**8.1. PI and FLC performances**

Figure 33 shows the rotation speed and motor torque evolution for PMSM DTC strategy by using PI speed controller (green color) and speed FLC (red color). Indeed, the FLC has exhibited high performance in tracking the speed reference, as compared with speed PI controller. This figure confirms that the motor torque response with fuzzy controller is faster than PI controller during the start up regime and during a step change in load torque. The speed dynamic state imposes the motor torque response time because these two variables are regulated in cascade: the inner loop controls the motor electromagnetic torque and the outer loop regulates the motor rotation speed.

**Figure 33.** Rotation speed (on the left) and motor torque (on the right) performances under DTC for PMSM drive by using speed PI controller (green color) or speed FLC (red color)

#### **8.2. Classical and novel estimators under stator resistance variation**

The simulation results presented in this part shows the robustness of the classical and the novel flux and torque estimators, described at the beginning of this chapter, under stator resistance variation. Figure 34 shows the stator resistance variation applied to examine DTC for PMSM drive by using classical or novel estimator. In this case, the value of stator resistance was changed from the nominal value 1.59 Ω to the double of this value 3.18 Ω. Where, the reference stator flux and load torque are kept constant at 0.052 Wb and 0.8 Nm, respectively.

190 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**8. Effect of PMSM parameters variations and their compensation** 

This part is devoted to compare two speed controllers performances used in DTC under PMSM parameters variations. Also, a comparison between classical and novel torque and flux estimators has been developed in order to show their performances under PMSM

Figure 33 shows the rotation speed and motor torque evolution for PMSM DTC strategy by using PI speed controller (green color) and speed FLC (red color). Indeed, the FLC has exhibited high performance in tracking the speed reference, as compared with speed PI controller. This figure confirms that the motor torque response with fuzzy controller is faster than PI controller during the start up regime and during a step change in load torque. The speed dynamic state imposes the motor torque response time because these two variables are regulated in cascade: the inner loop controls the motor electromagnetic torque and the

**Figure 33.** Rotation speed (on the left) and motor torque (on the right) performances under DTC for

PMSM drive by using speed PI controller (green color) or speed FLC (red color)

of symmetrical SVM.

parameters variations.

**8.1. PI and FLC performances** 

outer loop regulates the motor rotation speed.

comparison with basic DTC, and also the current quality was improved. Figure 28 (on the left) shows that the current THD under DTC-SVM is 3.5 %, which is smother than that of basic DTC and FDTC. Also, it's seen that torque and flux ripples are greatly reduced under DTC-SVM when compared to DTC and FDTC (compare figures 26 and 28 with figures 8, 10, 19 and 21). Figure 32 shows that the THD of the current waveform under DTC-SPWM is 3.85%, which is almost the same as DTC-SVM, also DTC-SVM guarantees a constant switching frequency; as shown in figure 32 which allow to reduce torque and flux ripple as the same as DTC-SVM. Furthermore, the calculation time of the DTC-SPWM is much inferior to the DTC-SVM, this is because SPWM algorithm is very simple than SVM. Note that the SVM symmetry used in this work eliminates the harmonics which are around the uneven switching frequency (Chikh et al., 2011a). The same performances for DTC-SVM and DTC-SPWM can be obtained if an asymmetric SVM has been used instead

**Figure 35.** Motor torque (on the left) and stator flux (on the right) evolution by using classical estimator (green color) or by using novel estimator (red color)

**Figure 36.** Stator current waveform in case of classical estimator (on the left) and novel estimator (on the right)

It's seen in figure 35 that the estimated stator flux was affected, when the stator resistance was changed at t=0.75 s; when the stator flux was estimated by using classical estimator.

This figure shows that, in spite of stator resistance variation, the stator flux was maintained constant when it is estimated by the novel estimator, because this estimator does not depends to the stator resistance variation. This stator flux deviation is normal and forecasted because the estimated flux value by using classical estimator depends on the stator resistance. When the PMSM stator resistance varies; while this classical estimator still uses the nominal stator resistance to estimate the actual stator flux; the estimated stator flux differ significantly from the real stator flux.

As shown in figure 35, the torque and flux ripples are increased when stator resistance varies in case of classical estimator, because the stator flux deviation causes the DTC algorithm to select a wrong switching state, which can result in unstable operation of the PMSM. Indeed, figure 36 shows that the stator current waveform in case of the novel estimator presents a good THD than the current in case of classical estimator, this is due to the wrong selection of the switching state.
