**9. Conclusion**

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

differ significantly from the real stator flux.

the wrong selection of the switching state.

novel estimator (red color)

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

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 simulation results below presents the DTC for PMSM performances in case of speed PI controller and Robust estimator, and speed FLC and this estimator under motor parameters variation, which are stator resistance, friction coefficient and motor inertia. Figure 37 (on the left) shows the variations, of these three parameters, applied to examine DTC robustness: the stator resistance was changed from the nominal value 1.59 Ω to the double of this value 3.18 Ω, the friction coefficient was changed from the nominal value f=0.00047 Nm.s/rd to f1=100\*f and

It's seen in figure 37 (on the right) that the speed FLC allows to achieve a faster response and reject the perturbations (motor parameters variations), whereas the speed PI controller takes much time, in comparison with FLC, to reject these perturbations. Also, a faster motor torque response has been achieved with speed FLC compared to speed PI controller; as shown in figure 38 (on the left). Indeed, combining speed FLC and the novel estimator allow DTC for PMSM to reject stator resistance variation thanks to this estimator and reject motor inertia and

**Figure 37.** PMSM parameters variation (on the left) and rotation speed evolution (on the right) in case of DTC for PMSM drive using speed PI controller and novel estimator (green color), and speed FLC and

**8.3. Classical and Robust estimators under PMSM parameters variation** 

the motor inertia was changed from the nominal value J=0.003573 Kg.m2 to J1=100\*J.

friction coefficient thanks to speed FLC, which is shown in figure 38 (on the right).

Another solution has been presented to overcome the problems associated to DTC for PMSM in case of motor parameters variation and/or nonlinear operating conditions, which utilize speed FLC and an independent stator resistance estimator. Of course, FDTC allows rejecting the perturbations and minimizing torque and flux ripple. For all these reasons, a fixed switching frequency (DTC-SVM or DTC-SPWM) presented in this chapter can be combined with speed FLC and this independent stator resistance estimator to develop a robust DTC for PMSM.
