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In this paper, the fast-scale or period doubling bifurcation in a chopper driven series connected DC motor operating in continuous conduction mode is analyzed and controlled. By employing the monodromy matrix approach, the system parameter values at which the nominal period-1 orbit loses stability is determined analytically. Then, by manipulation of the State Transition Matrix (STM) at the switching manifold of the unstable periodic orbit, we were able to control the onset of the fast-scale bifurcation and thus extend the system parameter range for nominal period-1 operation.

The existence of period-doubling bifurcation cascades and chaos in DC drives with full-bridge converter is well known. This paper reports for the first time the occurrence of coexisting attractors with a fractal basin of attraction in this relatively simple deterministic system. At some parameter values the trajectories converge on either a period-1 or a period-3 attracting set depending on the initial state of the system. The attempt to separate the basins of attractions of each attracting set revealed the existence of a riddled basin of attraction. This phenomenon has practical consequences in that it might render future prediction of the system's steady state behavior almost impossible. Using Filippov's method, we show analytically that the co-existing period-3 attractor is born due to a saddle node bifurcation that occurs at some critical parameter value, and thus it co-exists with the stable period-1 attractor.

Fast-scale instabilities in full-bridge converter dc drives are analysed in this paper using Filippov's method of differential inclusions. This method is very suitable for stability analysis of systems with switching nonlinearities and has been successfully applied to mechanical switching systems and dc-dc converter circuits. This paper presents the first application of the method in a variable speed drive application. By obtaining the state transition matrix over one complete cycle we were able to determine analytically the parameter values at which the nominal period-1 orbit loses stability. Based on the structure of the state transition matrix across the switching manifold (the saltation matrix) an optimal controller was developed capable of extending the parameter range for safe period-1 operation. (6 pages)