Robust active vibration control of piezoelectric flexible structures using deterministic and probabilistic analysis

Abstract

The main objective of this article is to propose a general and systematic robust control methodology for active vibration control of piezoelectric flexible structures such that the probabilistic information of parametric uncertainties can be investigated, and the robustness properties of the closed-loop system can be quantitatively ensured. For the purpose, the modal parameter identification is performed based on the finite element analysis to have the reduced nominal dynamical models. The generalized polynomial chaos framework is employed for uncertainty analysis to obtain the probabilistic information of parametric uncertainties. In the presence of probabilistic parametric and dynamic uncertainties, phase and gain control policies–based $H_{\infty }$ output feedback control is used for the controller design to ensure a set of control objectives simultaneously, and then deterministic and probabilistic robustness analyses are conducted to quantitatively verify the robustness properties of the closed-loop system both in the deterministic sense and in the probabilistic one. The design process and the effectiveness of the proposed control methodology are illustrated via active vibration control of a piezoelectric cantilever beam.