Linear quadratic distributed self tuning control of vibration in one dimensional cantilever beams

Abstract

In this paper a new method of distributed adaptive control of vibration in one dimensional flexible cantilever beams is presented. It is based on finite element approximation from which the auto-regressive (AR) parametric representation of the beam is obtained. This representation is used to estimate the structural parameters, viz., mass, stiffness and damping coefficient of the beam. The finite dimensional model is then used to design a state-space controller based on the linear quadratic regulator (LQR) principle. The on-line structural parameter estimation and the controller are then combined using the certainty equivalence principle to obtain a linear quadratic self-tuning controller for vibration suppression in cantilever beams. Experimental results on the control of vibration in an aluminium cantilever beam using piezoelectric sensors/actuators are presented.