5.7 Direct Torque Control of Sinusoidal Permanent Magnet Synchronous Motors (SPMSM)
Permanent magnet synchronous machines (SPMSMs) are categorized on the basis of the waveform of the induced electromotive force; they are either sinusoidal or trapezoidal. The SPMSMs with sinusoidal wave-shape of emf are called PMSMs, and the PMSMs with trapezoidal wave-shape of emf are known as Brushless DC Machines (BLDCs) . This sub-section discusses the DTC of SPMSMs, which has a sinusoidal distribution of air-gap flux.
The machines are of surface magnet structure, where the magnets are placed in the grooves of the outer periphery of the rotor lamination to provide high flux density in the air gap and also uniform cylindrical surface of the rotor for the mechanical robustness .
Mathematical equations for dynamic models of the SPMSMs are presented in the next sub-section.
5.7.2 Mathematical Model of Sinusoidal PMSM
The mathematical model for SPMSMs are shown in equations (5.47) to (5.52). The dynamic model is in the rotor flux oriented reference frame. The rotating speed of rotor and rotor flux space vector are the same for the synchronous motor, and they are also equal to the rotating speed of the reference frame :