Estimation of minimum conditions for forced oscillations in relay feedback systems

This paper examines the behaviour of a single loop relay feedback system (KFS) in the presence of an external forcing sinusoid. It is well known that such a closed loop system sometimes undergo a forced oscillation (FO) phenomenon while at other times, subharmonic oscillations (SO) may be observed. This paper examines the conditions under which these can occur. It was found that for either FO or SO to occur, the external forcing signal must satisfy a certain minimum amplitude. Whether a FO or SO occurs, the minimum amplitude of the external forcing signal can be determined accurately using a graphical approach and a numerical method. Simulation studies are presented to illustrate the results.