Optimal control of a distributed parameter system with applications to beam vibrations using piezoelectric actuators |
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| Authors: | Ismail Kucuk Ibrahim Sadek Yalcin Yilmaz |
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| Institution: | 1. Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates;2. Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey;3. Department of Mathematics, Sakarya University, Adapazari, Turkey |
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| Abstract: | This paper addresses the issue of the active vibration control of the transverse modes in a flexible elastic systems. The control is implemented by discrete sets of piezoelectric actuators that apply the optimal forces. The performance index is a time-dependent quadratic functional of state variables and their time derivatives, and control forces which are determined by minimizing the objective functional subject to a penalty term on the control functions. A combination of Galerkin and variational approaches are employed to determine the control forces in the time domain explicitly in terms of coupled amplitudes and velocities. The effectiveness of the proposed method is demonstrated by applying it to a physical problem controlled by piezoelectric patch actuators. |
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