Analytical approaches to non-linear sampled-data control systems

Abstract

The analysis of non-linear oscillations in sampled-data control systems is treated. The system considered here has the non-linear element in discrete signal portions. In the first half of the paper the strict analytical method is proposed. By using it, the periodic equilibrium states and their stability can be strictly analysed, without any assumption on the waveform, if the period of the oscillation is an integer multiple of the sampling period. In the second half, two different applications of describing function methods to the sampled-data systems are proposed. One is defined in the same way as in continuous systems, and it is accurately applicable to the sinusoidal oscillation of which the period is sufficiently larger than the sampling period. The other is defined by considering the phase relation of oscillations at sampling instants, and it is applicable when both frequencies are closely approached. Moreover, in some examples illustrated, the existence of ‘hard self-excitations’ in sampled-data systems is suggested.