Desiginig of active vibration control system for smart structure 2-D with non-collocated piezo-elements

Abstract

To design vibration control system for flexible structures their mathematical model should be reduced. In the paper we consider the influence of the model reduction on the dynamics of the real closed-loop system. A SFSF smart plate as a TITO system is an object of consideration since we are able to formulate the exact analytical model of such structure. As a result of reduction the model with low frequency resonances is usually separated from the high frequency dynamics because high frequency part of the model is naturally strong damped. In order to estimate dynamical system for control purposes in the paper we applied a few orthogonal methods such as: modal and Schur decompositions. As it is shown all methods well calculate resonances frequencies but generate different anti-resonances frequencies. From control strategy in point of view of the flexible structures these anti-resonances have significantly influence on the stability and dynamics of the closed-loop systems.