Optimal active control of a circular plate vibration

Abstract

An optimal active control system to reduce the vibration of a circular plate is presented, using modern optimal control theory and theory of observer. State space model for active control is formed by truncated model expansion by the lower four modes among the innumerable eigenmodes of circular plate vibration. For this state space model, optimal control law is so chosen that quadratic performance index representing system energy is minimized. The theory of observer is applied to the estimation of all state variables of model from the measurement of displacement only. Locations of actuators are chosen based on optimal effectiveness of the closed-loop control and the parameters of the optimal observer (sensor locations and observer gain) are chosen so as to assign its eigenvalues to desired locations and at the same time a measure of the deviation of the estimate of the observed state from its actual value is minimized Optimal results for from one to three actuators case and from one to two sensors case are obtained and compared each other. Also effect of weighting factors in performance index on optimal location and modal damping is investigated.