ANALYSIS OF THE NEIMARK-SACKER BIFURCATION IN DC CHOPPER FED DC DRIVES VIA THE MONODROMY MATRIX

The nominal behaviour of a DC chopper fed DC drive under proportional integral (PI) control is a periodic orbit whose period equals that of the clock. But as some controller parameters are varied, this nominal orbit loses stability via a Neimark-Sacker bifurcation leading to the birth of a quasi periodic orbit (the so called torus) with a considerable impact on the losses and lifetime of the system. Further variation of the system parameters leads to several period-adding, phase-locking and chaotic phenomena as the torus breaks down. In this paper, by employing the Monodromy matrix, we were able to determine analytically when this occurs, and hence appropriate action can be taken when the controller is designed. Analytical and numerical results validate our findings.