200] A multiplier 11b2 multiplies the gain Ga6 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 11b.

[0201] Next, the effects of the d-axis current instruction unit 11bwhich is one of the main features of the present invention will be explained below. The calculated slip frequency is proportional to the torque.

[0202] 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.

[0203] Id**=Id*+F(ωs**)·ΔId*  (29)

[0204] provided that the output Ga6 of F(ωs**) is as follows:

[0205] that is;

[0206] if |ωs**|=0, then Ga6 0, and

[0207] if |ωs**|>0, then 0<Ga6≦1.

[0208] If Id obtained by the equation (29) is used,

[0209] without a load (|ωs**|=0), Id**=Id*, and

[0210] with a load (|ωs**|>0), Id**>Id*.

[0211] 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.

[0212] 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.

[0213] 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.