JPH0532998B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a vector control device for an induction motor. In recent years, as a control method to improve the quick response of induction motors, the primary current of the motor is controlled by dividing it into an excitation current and a secondary current, and the secondary magnetic flux and secondary current vector are always orthogonal, so that the motor is equivalent to a DC motor. A vector control method has been proposed that attempts to obtain high responsiveness. However, when a voltage source inverter such as a pulse width modulation (PWM) inverter is used in the power converter that is actually used, the voltage becomes the manipulated variable even though the primary current is controlled. There was a problem in that the primary current did not flow as per the settings, resulting in poor response and making accurate variable speed control difficult. In the primary voltage control of the electric motor, the present invention uses vector control that can cancel mutual interference between the secondary magnetic flux and the secondary current.
It is an object of the present invention to provide a vector control device that solves conventional problems and also provides the effects described below. EMBODIMENT OF THE INVENTION Hereinafter, following the principle explanation of the present invention, embodiments will be explained in detail. First, the voltage equation expressed by the α-β axis that rotates the induction motor in synchronization with the primary voltage is the following equation (1).
The generated torque T is expressed as Equation (2).

【table】

[Table] Equations (1) and (2) above are expressed as the first block diagram.
As shown in the figure, for the two-phase voltages e ₁ 〓, e ₁ 〓, the α-axis and β-axis components of the primary current and secondary magnetic flux i ₁ 〓, i ₁ 〓,
This is an equivalent block diagram of an induction motor that generates λ' ₂ 〓, λ' ₂ 〓 and torque T. Here, the α and β axes, which rotate in synchronization with the primary voltage, may be set at any phase, but if the α axis is set in the direction of the secondary magnetic flux, the condition that the secondary current matches the β axis, that is, , the conditions for the secondary current to be orthogonal to the magnetic flux are λ′ ₂ 〓=constant λ′ ₂ 〓0 ……(3), and the primary frequency ω ₀ is ω ₀ as clarified by vector control theory. =ω _r +Mr ₂ /L ₁ λ′ ₂ 〓・i ₁ 〓 ...(4). In this way, when the α and β axes are determined, the primary current i ₁
The α-axis component i ₁ 〓 (=constant) is a primary current corresponding to the magnetic flux λ′ ₂ , and the β-axis component i ₁ 〓 is a primary current corresponding to the secondary current i′ ₂ . Next, when the conditions of equations (3) and (4) above are inserted into the block diagram of FIG. 1, the block diagram shown in FIG. 2 is obtained. That is, point a in FIG. 1 is controlled to zero from the relationship of equation (4). Since point c is λ′ ₂ 〓=0, all the quantities connected to this point are zero, and similarly i′ ₂ 〓
The quantity connected from =0 to point d is also zero, and since λ' ₂ = constant, its differential at point b is also zero. Then, when calculating the part of the broken line block A in Fig. 1 under the same conditions, L ₂ /r ₂ = r ₂ , L = [(L ₁ L ₂ - M ² )/L ₃ ], and (L 〓＋M／L ₂ r ₂・L ₂ ／L ₂ P＋r ₂・M／L ₂ )ω ₀ i ₁ 〓 = (L〓＋M ² /L ₂ /τ ₂ P+1)ω ₀ i ₁ 〓 =L〓τ ₂ P＋L ₁ L ₂ −M ² ／L ₃ ＋M ² ／L ₂ ／τ ₂ P＋１ω ₀ i ₁
〓 =L〓/L ₁ τ ₂ P+1/τ ₂ P+1L ₁ ω ₀ i ₁ 〓 Here, since i ₁ 〓=constant, let P=0 =L ₁ ω ₀ i ₁ 〓 In this way, the first The block diagram in the figure is
This becomes the block diagram shown in the figure. As is clear from Fig. 2, the secondary magnetic flux λ′ ₂ 〓 cannot be uniquely set by the α-phase primary voltage e ₁ 〓, but is set by +L 〓 by the β-phase primary current i ₁ 〓.
There is interference of ω ₀ i ₁ 〓, and the secondary current i ₂ 〓 cannot be uniquely set by the β-phase primary voltage e ₁ 〓, but −L ₁ ω ₀ i due to the α-phase primary current i ₁ 〓. There is an interference of ₁ 〓. Therefore,
In the present invention, _the primary voltage e _{1 〓} ,
Correct e ₁ 〓. For this correction, L〓ω ₀ i ₁ 〓 which is added to the primary voltage e ₁ 〓 is taken into account and L〓 is added to the setting of the voltage e ₁ 〓.
