**7. Switching table construction and control algorithm design**

To maintain a decoupled control, a pair of hysteresis comparators receives the stator flux and torque errors as inputs. Then, the comparators outputs determine the appropriate voltage vector selection. However, the choice of voltage vector is not only depending on the output of hysteresis controllers but on the position of stator flux vector also. Thus, the circular stator flux vector trajectory will be divided into six symmetrical sectors (**Table 1**).

For each sector, the vectors (*Vi and V3+i*) are not considered because both of them can increase or decrease the torque in the same sector according to the position of flux vector on the first or the second sector. If the zero vectors V0 and V7 are selected, the stator flux will stop moving, its magnitude will not change, and the electromagnetic torque will decrease, but not as much as when the active voltage vectors are selected. The resulting look-up table for DTC which was proposed by Takahashi is presented in **Table 2**.


Ctrq = �1 V5 V6 V1 V2 V3 V4 Three-level

#### **Table 2.**

*Look-up table for basic direct torque control.*

#### **8. Global scheme of conventional direct torque control**

The global control scheme of conventional direct torque control strategy is shown in **Figure 5**. It is composed of speed regulation loop; the proportionalintegral (PI) controller is used for the regulation. It is performed by comparing the speed reference signal to the actual measured speed value. Then the comparison error becomes the input of the PI controller. The pole placement method is used to determine the controller gains. The used PI controller in our work in the outer speed loop is the anti-windup controller. It allows to enhance speed control performance by canceling the windup phenomenon which is caused by the saturation of the pure integrator [20]. **Figure 6** shows the speed anti-windup PI controller diagram block. is passed through a gain block (tracking time constant *Ti*) before arriving as feedback to the integrator. As well flux and torque hysteresis controllers, look-up switching table, an association of VSI-Induction motor, voltage and current calculation blocks with 3/2 (Concordia) transformation and flux/torque estimators with

*Direct Torque Control Strategies of Induction Machine: Comparative Studies*

**9. Constant switching frequency direct torque control using SVM**

to the system-parameter variations and the inadequate rejection of external disturbances and load changes [28, 29]. To cope with this disadvantage, it is suggested to replace the conventional regulators used for the speed control, flux, and electromagnetic torque by intelligent controllers by adaptive fuzzy-PI and fuzzy logic to make the control more robust against the disturbances of the

This technique is much requested in the field of control in that the reference voltages are given by a global control vector approximated over a modulation period *Tz*. The principle of SVM is the prediction of inverter voltage vector by the

two non-zero switching states. For two-level inverters, the switching vector diagram forms a hexagon divided into six sectors, each one is expanded by 60° as

the rest of the time period will be spent by applying the null vector.

*T*<sup>1</sup> ¼

The application time for each vector can be obtained by vector calculations, and

2*Vdc*

ffiffi 2 <sup>p</sup> � *Vs<sup>β</sup> Vdc*

2 <sup>p</sup> � *Vs<sup>β</sup>*

When the reference voltage is in sector 1 (**Figure 8**), it can be synthesized by

The determination of times T1 and T2 corresponding to voltage vectors are

ffiffiffi 6 <sup>p</sup> � *Vs<sup>α</sup>* � ffiffi

*T*<sup>2</sup> ¼

*<sup>s</sup>* between adjacent vectors corresponding to

*T* (21)

� *T* (22)

The conventional direct torque control has several disadvantages, among which the variable switching frequency and the high level of ripples. Consequently, they lead to high-current harmonics and an acoustical noise and they degrade the control performance especially at low speed values. The ripples are affected proportionally by the width of the hysteresis band. However, even with choosing a reduced bandwidth values, the ripples are still important due to the discrete nature of the hysteresis controllers. Moreover, the very small values of bandwidths increase inverter switching frequency. In order to overcome these drawbacks, most of the studies presented in the literature have been oriented towards modification in the conventional DTC method by the introduction of a vector modulator [21, 22]. The vector PWM technique (SVM) is used to apply a voltage vector with a fixed switching frequency. The control system consists of replacing the switching table and the hysteresis comparators with proportional and integrating controllers (PI) for controlling the stator flux and the electromagnetic torque, [6, 23–27]. The main drawbacks of DTC-SVM using PI controllers are the sensitivity of the performances

position/sector determination.

*DOI: http://dx.doi.org/10.5772/intechopen.90199*

parameters of the machine.

shown in **Figure 7**.

**25**

**9.1 Space vector modulation algorithm**

projection of the reference vector *V* <sup>∗</sup>

using the vectors V1, V2, and V0 (zero vector).

obtained by simple projections (**Figure 9**).

where Vdc is the DC bus voltage.

This strategy consists on the correction of the integral action based on the difference between the control signal and the saturation limit. The difference value

**Figure 5.** *Global control scheme of basic direct torque control.*

**Figure 6.** *Speed anti-windup PI controller.*

*Direct Torque Control Strategies of Induction Machine: Comparative Studies DOI: http://dx.doi.org/10.5772/intechopen.90199*

is passed through a gain block (tracking time constant *Ti*) before arriving as feedback to the integrator. As well flux and torque hysteresis controllers, look-up switching table, an association of VSI-Induction motor, voltage and current calculation blocks with 3/2 (Concordia) transformation and flux/torque estimators with position/sector determination.
