Implementation of coupled mode optimal structural vibration control using approximated eigenfunctions

With the approximately normalized eigenfunctions and matching modal equations obtained in a differential form, we have implemented the structural vibration control successfully. In applying the steady-state quadratic coupled mode optimal control algorithm for the control structure, i.e. the all-clamped square plate, the non-orthogonalized extra terms are evaluated. By the suitable formulation of a control system, we could simulate the modal responses of the first six modes showing the validity of proposed modal equations and all the control procedures are considered to be reliable as a structural vibration control scheme. Modal responses for single and double actuators are observed and by changing the other control factors such as impulse position and weighting matrices we could compare the control performance. Moreover, these simulation results provide ideas on how to select the optimal number and positions of the actuators.