**3. Classification of IM control strategies**

The various IM control techniques are classified in to scalar and vector control methods. The general classification of IM control strategies [8, 9] which are based on the variable frequency control is shown in **Figure 4**.

#### **3.1 Scalar control**

The various scalar control methods are as follows 1. Stator voltage control 2. frequency control 3. Voltz/Hertz (V/F) control 4. Rotor Voltage control 5. Changing the number of poles. Out of these scalar methods, V/F control method is the best scalar control method. It can able to adjust the speed of the Induction motor by controlling the amplitude and frequency of the stator voltage of induction motor, the ratio of stator voltage to frequency should be kept constant so that, it is called as V/F control of induction motor drive. The vector control is preferred over scalar control methods due to the following disadvantages of scalar methods 1. Control of

*Me* ¼ *pb*

component *Isq* as given in the Eq. (2) and this equation is written as:

*Me* ¼ *pb*

*ms* 2

angle *δ* is considered whereas angle *δΨ* is considered for DTC techniques.

*Me* ¼ *pb*

*UsK* ¼ *RsIsK* þ

From the motor voltage Eq. (5) for the omitted voltage drop on the stator

From the mathematical model of IM, the electromagnetic torque equation is

*ms* 2

zero and the electromagnetic torque Eq. (4), the following Eq. (5) is derived.

*dΨ<sup>s</sup>*

Taking into consideration the fact that in the cage motor the rotor voltage equals

*dΨsK*

*Im Ψ* <sup>∗</sup> *<sup>s</sup> Is*

The Eq. (2) is transformed into the Eq. (3)

*Torque Ripple Reduction in DTC Induction Motor Drive*

*DOI: http://dx.doi.org/10.5772/intechopen.94225*

*Me* ¼ *pb*

The vector diagram of IM is shown in **Figure 5**.

resistance, the stator flux can be expressed.

given in the Eq. (4)

**Figure 5.**

**141**

*Vector diagram of induction motor.*

*ms* 2 *LM Lr*

The motor torque is expressed by rotor flux magnitude *Ψ<sup>r</sup>* and stator current

*ms* 2 *LM Lr*

*LM*

where *δ* is the angle between rotor flux vector and stator current vector and *δΨ* is the angle between rotor and stator flux vectors. The torque value depends on the magnitude of stator and rotor flux as well as the angle *δΨ* . For FOC methods, the

*ΨrIsq* (1)

*ΨrIssinδ* (2)

(4)

*dt* <sup>þ</sup> *<sup>j</sup>*Ω*KΨsK* (5)

*dt* <sup>¼</sup> *Us* (6)

*LrLs* � *Lm*<sup>2</sup> *<sup>Ψ</sup>sΨ<sup>r</sup> sin δΨ* (3)

#### **Figure 4.**

*General classification of control strategies of induction motor.*

Voltage/Current/frequency magnitude is based on steady state equivalent circuit model which ignores transient conditions. 2. Coupling of torque and flux exists, and they are functions of frequency and voltage which leads to sluggish dynamic responses [6].

### **3.2 Vector control methods**

## *3.2.1 Field oriented control (FOC)*

The FOC method is implemented based on the analogy of controlling a DC motor. It does not guarantee an exact decoupling of the torque and flux in dynamic and steady state operations. The full information about motor state variable and load torque is required for controlling the IM. The relationship between regulated value and control variables is linear only for constant rotor flux amplitude. The current controllers, coordinate transformations and a PWM algorithm are required. For direct FOC, flux estimator is required. In indirect FOC mechanical speed sensor is needed. This method is very sensitive to rotor time constant**.**

### *3.2.2 Direct torque control (DTC)*

The DTC is one of the high performance control strategies for the control of AC machine. In a DTC drive applications, flux linkage and electromagnetic torque are controlled directly and independently by the selection of optimum inverter switching modes of operation. To acquire a faster torque output, low inverter switching frequency and low harmonic losses in the model, the selection is made to restrict the flux linkages and electromagnetic torque errors within the respective flux and torque hysteresis bands. The required optimal switching vectors can be selected by using the optimum switching voltage vector look-up table. This can be obtained by simple physical considerations involving the position of the stator-flux linkage space vector, the available switching vectors, and the required torque flux linkage.

