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Keywords: smart beams, finite element formulation, uncertainty, robust stability, robust performance, nominal performance, piezoelectric material.

Summary

A mathematical formulation and finite element model for the vibration suppression of laminated smart beams with embedded piezoelectric material is considered in this paper. Cubic and quadratic Lagrangian polynomials are used for the transverse and rotational displacements, respectively, and the differential equations of the beam are based on the Timoshenko beam theory.

The design of the piezoelectric active control using LQG and H_infinity control theory has been studied. The fact that the system is influenced by disturbances, such as the external loading which may be caused from a wind power or the unavoidable noise of measurements or even some damage of the structure, is taken into account. At the beginning the classical optimal linear quadratic regulator is used. In order to take into account our incomplete information about the damage and the external disturbances the theory of a robust H_infinity feedback controller is also used. The following three steps are followed in the robustness analysis:

Expression of the uncertainty set by a suitable mathematical model.
Robust stability (RS): check if the system remains stable for all plants within the uncertainty set.
Robust performance (RP): if the system is robustly stable, check whether the performance specifications are met for all plants within the uncertainty set.

After the analysis of the system we check the robust stability and performance of the system. We encounter the solution to robust stability but not to the problem of robust performance, event though the criteria of nominal performance is very satisfactory and the beam keeps in equilibrium with controls within limits. The H_infinity feedback controller has been determined by using a nonconvex, nondifferentiable optimization approach with the use of HIFOO software within MATLAB.

The numerical results show that the proposed method is effective and that the control behavior of the beam permits us to keep the structure in service up to the given limits of uncertainties. The control behavior of the beam achieves the predicted characteristics. Simulations show that the control strategy produces very good results by reducing the disturbances within the limits of the piezoelectric effect's resistance.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 35 Modeling with Uncertainty and Robust Control of Smart Beams A. Moutsopoulou¹, A. Pouliezos² and G.E. Stavroulakis² ¹Department of Civil Engineering, Technological Educational Institute of Crete, Heraclion, Greece ²Department of Production Engineering and Management, Technical University of Crete, Chania, Greece doi:10.4203/ccp.88.35 purchase the full-text of this paper Full Bibliographic Reference for this paper A. Moutsopoulou, A. Pouliezos, G.E. Stavroulakis, "Modeling with Uncertainty and Robust Control of Smart Beams", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 35, 2008. doi:10.4203/ccp.88.35 Keywords: smart beams, finite element formulation, uncertainty, robust stability, robust performance, nominal performance, piezoelectric material. Summary A mathematical formulation and finite element model for the vibration suppression of laminated smart beams with embedded piezoelectric material is considered in this paper. Cubic and quadratic Lagrangian polynomials are used for the transverse and rotational displacements, respectively, and the differential equations of the beam are based on the Timoshenko beam theory. The design of the piezoelectric active control using LQG and H_infinity control theory has been studied. The fact that the system is influenced by disturbances, such as the external loading which may be caused from a wind power or the unavoidable noise of measurements or even some damage of the structure, is taken into account. At the beginning the classical optimal linear quadratic regulator is used. In order to take into account our incomplete information about the damage and the external disturbances the theory of a robust H_infinity feedback controller is also used. The following three steps are followed in the robustness analysis: Expression of the uncertainty set by a suitable mathematical model. Robust stability (RS): check if the system remains stable for all plants within the uncertainty set. Robust performance (RP): if the system is robustly stable, check whether the performance specifications are met for all plants within the uncertainty set. After the analysis of the system we check the robust stability and performance of the system. We encounter the solution to robust stability but not to the problem of robust performance, event though the criteria of nominal performance is very satisfactory and the beam keeps in equilibrium with controls within limits. The H_infinity feedback controller has been determined by using a nonconvex, nondifferentiable optimization approach with the use of HIFOO software within MATLAB. The numerical results show that the proposed method is effective and that the control behavior of the beam permits us to keep the structure in service up to the given limits of uncertainties. The control behavior of the beam achieves the predicted characteristics. Simulations show that the control strategy produces very good results by reducing the disturbances within the limits of the piezoelectric effect's resistance. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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