Abstract
The structure uncertainty effect is considered on actively controllable composite beam that is a part of the structure of a civil building in a seismodangerous zone. The solution of the problem for active control of vibrations of the composite beam is based on the introduction of a simplified model of sensors and an actuator, which are implemented in the form of piezoelectric plates pasted on two opposite planes of the beam. A suggestion is made of the practical approach that affords the robust control of the composite beam and is founded on the modern H 2- and H ∞-methods of the theory of control. The effectiveness of the suggested approach for the suppression of vibrations of the composite beam under consideration is illustrated by the examples of numerical modeling.
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Trindade, M.A., Benjeddou, A., and Ohayon, R., Piezoelectric Active Vibration Control of Damped Sandwich Beams, J. Sound Vibrat., 2001, vol. 246(4), pp. 653–677.
Balamurugan, V. and Narayanan, S., Finite Element Formulation and Active Vibration Control Study on Beams Using Smart Constrained Layer Damping (SCLD) Treatment, J. Sound Vibrat., 2002, vol. 249(2), pp. 227–250.
Foutsitzi, G., Marinova, D.G., Hadjigeorgiou, E., and Stavroulakis, G.E., Finite Element Modeling of Optimally Controlled Smart Beams, Venkov, G. and Marinov, M., Eds., in Proc. 28 th Int. Summer School “Appl. Math. Engineer. Econom.,” Sozopol, Bulgaria, 2002, Sofia: Bulvest 2000 Press and Faculty of Applied Mathematics and Informatics, Tech. Univ. Sofia, 2003, pp. 199–207.
Stavroulakis, G.E., Foutsitzi, G., Hadjigeorgiou, E., et al., Design of Smart Beams for Suppression of Wind-Induced Vibration, Proc. Ninth Int. Conf. Civil and Structural Engin. Comput., Topping, B.H.V., Ed., Stirling: Civil-Comp Press, 2003, p. 114.
Arvanitis, K.G., Zacharenakis, E.C., Soldatos, A.G., and Stavroulakis, G.E., New Trends in Optimal Structural Control, Selected Topics in Structronic and Mechatronic Systems, Belyaev, A. and Guran, A., Eds., Series on Stability, Vibrat. Control Syst., Singapore: World Academic Publishers, 2003, ser. B, vol. 3, pp. 321–416.
Zhang, X., Shao, C., Li, S., and Xu, D., Robust H∞ Vibration Control for Flexible Linkage Mechanism Systems with Piezoelectric Sensors and Actuators, J. Sound Vibrat., 2001, vol. 243(1), pp. 145–155.
Foutsitzi, G., Marinova, D.G., Hadjigeorgiou, E., and Stavroulakis, G.E., Robust H2 Vibration Control of Beams with Piezoelectric Sensors and Actuators, Int. Conf. “Physics and Control,” St.Petersburg, Russia, 2003, vol. 1, pp. 157–62.
Aldraihem, O.J., Wetherhold, R.C., and Sigh, T., Distributed Control of Laminated Beams: Timoshenko Theory vs. Euler-Bernoulli Theory, J. Intelligent Mat. Syst. & Struct., 1997, vol. 8, pp. 149–155.
Reddy, J.N., Mechanics of Laminated Composite Plates, Boca Raton: CRC Press, 1997.
Kwon, Y.K. and Bany, H., The Finite Element Method Using MATLAB, Boca Raton: CRC Press, 1997.
Zhou, K., Essentials of Robust Control, Upper Saddle River, New Jersey: Prentice Hall, 1998.
Petkov, P. and Konstatinov, M., Rubustni sistemi za upravlenie. Analiz i sintez s MATLAB (Robust Control Systems Analysis and Synthesis with MATLAB), Sofia: ABC Tekhnika, 2002.
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Original Russian Text © D. Marinova, 2009, published in Avtomatika i Telemekhanika, 2009, No. 6, pp. 74–89.
This work is implemented according to the agreement of April 2, 2007 between the Institute of Control Sciences of the Russian Academy of Sciences, Moscow, Russia, and the Technical University, Sofia, Bulgaria.
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Marinova, D. Robust control of composite beams. Autom Remote Control 70, 982–996 (2009). https://doi.org/10.1134/S000511790906006X
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DOI: https://doi.org/10.1134/S000511790906006X