Projeto robusto H∞ aplicado no controle de vibrações em estruturas flexíveis com materiais piezelétricos incorporados

Abstract

This work focus on the application of active control technology by using piezoelectric materiais for the structural vibration control in beam and plate structures. A finite element approach and the assumed modes method are used for constructing the nominal model of the plant. The dimension of the model is then reduced by a combination of modal reduction techniques and system controllability and observability analysis. The effects caused by this reduction are analyzed and incorporated in the mathematical model of the plant used for the controller design. The operation principie of piezoelectric materiais is verified by numerical validation tests and the results obtained by the above mentioned modeling techniques are compared with the data generated from simulation software. The problem of choosing the optimum locations along the structure for the piezoelectric elements is solved by an optimization function that considers the participation of each vibration mode in the system response. Due to inherent uncertainties inserted in the mathematical formulation procedure, the present work proposes the robust controller design for this control problem. The fundamental formulation of this controller is discussed and its robustness, stability and performance are shown through numeric simulations. An experimental apparatus representing a flexible beam type structure is used to identify the main parameters and to evaluate a robust controller that suppresses the structural vibrations minimizing a spatial infinite norm. This work is concluded presenting the potentialities of the design methodology proposed and future developments to be implemented.