Amplitude Dependent Stability Analysis for Non-Linear Sampled-Data Control Systems in a Frequency Domain

Abstract

This paper analyzes the amplitude dependent behavior of nonlinear sampled-data control systems in a frequency domain. First, a robust stability condition for nonlinear discrete-time feedback systems (which was derived in our previous papers) is applied to a sampled-data control system containing a single time-invariant nonlinear element in the forward path. Then, an instability condition for that type of nonlinear feedback system is derived. By considering restricted areas (sectors) in the nonlinear characteristic, the existence of a sustained oscillation (whether it is periodic or not) can be predicted and estimated accurately. Numerical examples will be presented to illustrate the theory. The concept described herein can be expanded to multi-loop nonlinear sampled-data control systems. A robust stability condition for the multi-loop system will be given at the end of this paper.