Numerous subharmonic states in Direct Torque Controlled Induction Machine

The scope of the paper is the strange behavior of direct torque controlled (DTC) induction machine (IM) resulting from the nonlinearity of hysteresis comparators. A piecewise-defined, non-stroboscopic, discrete-time Poincare map can be constructed for the system. The movement of the two controlled state variables, the stator flux linkage and the electric torque, within the hysteresis loops had to be determined from switch to switch. This complex Poincare map takes into account the fast switching operations of the voltage source converter (VSC). Periodic, subharmonic, chaotic and intermittent chaotic states along a special bifurcation series caused by discontinuity of the Poincare mapping function were detected. In order to give a better insight into the system operation, a one-dimensional piecewise linear map is developed, numerous subharmonic states were analyzed.