Subtract ω ₀ i ₁ 〓 and it will be subtracted to the primary voltage e ₁ 〓
Considering L ₁ ω ₀ i ₁ 〓, L ₁ ω ₀ i ₁ 〓 is added to the setting of the voltage e ₁ 〓. By this correction, it is possible to set the primary voltages e 1 〓 and e ₁ 〓 that control the secondary magnetic flux λ′ ₂ 〓 and the secondary current i ₂ 〓 in a non-interfering _manner . FIG. 3 is a block diagram showing one embodiment of the present invention. In controlling the motor 1 by supplying a voltage-controlled primary voltage from the PWM inverter 2 so that the magnetic flux and secondary current of the motor 1 are orthogonal to each other, the settings of α and β phase voltages e ₁ 〓 and e ₁ 〓 The correction calculation circuit 3 performs the above-described correction. The correction calculation circuit 3 includes a coefficient unit 3 of a primary resistance _r 1 for setting the α-phase primary voltage e ₁ 〓 and an α-phase primary current setting value i ^* ₁ 〓 for controlling the secondary magnetic flux λ′ ₂ of the motor to be constant. A correction value for correcting the interference shown in FIG. 2 due to the β-phase primary current i ₁ 〓 is subtracted from the value passed through ₁ . This correction value is obtained by multiplying the β-phase primary current setting value i ^* ₁ 〓 for controlling the secondary current i′ ₂ by the power supply angular frequency ω ₀ using a multiplier 3 ₂ .
This multiplication result is obtained by passing it through a coefficient unit ₃₂ having an equivalent leakage inductance L as a coefficient. In addition, the correction calculation circuit 3 sets the β-phase primary voltage e ₁ 〓 by applying the α ^- axis primary current i ₁ 〓 to the value obtained by passing the set value i ^* 1 〓 through a coefficient unit 3 ₄ of the primary resistance r ₁ 〓. A correction value for correcting the interference shown in FIG. 2 is added in advance. This correction value is obtained by multiplying the current setting value i ^* ₁ 〓 by the power source angular frequency ω ₀ in a multiplier ₃₅ , and passing this multiplication result through a coefficient multiplier ₃₆ having a primary inductance _L1 as a coefficient. The β-phase primary current set value i ^* ₁ 〓 is a speed adjustment that performs proportional integral calculation (PI) of the deviation between the speed set value V ^* s and the detected value (rotor angular frequency ω _r ) of the speed detector 4 coupled to the motor 1. It is obtained as the output of the device 5. The power supply angular frequency ω ₀ is obtained by the angular frequency calculation circuit 6. This arithmetic circuit 6 includes a divider ₆₁ that divides the set value i ^* ₁ 〓 and i ^* ₁ 〓, and multiplies this division result i ^* ₁ 〓/i ^* ₁ 〓 by a coefficient 1/τ ₂ coefficient multiplier 6 ₂ and slip angular frequency ω _s
is calculated, and the rotor angular frequency ω _r is added to this slip angular frequency ω _s to obtain the power supply angular frequency ω ₀ . Calculation of the slip angular frequency ω _s by the divider 6 ₁ and the coefficient unit 6 ₂ is based on the following conditions mentioned above in the second term on the right side of equation (4) and from _{FIG .} Substitute 〓・M and get i ^* ₁ 〓/
It is replaced by (i ^* ₁ 〓・τ ₂ ). L〓=L ₁ L ₂ −M ² /L ₂ τ ₂ =L ₂ /r _2The primary voltages e ₁ 〓 and e ₁ 〓 of the α and β phases with the interference corrected in this way are calculated by the phase voltage calculation circuit 7 2 phase -
Three-phase conversion is performed, the three-phase voltage setting values e ^* _a , e ^* _b , e ^* _c of inverter 2 are taken out, and according to this setting value
By controlling the primary voltage of the PWM waveform, speed or torque control is realized in the motor 1 with magnetic flux and secondary current not interfering with each other. Next, for 2-phase to 3-phase conversion in the phase voltage calculation circuit 7, a sine wave SINω ₀ t is obtained from the trigonometric function generation circuit 8 using the power supply angular frequency ω ₀ . Also,
To obtain the PWM waveform in inverter 2,
A constant multiplied triangular wave synchronized with the power source angular frequency ω ₀ is extracted from the triangular wave generation circuit 9 using the power supply angular frequency ω ₀ , and this triangular wave is converted into PWM by comparing the level with the set voltages e ^* _a , e ^* _b , e ^* _c I am getting a waveform. Note that the phase voltage calculation circuit 4 performs calculations based on the following equations (5) and (6).