The torque is controlled by the stator current component *Isq* in the classical vector control strategy of FOC according to the Eq. (1)

*Torque Ripple Reduction in DTC Induction Motor Drive DOI: http://dx.doi.org/10.5772/intechopen.94225*

$$M\_{\epsilon} = p\_b \frac{m\_s}{2} \frac{L\_M}{L\_r} \Psi\_r I\_{sq} \tag{1}$$

The motor torque is expressed by rotor flux magnitude *Ψ<sup>r</sup>* and stator current component *Isq* as given in the Eq. (2) and this equation is written as:

$$M\_{\epsilon} = p\_b \frac{m\_s}{2} \frac{L\_M}{L\_r} \Psi\_r I\_s \sin \delta \tag{2}$$

The Eq. (2) is transformed into the Eq. (3)

$$M\_e = p\_b \frac{m\_s}{2} \frac{L\_M}{L\_r L\_s - L\_m^2} \Psi\_s \Psi\_r \sin \delta\_{\Psi} \tag{3}$$

where *δ* is the angle between rotor flux vector and stator current vector and *δΨ* is the angle between rotor and stator flux vectors. The torque value depends on the magnitude of stator and rotor flux as well as the angle *δΨ* . For FOC methods, the angle *δ* is considered whereas angle *δΨ* is considered for DTC techniques.

The vector diagram of IM is shown in **Figure 5**.

From the motor voltage Eq. (5) for the omitted voltage drop on the stator resistance, the stator flux can be expressed.

From the mathematical model of IM, the electromagnetic torque equation is given in the Eq. (4)

$$M\_{\epsilon} = p\_b \frac{m\_s}{2} \operatorname{Im} \left( \Psi\_s^\* I\_s \right) \tag{4}$$

Taking into consideration the fact that in the cage motor the rotor voltage equals zero and the electromagnetic torque Eq. (4), the following Eq. (5) is derived.

$$U\_{sK} = R\_s I\_{sK} + \frac{d\Psi\_{sK}}{dt} + j\Omega\_K \Psi\_{sK} \tag{5}$$

$$\frac{d\Psi\_s}{dt} = U\_s \tag{6}$$

**Figure 5.** *Vector diagram of induction motor.*

Taking into consideration the output voltage of the inverter in the above Eq. (6) it can be written as

$$\Psi\_s = \int\_0^t U\_v dt \tag{7}$$

where

$$U\_v = \begin{cases} \frac{2}{3} U\_{dc} e^{j(v-1)\pi/3} & v = 1 \dots 6\\ 0, \text{ } \dots \text{ } \dots \text{ } \dots \dots \dots \dots \quad v = 0,7 \end{cases} \tag{8}$$

The Eq. (7) describes eight voltage vectors which correspond to possible inverter states. These vectors are shown in **Figure 6**. There are six active vectors U1 to U6 and two zero vectors U0, U7.

It can be seen from the Eq. (7) that the stator flux directly depends on the inverter voltage Eq. (8). By using one of the active voltage vectors the stator flux vector moves to the direction and sense of the voltage vector. Stator flux changes direction for the cycle sequence of the active voltage vectors. Inherently the rotor flux of IM moves slowly but the stator flux could be changed immediately. In DTC methods the angle *δΨ* between stator and rotor flux is varied to control the torque. By adjusting the stator voltage, stator flux could be controlled in simple way. The above consideration and equations could be used in the analysis of classical DTC techniques and SVM-DTC methods. In the classical DTC method the control plane is divided for the six sectors shown in **Figure 7**, that are defined as:

$$
\gamma\_{\alpha} \in \left( -\frac{\pi}{6}, +\frac{\pi}{6} \right) \tag{9}
$$

*<sup>γ</sup>ss* <sup>∈</sup> � <sup>5</sup>*<sup>π</sup>*

*<sup>γ</sup>ss* <sup>∈</sup> � *<sup>π</sup>* 2 , � *π* 6

The solving of integration in Eq. (7) is stopped.

