Robust strategies for active vibration control of plate-like structures: theory and experiment

The theoretical modelling of the vibration of a plate-like active structure incorporating piezoelectric actuators is presented using the Rayleigh-Ritz method. The model was used to design multi-variable controllers (linear qu adratic Gaussian and H infinity) for a cantilever plate with two piezoelect ric actuators providing the controlled strain input to the plate with two n on-collocated sensors providing the feedback signals. A technique for the o ptimal placement of piezoelectric actuators is developed using modal contro llability and a genetic algorithm as the search engine. The proposed contro llers were then implemented experimentally and the measured results compare d favourably with those predicted from simulation studies. The results show that considerable disturbance attenuation can be achieved in lightly dampe d modes of the structure using optimal placement of piezo-electric actuator s and multi-variable controllers.