Act and wait control concept

Péter Szalai

Position control of a block using a digital a PD controller is investigated. It is known that feedback delay in the control loop strongly affects stability properties. One possible technique to overcome the destabilization effect of the feedback delay is the act-and-wait control concept: the control force is switched off and on periodically in time. If the switch-off period is larger than the feedback delay, then the system can be described by a discrete map of dimension equal to the dimension of the open loop system. Two criteria, which are often set to control problems, are investigated: the overshoot and the settling time. It is shown that there is no overshoot if the critical (largest in modulus) characteristic multiplier is a positive real number, while the settling time is related to the magnitude of the critical characteristic multiplier. Stability diagrams representing this information are presented and the behavior of the system at different control parameters is demonstrated by numerical simulations. It is shown that the act-and-wait concept result in a better performance with respect to both criteria, while it allows the application of significantly larger proportional control gains, which is a useful feature to avoid position error against friction.