On the Periodic Modes of Oscillation in Pulse-Width-Modulated Feedback Systems

A general procedure for obtaining information on the periodic modes of oscillation in PWM and nonlinear sampled-data feedback systems is considered in this paper. Based on the equivalence of PWM in the state of limit cycles to the finite pulsed systems with the periodically varying sampling pattern, the methods of analysis applied to the latter are extended to obtain these limit cycles. In particular, the final value theorem is applied to obtain the fundamental response equation which gives rise to the limit cycles for the various specified modes. The theory is applied to systems with and without integrator and the results are checked by the phase-plane approach. Two kinds of nonlinearities, namely, pulse-width modulation and saturating gain, are discussed among the various nonlinearities, and examples are presented for each of these cases. Furthermore, both self-excited and forced oscillations are examined as well as the possible existence of limit cycles for certain specified modes. This approach to examining the periodic modes is not restricted to the type of non-linearity or the order of the system and thus can be applied to various forms of nonlinear discrete systems. However, it is based on the assumption that the mode of the limit cycle is specified, as can be done in certain cases, and thus the method of this paper permits the study of the conditions that sustain those oscillations.