Robust vibration control of a functionally graded beam with a variable cross section

Rahmani, Behroz; Naghmehsanj, Mohamma Reza

Document Type : Research Paper

Authors

Department of Mechanical Engineering, Yasouj University, Yasouj, Iran

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 state-space form. Since the data measurement is done in sampling intervals, the system is considered as sampled-data. 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.

Keywords

Main Subjects

Sound and Vibration

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Robust vibration control of a functionally graded beam with a variable cross section

References

Volume 2, Issue 2 - Serial Number 2September 2015Pages 17-30

Volume 2, Issue 2 - Serial Number 2
September 2015
Pages 17-30