**2.6 Simulations and discussions: A comparative study**

The ratings and parameters of the induction machine, used in the simulation study, are listed in **Tables 2** and **3** respectively.


#### **Figure 2.**

**2.5 Concept of DTC-SVM with hysteresis controllers based position control**

*c<sup>ϕ</sup>* **+1 1**

*V*1 (101)

*V*2 (100)

*V*3 (110)

*V*<sup>4</sup> (010)

*V*5 (011)

*V*6 (001)

*Look-up table with zero-voltage vectors substituted by active ones.*

*cr* **+1 0 1 +1 0 1**

*V*6 (001)

*V*1 (101)

*V*2 (100)

*V*3 (110)

*V*<sup>4</sup> (010)

*V*5 (011)

*V*3 (110)

*V*<sup>4</sup> (010)

*V*5 (011)

*V*6 (001)

*V*1 (101)

*V*2 (100)

*V*<sup>4</sup> (010)

*V*5 (011)

*V*6 (001)

*V*1 (101)

*V*2 (100)

*V*3 (110)

*V*5 (011)

*V*6 (001)

*V*1 (101)

*V*2 (100)

*V*3 (110)

*V*<sup>4</sup> (010)

lers applied to the position regulation of an induction motor drive is shown in **Figure 2**. It has the same layout as the one of the basic DTC strategy proposed in section II, except that the SVM bloc is added to the control system that ensures an

imposed switching frequency [7–12].

**Figure 1.**

S1 *V*<sup>2</sup>

S2 *V*<sup>3</sup>

S4 *V*<sup>4</sup>

S4 *V*<sup>5</sup>

S5 *V*<sup>6</sup>

S6 *V*<sup>1</sup>

**Table 1.**

**42**

(100)

(110)

(010)

(011)

(001)

(101)

*IM position regulation based on basic DTC strategy.*

*Direct Torque Control Strategies of Electrical Machines*

The implementation scheme of the DTC-SVM strategy with hysteresis control-

*Induction motor position regulation based on the DTC-SVM strategy.*


**Table 2.** *Induction machine ratings.*


#### **Table 3.**

*Induction machine parameters.*

**Figure 3.**

*Induction motor position regulation under the basic Takahashi DTC strategy, (a): Rotor position θ and its reference, (b): Speed* Ω*m, (c): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

**Figures 3**–**5** show the induction motor dynamic following the application of a dual-step reference position under the basic *Takahashi* DTC strategy, the modified *Takahashi* one, and the DTC-SVM strategy with a controlled commutation frequency, respectively. In order to highlight performances gained by the DTC-SVM scheme, resulting features are compared to the obtained ones following the implementation of the basic DTC strategy. The analysis of these results leads to the following remarks:


**Figure 5.**

**45**

**Figure 4.**

*Induction motor position regulation under the DTC-SVM strategy with a constant commutation frequency of 6.5 kHz, (a) rotor position θ, (b): Speed* Ω*m,: (b): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

*Induction motor position regulation under the modified Takahashi DTC strategy, (a): Rotor position θ and its*

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.94436*

*reference, (b): Speed* Ω*m, (c): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications DOI: http://dx.doi.org/10.5772/intechopen.94436*

**Figure 4.**

**Figures 3**–**5** show the induction motor dynamic following the application of a dual-step reference position under the basic *Takahashi* DTC strategy, the modified *Takahashi* one, and the DTC-SVM strategy with a controlled commutation frequency, respectively. In order to highlight performances gained by the DTC-SVM scheme, resulting features are compared to the obtained ones following the

*Induction motor position regulation under the basic Takahashi DTC strategy, (a): Rotor position θ and its*

*reference, (b): Speed* Ω*m, (c): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

*rs* ¼ 0*:*29Ω *rr* ¼ 0*:*38Ω *M* ¼ 47*:*3mH *Ls* <sup>¼</sup> *Lr* <sup>¼</sup> 50mH *Np* <sup>¼</sup> <sup>2</sup> *<sup>J</sup>* <sup>¼</sup> <sup>0</sup>*:*5Kg*:*m<sup>2</sup>

implementation of the basic DTC strategy. The analysis of these results leads to the

• **Figures 3a**–**5a** show that the three DTC strategies exhibit almost the same

• Performances of the flux loop of the basic *Takahashi* DTC strategy is affected by the demagnetized phenomenon (**Figure 3d**). In fact, the analysis of the *Takahashi* strategy highlights low performances at low speed operations. Under such conditions, and for steady state operations, the motor turns to be

• In order to overcome the demagnetization problem caused by zero-voltage vectors included in the look-up table of the basic DTC strategy, these have

following remarks:

**Figure 3.**

**Table 3.**

*Induction machine parameters.*

*Direct Torque Control Strategies of Electrical Machines*

demagnetized.

