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Title

ROBUST VIBRATION CONTROL OF A FUNCTIONALLY GRADED BEAM WITH A VARIABLE CROSS SECTION

Pages

 Start Page 17 | End Page 29

Abstract

 In this paper, robust VIBRATION CONTROL of a thin functionally graded beam with a variable cross-section has been investigated. For this purpose, piezoelectric patches are used as sensors to measure the displacement of the beam and as actuators to apply control forces. In this way, firstly, Euler-Bernoulli theory is used to derive the governing dynamical partial differential equation, through the Hamilton’s principle. Approximate solution of these equations is achieved using finite difference method, and the PROPER ORTHOGONAL DECOMPOSITION is then used to obtain vibration mode shapes. After that, time-dependent ordinary differential equations are attained using Galerkin projection scheme and then represented in the statespace form. Since the data measurement is done in sampling intervals, the system is considered as sampleddata. In this way, direct digital control design methodology is used. For this purpose, based on its zero-order hold equivalent model, a robust discrete-time, observer-based, output feedback controller is designed. In this regard, controller and observer gains are designed by a Lyapunov-based method. This procedure is done by solving a set of linear matrix inequalities. Simulation studies show the effectiveness of the proposed method.

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