Forced oscillations and suppression of oscillations in nonlinear sampled-data systems

In this paper, a procedure is developed to investigate and predict the properties of certain types of forced oscillations in a class of nonlinear sampled-data control systems. Use is made of the discrete describing function, and the results are checked on the IBM 7094 digital computer. A sinusoidal input signal with variable amplitude and phase is applied to a relay-type sampled-data control system. It is shown that the input signal has the effect of changing the shape of the critical regions of the negative-inverse of the discrete describing function. The amplitude, phase, and frequency of the forced oscillation can be computed from the intersection between the critical region and frequency loci of the linear portion of the system. Proper selections of amplitude, phases and frequency of the forcing sinusoidal signal permit the elimination and suppression of certain types of sustained oscillations in the system.