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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.

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)