*Torque Ripple Reduction in DTC Induction Motor Drive*

*DOI: http://dx.doi.org/10.5772/intechopen.94225*

control and it is block diagram is shown in **Figure 8**.

SC which are generated form the switching table.

based on the above considerations.

**Figure 7.**

**Table 1.**

**143**

*Optimum switching table.*

*Sectors in classical DTC.*

In order to increase magnitude of the stator vector in sector 1, the following voltage vectors **U1 U2 U6** are selected. Conversely to decrease, **U3 U4 U5** are selected. The stator flux is not changed when any one of the zero vectors **U0** or **U7** is applied.

To increase the motor torque, the voltage vectors **U2 U3 U4** are selected and for decreasing the torque **U1 U5 U6** are selected. The switching **Table 1** is constructed

I. Takahashi and T. Nogouchi proposed the control scheme for Direct torque

selected by the digitized output variables *d<sup>Ψ</sup>* , *dM* and the stator flux position

According to the Eq. (15) the torque and flux errors are calculated.

The reference signals such as stator flux amplitude *Ψsc* and the electromagnetic torque *Mc* are compared with the estimated flux amplitude *Ψ*^ *<sup>s</sup>* and electromagnetic torque *M*^ *<sup>e</sup>* values respectively. The error values such as *e<sup>Ψ</sup>* and torque *eM* are sent to the hysteresis controllers. The appropriate voltage vector from the switching table is

sector *γss*ð Þ *N* . The power switches in the inverter are controlled by the pulses SA, SB,

*S<sup>Ψ</sup> Sm S***<sup>1</sup>** *S***<sup>2</sup>** *S***<sup>3</sup>** *S***<sup>4</sup>** *S***<sup>5</sup>** *S***<sup>6</sup>** 1 1U2 U3 U4 U5 U6 U1

0 1U3 U4 U5 U6 U1 U2

0 U7 U0 U7 U0 U7 U0 �1 U6 U1 U2 U3 U4 U5

0 U0 U7 U0 U7 U0 U7 �1 U5 U6 U1 U2 U3 U4

<sup>6</sup> , � *<sup>π</sup>* 2

(13)

(14)

$$
\gamma\_n \in \left( +\frac{\pi}{6}, -\frac{\pi}{2} \right) \tag{10}
$$

$$\gamma\_{\pi} \in \left( +\frac{\pi}{2}, +\frac{5\pi}{6} \right) \tag{11}$$

$$\gamma\_{\alpha} \in \left( + \frac{5\pi}{6}, -\frac{5\pi}{6} \right) \tag{12}$$

**Figure 6.** *Inverter output voltage represented as space vectors.*

*Torque Ripple Reduction in DTC Induction Motor Drive DOI: http://dx.doi.org/10.5772/intechopen.94225*

**Figure 7.** *Sectors in classical DTC.*

$$\chi\_{\alpha} \in \left( -\frac{5\pi}{6}, -\frac{\pi}{2} \right) \tag{13}$$

$$\gamma\_{sr} \in \left( -\frac{\pi}{2}, -\frac{\pi}{6} \right) \tag{14}$$

In order to increase magnitude of the stator vector in sector 1, the following voltage vectors **U1 U2 U6** are selected. Conversely to decrease, **U3 U4 U5** are selected. The stator flux is not changed when any one of the zero vectors **U0** or **U7** is applied. The solving of integration in Eq. (7) is stopped.

To increase the motor torque, the voltage vectors **U2 U3 U4** are selected and for decreasing the torque **U1 U5 U6** are selected. The switching **Table 1** is constructed based on the above considerations.

I. Takahashi and T. Nogouchi proposed the control scheme for Direct torque control and it is block diagram is shown in **Figure 8**.

The reference signals such as stator flux amplitude *Ψsc* and the electromagnetic torque *Mc* are compared with the estimated flux amplitude *Ψ*^ *<sup>s</sup>* and electromagnetic torque *M*^ *<sup>e</sup>* values respectively. The error values such as *e<sup>Ψ</sup>* and torque *eM* are sent to the hysteresis controllers. The appropriate voltage vector from the switching table is selected by the digitized output variables *d<sup>Ψ</sup>* , *dM* and the stator flux position sector *γss*ð Þ *N* . The power switches in the inverter are controlled by the pulses SA, SB, SC which are generated form the switching table.


