Bifurcations and Chaos in a Linear Control System with Saturated Input

Abstract

An analysis of the dynamical behavior of a saturated input, second-order, linear plant feed back with a simple proportional controller is presented. The synthesized control signal is passed through a saturator before being applied to the plant. Existence and stability of equilibria depending on the controller gain are analyzed. Existence of periodic and homoclinic orbits is also discussed. It is shown that a periodic disturbance and a negative gain can cause the closed-loop system to have a strange (chaotic) invariant set. Numerical and experimental results illustrate the analysis presented.