[Table] 〓 〓 〓 2 2 〓
Although a PWM signal waveform is obtained by such phase voltage calculation and triangular wave modulation, if both signals are not synchronized, DC components and even harmonics will be generated due to the modulation, causing torque fluctuations in the motor 1. To synchronize this phase voltage setting value with the triangular wave, convert the sine wave SINω ₀ and cosine wave CCSω ₀ t used for phase voltage calculation to the triangular wave.
It would be fine if it was synchronized with _Tri . This includes function generators shown as a triangular relation generating circuit 8 and a triangular wave generating circuit 9, which generate sine/cosine waves and triangular waves using clock pulses based on the same pulse signal proportional to the power supply angular frequency ω ₀ . An equal pulse PWM control method can be considered in which the number of triangular waves in one wave cycle is constant. However, according to this equal pulse PWM control method, as the power supply angular frequency ω ₀ becomes smaller (low speed operation), the frequency of the triangular wave also decreases at a constant ratio. Since the period of this triangular wave corresponds to dead time in terms of control, there is a problem that the lower ω ₀ is, the slower the response is and the higher the harmonic current is. Therefore, the trigonometric function generating circuit 8 and the triangular wave generating circuit 9 according to the present invention adjust the ratio of the sine/cosine wave frequency and the triangular wave frequency to the change in the power supply angular frequency ω ₀ while synchronizing the sine/cosine wave and the triangular wave, respectively. I'm trying to change it appropriately. FIG. 4 shows an embodiment of the trigonometric function generating circuit 8 and the triangular wave generating circuit 9. The absolute value circuit 11 obtains the absolute value |ω ₀ | since the power source angular frequency ω ₀ changes to positive or negative as the motor 1 rotates forward or backward. A voltage-frequency converter (V/F converter) 12 generates a pulse at a frequency corresponding to the output |ω ₀ | of the absolute value circuit 11 . The 1/2 frequency divider circuits 13, 14, and 15 are connected in series and divide the output pulse of the V/F converter 12 by 1/2, respectively. The pulse number switching switch 16 switches and outputs the output pulses of the V/F converter 12 and each of the frequency dividing circuits 13 to 15 in accordance with the switching signal _AS0 . The pulse switching circuit 17 generates the above-mentioned switching signal AS ₀ in response to the output |ω ₀ | of the absolute value circuit 11. The up-down counter 18 uses the output pulse of the changeover switch 16 as a counting input, and alternately repeats counting addition (UP) and counting subtraction (DOWN) up to a predetermined value, and sends a carry signal (CURRY) to repeat this addition and subtraction. The output of the 1/2 frequency divider circuit 19, which inputs , is given as an addition/subtraction switching signal. A digital-to-analog converter (D/A converter) 20 converts the contents of counter 18 into an analog signal. The inverting amplifier 21 inverts and amplifies the output of the D/A converter 20 (gain of 1). The positive/negative switching switch 22 switches the outputs of the D/A converter 20 and the inverting amplifier 21 in response to the positive/negative switching signal _AS1 , and outputs it as a triangular wave (carrier wave) _Tri . The positive/negative switching signal AS ₁ is the frequency divider circuit 19
It is given by the output of the 1/2 frequency divider circuit 23 which receives the output of . Next, the positive/negative detection circuit 24 detects the positive/negative (positive/reverse rotation of the motor) of the power supply angular frequency ω ₀ as an on/off signal. The up-down counter 25 is a frequency divider circuit 2 that divides the output pulse of the frequency divider circuit 15 by 1/6.
The output of 6 is used as a counting input, and counting addition and subtraction are switched according to the positive/negative detection output of the positive/negative detection circuit 24.
The read-only memory (ROM) 27 uses the count contents of the counter 25 as an address and stores it in a different bit digit (8 in the figure) from the half-cycle sample data of the cosine wave.
