Vibration Suppression Of Spatial H_∞ Control On Smart Structures

This paper introduces a feedback spatial H_∞controller to suppress vibration of a flexible cantilever beam using collocated piezoelectric actuator-sensor pairs. The modal approach to modeling of the structure results in infinite-dimensional models, for control design purposes, the infinite-dimensional model is simplified by removing higher modes which lie out of the bandwidth of interest. The direct truncation can considerably perturb the zeros of the truncated model. For settling the problem, this thesis applies the method of minimizing the effect of removed higher order modes on the low-frequency dynamics of the truncated model by adding a feedthrough term to the low order of the system. The feedthrough term is incorporated into the flexible-structure model to correct the locations of the in-bandwidth zeros. The corrected model is then used to design spatial H_∞controller.The controller is designed to minimize the spatial H_∞norm of the closed-loop system to ensure average reduction of vibration throughout the entire structure. The final controller is numerically implemented and the results illustrate the robust control performance of a cantilevered beam type structure. It is possible, for certain mode, to obtain the very satisfactory result of vibration reduction.