Vibration Spectrum of an Act‐and‐Wait Controlled System With Significant Damping

ABSTRACT Act‐and‐wait concept in control theory is a tool for enhancing the control quality by decreasing the destabilising effect of time delay. As was shown in other works, applying the act‐and‐wait concept to a PD position control increases the available range of proportional gains, which reduces the steady‐state error of dry friction. In this paper, we focus on the vibration phenomena at the boundaries of the dynamic stability from the aspect of the vibration spectrum. We consider a single‐degree‐of‐freedom mechanical model of DC actuators that contains significant effective damping. At different types of stability limits, new analytical and semi‐analytical results are derived for the vibration spectrum. The results are validated by numerical calculations and experiments on a linear DC actuator.