Bits 0 to ₇ have a code (“1” or “0”) that means reading up to the cos (π/2) sample data, and the cos (π/2) sample data and other sample data are It is differentiated. Similarly, the ROM 28 sequentially outputs sample data corresponding to a half period of a sine wave using the count contents of the counter 25 as an address, and also has a bit digit indicating sinπ sample data. D/
The A converters 29 and 30 input the sample data outputs of the ROMs 27 and 28, respectively, and convert them into corresponding analog signals. Inverting amplifiers 31 and 32 invert and amplify (gain 1) the analog outputs of D/A converters 29 and 30, respectively. Positive/negative switch 33, 34
is a cosine wave by switching the outputs of the D/A converter and the inverting amplifier by the positive/negative switching signals AS ₂ and AS ₃ , respectively.
Output as cosω ₀ t ₀ sine wave SINω ₀ t. The positive/negative switching signals AS ₂ and AS ₃ are the cos of the ROMs 27 and 28, respectively.
(π/2), sinπ sample data is output from frequency dividing circuits 35 and 36 which divide the frequency of the bit-digit signal by 1/2. The bit-digit signal representing the sample data of sinπ in the ROM 28 is input to the frequency divider circuit 36 as well as to the clear (reset) signal of the counter 25.
Also made into CL. The operation of the function generator having such a configuration will be explained below. The absolute value circuit 11, the V/F converter 12, and the frequency dividing circuits 13 and 15 are connected to the power supply angular frequency ω ₀ , which switches between positive and negative depending on the positive and reverse driving of the electric motor 1.
In the configuration, a pulse with a frequency corresponding to the absolute value |ω ₀ | is generated, and the output of the frequency dividing circuit 13 becomes 1/2 frequency with respect to the output pulse of the V/F converter 12,
The output of frequency divider circuit 14 is 1/4 frequency, frequency divider circuit 15
The output will be 1/3 the number. These pulse signals are changed to a frequency ω ₀ by a switching circuit 17 and a switching switch 16.
It is selected based on the magnitude of , and is input to the up-down counter 18 . In this switching, a lower frequency division is selected as the frequency ω ₀ becomes lower. Counter 1 that counts the pulses passed through the changeover switch 16
8, the counting speed changes in accordance with the frequency ω ₀ and counts from the final value to the highest value. From that point on, counting is performed from the highest value to the lowest value, and this operation is repeated. Therefore, the output of the counter 18 repeats increasing and decreasing in steps at the speed of the pulse input frequency through the changeover switch 16. The output of this counter 18 is
The A converter 20 converts the output into an analog signal, and the outputs of the D/A converter 20 and inverting amplifier 21 are switched at half the cycle of increase/decrease of the counter 18. A triangular wave signal T _ri of positive and negative polarity shown in FIG. 5 can be obtained. In addition,
FIG. 5 shows a case where the counter 18 has a 3-bit configuration. Therefore, it is possible to divide the power supply angular frequency |ω ₀ | into a plurality of ranges (four in the figure) and change the ratio between |ω ₀ | and the triangular wave frequency for each range. Therefore, unlike conventional equal-pulse PWM control, the range of change in the triangular wave frequency can be arbitrarily determined by setting the division ratios of the frequency dividers 13 to 15 and the switching range of the switching circuit 17. However, it is possible to increase the triangular wave frequency to some extent to improve response and reduce harmonic current. Next, the operation of generating sine and cosine waves will be explained. The positive/negative detection circuit 24 detects the positive/negative of the power supply angular frequency ω ₀ and sets the counter 25 to add or subtract depending on whether the motor is in the forward or reverse direction. The counter 25 is the frequency dividing circuit 15
A counting input of pulses proportional to |ω ₀ | is obtained from the side. From this, the counter 25 for creating a sine wave,
Since the triangular wave generation counter 18 receives a signal obtained by frequency-dividing the output pulse of the V/F converter 12, the sine/cosine wave and the triangular wave are synchronized. By addition or subtraction of the counter 25, the ROM2
7 outputs a sample value of a cosine wave, and ROM 28 outputs a sample value of a sine wave. These ROM2
The outputs of 7 and 28 are converted into analog signals by D/A converters 29 and 30, respectively, and are further converted to analog signals by inverting amplifiers 31 and 30, respectively.
