Multi-Objective Robust Active Vibration Control of an Arbitrary Thick Piezolaminated Beam

Abstract

A multi-objective mixed / robust output feedback control synthesis with additional regional pole placement constraints in a linear matrix inequalities (LMI) framework is adopted for active vibration suppression of a simply supported, arbitrary thick, piezolaminated beam with continuously integrated sensor and actuator layers, in the face of high frequency unmodeled dynamics (residual uncertainties) and external disturbance. The structural formulation is based on a spatial state-space approach using the exact linear two-dimensional piezoelasticity theory and involving local/global transfer matrices. To assist control system design, subspace-based multivariable system identification is carried out by using the first four modes in the frequency range of 0–4000 rad/sec for control purpose, while the remaining high frequency (residual) modes in the control bandwidth are left as the uncertainty of modeling. The dynamic performance of vibration control system is demonstrated in both frequency and time domains for a three-layered sandwich beam including three pairs of piezoelectric actuator/sensor (Ba2NaNb5O15/PZT4) segments asymmetrically collocated on both sides of an orthotropic core for two different types of loading (i.e., impulsive load and random disturbance). The accuracy of dynamic analysis is established with the aid of a commercial finite element package and the data available in the literature.