According to the Eq. (15) the torque and flux errors are calculated.

**Table 1.** *Optimum switching table.*

**Figure 8.** *Block diagram of DTC scheme.*

$$
\varepsilon\_{\Psi\_s} = \frac{\hat{\Psi\_s} - \Psi\_{\text{sc}}}{\Psi\_{\text{sN}}} \text{ 100\%} \tag{15}
$$

*4.1.1 Modification in switching tables*

*Classification of DTC improvement strategies.*

*Torque Ripple Reduction in DTC Induction Motor Drive*

*DOI: http://dx.doi.org/10.5772/intechopen.94225*

**Figure 9.**

*4.1.1.1 Modified switching table*

*4.1.1.1.2 Modified classical DTC*

*Modified switching table with 6-sectors.*

**Table 2.**

**145**

states. **Table 2** illustrates this modification [12].

*4.1.1.1.1 Improvement in switching table*

The modifications are carried out in the DTC- basic switching table with the objective of improving starting and overload conditions which enable all the voltage vectors are applied in appropriate sequence. They are implemented by two methods namely 1. Six sector table and 2. Twelve sector table respectively. The zero voltage vectors are selected from the switching **Table 1** during starting and very low speed conditions and results in flux level reduction due to the drop in stator resistance [11].

In conventional DTC, the states v1 and v4 vectors are not used. Depending on if the position is in its first 39 degrees or in its second ones, they could increase or decrease the torque. It leads to modify the switching table and use the modified DTC. In the modified DTC, the vectors v3 and v6 are not used. The reason is the

By applying zero voltage vectors V0, V7 for the states of decreasing in torque, **Table 1** is modified accordingly. The inertia of the motor is reduced when zero voltage vectors are applied, torque ripple is reduced. It is more suitable than the percent given by applying the voltage vectors in **Table 1** for the torque decrease

**Voltage vectors Classical DTC DTC with changes of zones**

V1 +30° to �30° 0° to �60° V2 +90° to +30° +60° to 0° V3 +150° to +90° +120° to +60° V4 �150° to +150° +180° to +120° V5 �90° to �150° �120° to �180° V6 �30°to �90° �60° to �120°

ambiguity in flux instead of torque as if it was in conventional DTC [12].

#### *3.2.3 Problems in conventional DTC*

Despite its simplicity and robustness, the conventional DTC control has major drawback. The use of hysteresis controllers causes high ripples in the flux and electromagnetic torque at low speeds. It results in undesirable mechanical vibrations and acoustic noise, and subsequently leads to degradation of the machine performances. Thus the variable switching frequency and current distortions could detoriate the quality of the output power. The negligence in the calculation of stator resistance leads to problems at low speed. Moreover, the practical implementation of nonlinear components of the hysteresis type needs low sampling period. Many DTC strategies are developed based on the principle of instantaneous torque and stator flux regulation in order to rectify the drawbacks of classical DTC. The direct determination of the inverter control signals from the switching table is implemented [9].

### **4. Types of control strategies for torque ripple reductions in DTC**

The DTC control strategies are divided into two groups: 1.Typical 2.Modern control strategies. They are classified into few other control techniques such as space vector modulation (SVM-DTC), modified switching table (m-DTC), Artificial Neural Network controller based (ANN-DTC), Fuzzy Logic controller based (FLC-DTC), Genetic algorithm based (GA-DTC), Model predictive controller based (MPC-DTC), Sliding mode based (SMO-DTC) [9, 10] as shown in **Figure 9**.

#### **4.1 Modified DTC**

It covers modification in switching table and/or injection of dithering signals. Few attempts are made to avoid the drawbacks in convention DTC either by implementing dither signal injection method or modified switching table method. *Torque Ripple Reduction in DTC Induction Motor Drive DOI: http://dx.doi.org/10.5772/intechopen.94225*

**Figure 9.**

*Classification of DTC improvement strategies.*
