<title>Linear quadratic distributed self-tuning control of vibration in a cantilever beam</title>

Abstract

In this paper a new method of distributed adaptive control of vibration in flexible structures is presented. It is based on finite element approximation from which the auto-regressive parametric representation of the structure is obtained. This representation is used to estimate the structural parameters, viz., mass, stiffness and damping coefficient, using recursive least squares method. The finite dimensional model is then used to design a state-space controller based on the linear quadratic regulator principle. The on-line structural parameter estimation and the controller are then combined using certainty equivalence principle to obtain linear quadratic self-tuning controller for vibration suppression in flexible structures. The performance of the controller (without the self-tuning pat of the algorithm) in suppressing vibrations in an aluminum cantilever beam with surface mounted piezo-electric sensor and actuators is demonstrated experimentally. The spatial recursive algorithm to estimate transverse and angular displacement/velocity from the measured set of strain/strain-rate data, developed in the companion paper, is used as a state estimation algorithm for the state feedback controller.