Non-probabilistic robust reliability method and reliability-based performance optimization for active vibration control of structures and dynamic systems with bounded uncertain parameters

Abstract

Active vibration control of uncertain structures is an attractive issue and essentially a complicated multidisciplinary problem. In this research, the author focuses on dealing with parametric uncertainties of actively controlled structures and dynamic systems from the viewpoint of reliability. An efficient non-probabilistic robust reliability methodology for mixed H2/H∞ robust vibration control of uncertain structures and dynamic systems is presented systematically by describing the uncertain parameters as interval variables. The static output robust controller design is carried out by solving a reliability-based multiobjective optimization problem, by which the H2 and H∞ performances and robustness against uncertainties of the closed-loop system can be taken into account simultaneously in an integrated framework. By this method, a non-probabilistic robust reliability measure of an uncertain controlled dynamic system satisfying required H2/H∞ performance and desired decay rate can be obtained, and the robustness bounds of uncertain parameters such that the H2 and H∞ performances of the closed-loop system are guaranteed can be provided. The controller obtained may possess an optimal performance satisfying the condition that the system is robustly reliable to all admissible uncertainties. The non-probabilistic reliability model constructed in this paper is an integrated one and can be used directly for vibration control design of parametric uncertain structures and dynamic systems. Three numerical examples are investigated to demonstrate the effectiveness and feasibility of the presented method.