The optimal controller design framework for PID-based vibration active control systems via non-probabilistic time-dependent reliability measure

Vibration control is a significant problem in practical engineering. Because of the uncertainties in practical engineering, the controllers designed according to the deterministic systems have the possibility of failure when applied to practical systems. Taking the widely-used PID control as an example, a framework for designing PID controllers considering the time-dependent reliability (TDR for short) of practical systems with interval uncertainties is proposed in this paper. After quantifying uncertain parameters as non-probabilistic interval forms, the collocation method is utilized to obtain more accurate response intervals. After that TDR is calculated by the first-passage theory to design the optimal PID controllers by the simulated annealing optimization method. Two examples are presented to prove the practicability of this framework.