By obtaining the inverted analog signal at step 32 and switching it every half period and clearing the counter 25, one period's worth of sine wave and cosine wave signals COSω ₀ t,
SINω ₀ t can be obtained. The sixth example is a sine wave.
As shown in the figure. Therefore, the angular frequency of the sine/cosine wave becomes the power source angular frequency |ω ₀ | and becomes a signal synchronized with the triangular wave.
In addition, by switching the count addition and subtraction of the counter 25, SINω ₀ t and COSω ₀ t are obtained during addition, and - during subtraction.
SINω ₀ t and COSω ₀ t are output. When this is converted into three phases, the phase rotation of the phase voltage calculation outputs e ^* _a , e ^* _b , e ^* _c becomes positive phase during addition and negative phase during subtraction. This allows forward and reverse rotation. Furthermore, since the initial values of the positive and cosine waves do not change when switching between forward and reverse directions, switching between forward and reverse directions is performed smoothly. Next, the relationship between sine waves (cosine waves) and triangular waves will be explained. If sample data obtained by dividing a half period of a sine wave into 112 and quantizing the data is written in the ROM 28, one period of the sine wave is output when the counter 25 counts 224 times. As for the triangular wave, if the counter 18 has a 4-bit configuration, 1/4 cycle is output in 16 counts, and one cycle is 64 counts. From this, if the counting input synchronization of the counters 18 and 25 is the same, the frequency ratio of the triangular wave and the sine wave will be 2:7. However, since the counting input of the counter 18 is switched by the changeover switch 16, the frequency ratio of the triangular wave and the sine wave can be changed depending on the power supply angular frequency. For example, when the contact ₁₆₁ of the changeover switch 16 is closed and the output of the V/F converter 12 becomes the input of the counter 18, the input of the counter 25 becomes a pulse whose frequency is divided by 1/48 with respect to the input of the counter 18. 168 times (48
×7/2) triangular wave exists. Similarly, when contact ₁₆₂ of changeover switch 16 is closed, the frequency ratio of the sine wave and triangular wave is 84, 42 at contact ₁₆₃ , and 42 at contact 1.
6 ₄ gives a frequency ratio of 21. As described above, according to the present invention, when performing vector control of an induction motor using a voltage source inverter, the inverter set voltage e is determined from the motor's excitation current set value i ^* ₁ 〓 and the secondary current set value i ^* ₁ 〓. ₁ 〓, e ₁ 〓, in order to cancel the mutual interference due to the motor's primary currents i ₁ 〓, i ₁ 〓, the magnetic flux and secondary current including the interference variation due to the power source angular frequency ω ₀ are It is possible to control the vectors so that they are always orthogonal, and this has the effect of allowing accurate vector control over a wide control range. In addition, the sine/cosine wave frequency and triangular wave frequency ratio can be switched in response to changes in the power supply angular frequency ω ₀ while synchronizing the sine/cosine wave for phase voltage calculation and the triangular wave for PWM signal generation. It can be applied to vector control methods using PWM inverters to improve responsiveness in low speed ranges and reduce harmonic current. Further, by switching between addition and subtraction of the sine/cosine wave generation counter 25, the motor can be easily switched between forward and reverse directions.

[Brief explanation of the drawing]

Fig. 1 is an equivalent block diagram of an induction motor with respect to two-phase voltages e ₁ 〓, e ₁ 〓, Fig. 2 is an equivalent block diagram of vector control of an induction motor, and Fig. 3 is a control device showing an embodiment of the present invention. 4 is a circuit diagram showing an example of the trigonometric function generation circuit and the triangular wave generation circuit in FIG. It is a waveform diagram for explanation. 1... Induction motor, 2... PWM type voltage source inverter, 3... Correction calculation circuit, 4... Speed detector, 5... Speed regulator, 6... Angular frequency calculation circuit, 7... Phase voltage calculation Circuit, 8... Trigonometric function generation circuit, 9... Triangular wave generation circuit, 11... Absolute value circuit, 12... Voltage-frequency converter, 13, 14,
15, 19, 23, 26, 35, 36... Frequency divider circuit, 16, 22, 23, 24... Changeover switch,
18, 25...Up-down counter, 20, 2
9, 30...Digital-to-analog converter, 2
1, 31, 32... Inverting amplifier, 24... Positive/negative detection circuit, 27, 28... Read only memory.

