Saturation-Induced Limit Cycles in Observer-Based State Feedback Control

To avoid significant performance degradation due to control signal limitation usually termed as controller windup, feeding the actual limited plant input signal into the controller`s state observer is stipulated by state-of-the-art anti-windup schemes. Based on piecewise affine system description, this study presents necessary and suffcient conditions for such an observer-based controller structure to give rise to sustained non-linear oscillations. An effective numerical procedure is devised to evaluate period and the trajectories of the resulting limit cycles. To demonstrate that existence of limit cycles is related to the structure of anti-windup, it is shown that global closed-loop exponential stability can, on the contrary, be guaranteed for the case when the computed (unlimited) control signal is fed to the observer.