Possibilities of Optimal and Adaptive Control Laws Design in Piezoelectric Smart Structures

Abstract

AbstractPossibilities of the controller design for piezoelectric smart structures are considered in the paper. The modelbased approach, which relies on the finite element modal analysis of structures, is used. As an alternative, system identification is suggested in cases when the real plant or its prototype is available for studying. Dynamics of piezoelectric active materials used as actuators and sensors is taken into account in the modelling procedure. The aim of control is vibration suppression in the sense of magnitudes reduction as well as the isolation of undesirable frequencies from the response spectra. For known plant models and available a priori information on the type of excitation or disturbances, optimal LQ tracking control systems perform good behavior. Owing to the approximation of the real structure's behavior by the finite element model and by modal reduction, the full infinite‐dimensional dynamics of an elastic structure cannot be completely captured. Introduced inaccuracies could be compensated for if they are viewed as the source of the model parameters variation and therefore by employing adaptive control laws. The adaptive control design is considered from this point of view. The application possibilities are illustrated by examples of piezoelectrically controlled structures.