Claims (1)

[Claims] 1. An induction motor is driven by a voltage-type inverter, and two-phase three-phase voltage is generated from the α-phase voltage e ₁ 〓 that sets the magnetic velocity component of the induction motor and the β-phase voltage e ₁ 〓 that sets the secondary current. In the induction motor vector control device that obtains the a, b, c three-phase voltage set values e _a *, e _b *, e _c * of the voltage source inverter through conversion, α is used to set the magnetic flux component of the induction motor. Phase primary current setting value i ₁ 〓* as primary resistance r ₁
Set the secondary current of the induction motor from the value passed through the coefficient unit set to β-phase primary current setting value i ₁ 〓 * Multiply the angular frequency setting value ω ₀ of the voltage source inverter and equalize the equivalent leakage inductance Lσ Find the above voltage e ₁ 〓 by subtracting the value passed through the coefficient machine to be set, and add the above setting value i ₁ 〓* to the value passed through the coefficient machine that sets the primary resistance r ₁ to the above setting value i ₁ 〓*. An induction motor vector characterized in that it is equipped with a correction calculation circuit that multiplies the angular frequency setting value ω ₀ and adds a value passed through a coefficient unit to set the primary inductance L ₁ to obtain the voltage e ₁ 〓. Control device. 2 The value obtained by dividing the above setting value i ₁ 〓* by the setting value i ₁ 〓* is the ratio of secondary inductance L ₂ and secondary resistance r ₂ r ₂ /L ₂
Claim 1, further comprising: an angular frequency calculation circuit that calculates the angular frequency setting value ω ₀ by adding a detected rotor angular frequency value ω _r of the induction motor to a value passed through a coefficient unit set to ω 0 . A vector control device for an induction motor according to item 1. 3 Drive the induction motor with a pulse width modulation type voltage source inverter and set the magnetic flux of the induction motor α
A, b, c of the above-mentioned pulse width modulation type voltage source inverter are obtained by two-phase three-phase conversion from the phase voltage e _{1 〓} , the β-phase voltage e 1 〓 that sets the secondary current, and the sine wave signal and cosine wave signal. A vector control device for an induction motor that obtains three-phase voltage set values e _a *, e _b *, e _c * and obtains a pulse width modulation signal from these set values e _a *, e _b *, e _c * and a triangular wave signal. In this case, α-phase primary current setting value i ₁ 〓 * is set to the primary resistance r ₁ which sets the magnetic flux component of the induction motor. β-phase primary current setting which sets the secondary current component of the induction motor from the value passed through the coefficient machine. The value i ₁ 〓 * is multiplied by the angular frequency setting value ω ₀ of the voltage source inverter, and the value passed through the coefficient machine set to the equivalent leakage inductance Lσ is subtracted to find the voltage e ₁ 〓, and the above setting value i ₁ 〓 * is set to the primary resistance r ₁ The above setting value i ₁ 〓
A correction calculation circuit that multiplies * by the above angular frequency setting value ω ₀ and adds the value passed through a coefficient unit set to the primary inductance L ₁ to obtain the above voltage e ₁ 〓, and the above setting value i ₁ 〓 *. The rotor angular frequency detection value ω r of the induction motor is determined by dividing the set value i ₁ 〓* and passing it through a coefficient machine set to the ratio r ₂ /L ₂ of secondary inductance L ₂ and secondary resistance _{r 2 .} An angular frequency calculation circuit that calculates the above angular frequency setting value ω ₀ by adding the above angular frequency setting value ω 0 , and obtains a pulse that corresponds to the above angular frequency setting value ω ₀ and has a different frequency ratio depending on its frequency range, and obtains a set value of this pulse. A triangular wave generation circuit obtains a counted value by repeating counting addition and subtraction from the set value, and alternately switches an analog signal corresponding to this counted value and its inverted analog signal to obtain the triangular wave signal; A count value that corresponds to the angular frequency set value ω ₀ and that switches between repeating addition and subtraction up to the set value according to the positive and negative polarity due to forward and reverse driving of the induction motor is obtained, and this count value is used as a time axis to generate a sine wave and a cosine wave. A trigonometric function generating circuit that obtains sample data for half a period of a wave and alternately switches between an analog signal corresponding to this sample data and an inverted analog signal thereof to obtain the sine wave signal and cosine wave signal. A vector control device for an induction motor characterized by: