Stabilizing unstable systems by the act-and-wait concept – Case studies

The act-and-wait control is a special time-periodic control for systems with feedback delay, where the control gains are periodically switched on and off in order to neutralize the destabilizing effect of the delay. In this paper, we present two case studies to show how the act-and-wait type time-periodic control can be used to stabilize otherwise unstable systems. The first case study is a second order system subjected a PD controller with large feedback delay such that the system is always unstable if the feedback is continuously applied with constant gains. The second case study is a first order system subjected to the feedback of the second derivative of the state resulting in a differential equation of advanced type. It is shown that both unstable systems can be stabilized using the act-and-wait control concept.