Hybrid reliability-based sequential optimization for PID vibratory controller design considering interval and fuzzy mixed uncertainties

Abstract

Vibration control is an important problem in practical engineering. Optimal control is widely used, but the uncertainties in practical engineering may lead to the failure of the system. To reach a balance of safety and energy-consuming, taking the widely-used proportional-integral-differential control as an example, a framework for hybrid reliability-based sequential optimization for vibratory controller design considering interval and fuzzy mixed uncertainties is proposed in this paper. Firstly, the fuzzy uncertainties are transformed into interval uncertainties according to the cut-level strategy. Then the response interval under a certain membership can be calculated by the subinterval collocation method, which can guarantee the accuracy of the calculated response interval. In this process, to choose proper memberships as cut-levels and improve efficiency, the adaptive fitting method based on the differences of areas is adopted. Next, taking interval and fuzzy uncertainties into consideration, a novel non-probabilistic reliability evaluation is performed based on the area ratio, which is composed of upper and lower boundaries of the minimum value of the extreme state function. Finally, the sequential optimization is adopted to improve the efficiency of optimization, in which the constraint is changed according to the proposed non-probabilistic area-ratio reliability. Two engineering examples are presented to demonstrate the accuracy and practicability of this framework.