Design of Reduced-Order Robust Controllers for Smart Structural Systems

Abstract

This paper presents a method of designing reducedorder robust controllers for smart structural systems. We consider two kinds of uncertainties in the structural systems, norm bounded unstructured uncertainty and the variations of structural parameters. The smart structure with lead zirconate titanate (PZT) sensors and actuators is represented by a high order analytical model. Model error due to the uncertainties in structural parameters is modeled by parametric uncertainty in natural frequencies and damping ratios. By generalizing balanced truncation method for uncertain system, the high order model with uncertainties is reduced to a low order model with preserved parametric uncertainty. Based on linear matrix inequalities (LMIs) and Popov criterion, a robust controller is designed to suppress the lowfrequency vibrations caused by external disturbances and to guarantee the stability and performance of the closed-loop system under uncertainties. The order of the controller is further reduced by a frequency weighted model reduction method using LMI. The procedure was experimentally tested on a smart structural test article.