Non-fragile gains for simultaneous vibration suppression in structures

Abstract

One of the requirements in damage prognosis is to extend the life of the operational structure. Stable vibration suppression through stiffness and/or damping adjustments using a feedback control is one of the techniques useful in these problems. When a structural health monitoring technique through parameter estimation offers a new stiffness matrix, a non-fragile controller that simultaneously suppresses vibrations in healthy and damaged structures is required. In this paper, a procedure to determine such a controller is presented. Discrete and continuous structures are considered. Using velocity feedback, damping adjustments at the local nodes of the finite element model are illustrated. It is shown that in the neighbourhood of the matrix singularities of the Lyapunov matrix established in robust analysis literature, the controller designed based on a healthy model becomes fragile to damage. Thus a meaningful design for simultaneous vibration suppression calls for a non-singularity based controller away from the singularities of the Lyapunov matrix. For the cantilever beam and a spring-mass-damper model, this concept is illustrated using three velocity measurements and a lead zirconate titanate (PZT) patch at the root of the cantilever beam as an actuator.