**4. Fuzzy direct torque control for PMSM**

#### **4.1. FDTC strategy**

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

The PMSM parameters used in this simulation are shown in table II. These parameters will

f + J. S k� <sup>+</sup>

**Ωmes**

1

Rated output power (Watt) Rated phase voltage (Volt) Magnetic flux linkage (Wb) 500 190 0.052 Rated torque (Nm) Rated speed (r/min) Maximum speed (r/min) 0.8 1000 6000 d-axis inductance (mH) q-axis inductance (mH) Inertia (Kg.m2)

3.3 3.3 0.003573

3 1.59 0.00047

The models of the PMSM, VSI and basic DTC algorithm are developed in Matlab/Simulink in order to examine the complete behaviour of the basic DTC. The sampling period has been chosen equal to 50 µs (20 KHz) for basic DTC. Various tests have been carried out in order to investigate the drive performance and to characterize the steady-state and transient behavior.

**Figure 8.** Mechanical speed (on the left) and electromagnetic torque (on the right) tracking performance

Poles Stator resistance (Ω) friction coefficient (Nm.s/rd)

where τ� = 0.1 second

k� S

PI Speed Controller

 k� <sup>=</sup> � ��.��

**Ωref**

and k� <sup>=</sup> �

**Figure 7.** Closed loop PI speed controller

be used in all the simulations of this chapter.

**3.6. Simulation results** 

**Table 2.** PMSM parameters

under load variations in case of basic DTC

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Figure 11 shows the complete FDTC structure which combines FDTC and PI-Fuzzy speed controller. Indeed, the switching table used in basic DTC and the hysterisis controllers are replaced by a fuzzy switching table, whose inputs are electromagnetic torque and stator flux errors denoted respectively ΔГ and ΔФs, and the argument θ�of the stator flux (should remain between ±π).Whereas its outputs are the states of the VSI switches. In other hand, the classical speed PI corrector is replaced by a PI-Fuzzy speed controller in order to improve the dynamic performance of the DTC.

**Figure 11.** Fuzzy logic switching table used in FDTC

Figure 12 shows the design of this fuzzy logic system in Matlab/Simulink and also the configuration of its inputs and outputs as membership functions.

**Figure 12.** Matlab/Simulink design of the fuzzy logic switching table used in FDTC