**44**

position and speed dynamics,

*Induction motor position regulation under the modified Takahashi DTC strategy, (a): Rotor position θ and its reference, (b): Speed* Ω*m, (c): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

**Figure 5.**

*Induction motor position regulation under the DTC-SVM strategy with a constant commutation frequency of 6.5 kHz, (a) rotor position θ, (b): Speed* Ω*m,: (b): Electromagnetic torque Tem, (d): Stator flux* Φ*s.*

been substituted by active vectors. Obtained results are illustrated in **Figure 4**. Referring to **Figure 4d**, one can notice that the demagnetization problem has been removed, while performances of the motor, for high speeds, are not affected. However, the torque ripple amplitudes rise considerably (**Figure 4c**) with respect to the one yielded by the *Takahashi* DTC strategy, which represents a severe drawback.

done considering the three DTC strategies. Obtained results are shown in **Figure 6**. One can notice, easily, that the DTC-SVM strategy with hysteresis regulators and with an imposed commutation frequency yields to the smoothest

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications*

**3. Concept of PI DTC-SVM based position control**

**3.1 Computing of flux reference coordinates**

ð Þ *<sup>α</sup>*, *<sup>β</sup>* , coordinates of the reference stator flux *<sup>ϕ</sup>*<sup>∗</sup>

**3.2 Computing of voltage reference coordinates**

determined by the following equations:

inverter switches ð Þ *Sa*, *Sb*, *Sc* .

**3.3 Position control loop**

**Figure 8.**

**47**

*Position control loop.*

The coordinates of references of voltage vectors *v* <sup>∗</sup>

polar coordinates according to the following expressions:

*ϕ*∗ *<sup>α</sup><sup>s</sup>* <sup>¼</sup> <sup>∣</sup>Φ<sup>∗</sup>

8 < :

*V* <sup>∗</sup> *<sup>α</sup><sup>s</sup>* <sup>¼</sup> *<sup>ϕ</sup>*<sup>∗</sup>

8 >>>><

>>>>:

*V* <sup>∗</sup> *<sup>β</sup><sup>s</sup>* <sup>¼</sup> *<sup>ϕ</sup>*<sup>∗</sup>

*ϕ*∗ *<sup>β</sup><sup>s</sup>* <sup>¼</sup> <sup>∣</sup>Φ<sup>∗</sup>

The slip angular reference speed *ω*<sup>∗</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.94436*

Finally, we have involved in the assessment of the average commutation frequencies of both basic and modified *Takahashi* DTC strategies. Obtained results have been showing in **Figure 7**. It is to be noted that the basic DTC strategy and the DTC-SVM with an imposed commutation frequency ð Þ *Fc* ¼ 6*:*25*kHz* strategy offer lower commutation frequencies than the modified *Takahashi* DTC strategy.

be used to calculate the argument of the stator flux reference. In the reference frame

*<sup>s</sup>* ∣ cos *θ* <sup>∗</sup> *s*

*<sup>s</sup>* ∣sin *θ* <sup>∗</sup> *s*

*<sup>α</sup><sup>s</sup>* � *ϕα<sup>s</sup> Te*

*<sup>β</sup><sup>s</sup>* � *ϕβ<sup>s</sup> Te*

Finally, they are introduced to the SVM block, which uses them to control the

The objective is the design of a suitable controller as described by **Figure 8**.

þ *Rsi<sup>α</sup><sup>s</sup>*

þ *Rsi<sup>β</sup><sup>s</sup>*

*<sup>r</sup>* , which is the output of the PI controller, will

*<sup>β</sup><sup>s</sup>* are calculated from the

*<sup>β</sup><sup>s</sup>* in ð Þ *α*, *β* frame are

(5)

(6)

*<sup>α</sup><sup>s</sup>* and *ϕ*<sup>∗</sup>

*<sup>α</sup><sup>s</sup>* and *v* <sup>∗</sup>

circular locus.

• **Figure 5** shows that the DTC-SVM strategy exhibits high dynamical performances. In fact, this approach presents a low torque ripple amplitude (**Figure 5c**). Moreover, it completely eliminates the demagnetization phenomenon (**Figure 5d**).

Further investigation of the stator flux has been achieved through the representation of the stator flux vector extremity locus in the ð Þ *α*, *β* plane. This has been

#### **Figure 6.**

*Locus of the extremities of* Φ*s, with (a) basic Takahashi DTC strategy, (b) modified Takahashi DTC strategy and (c) DTC-SVM strategy with a constant commutation frequency.*

**Figure 7.**

*Average commutation frequency of the inverter power switches, (a) basic Takahashi DTC strategy, (b) modified Takahashi DTC strategy.*

*DTC-SVM Approaches of an Induction Motor Dedicated to Position Control Applications DOI: http://dx.doi.org/10.5772/intechopen.94436*

done considering the three DTC strategies. Obtained results are shown in **Figure 6**. One can notice, easily, that the DTC-SVM strategy with hysteresis regulators and with an imposed commutation frequency yields to the smoothest circular locus.

Finally, we have involved in the assessment of the average commutation frequencies of both basic and modified *Takahashi* DTC strategies. Obtained results have been showing in **Figure 7**. It is to be noted that the basic DTC strategy and the DTC-SVM with an imposed commutation frequency ð Þ *Fc* ¼ 6*:*25*kHz* strategy offer lower commutation frequencies than the modified *Takahashi* DTC strategy.
