Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2014, Special Issue (2013), Article ID 527530, 10 pages.

TLCD Parametric Optimization for the Vibration Control of Building Structures Based on Linear Matrix Inequality

Linsheng Huo, Chunxu Qu, and Hongnan Li

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Passive liquid dampers have been used to effectively reduce the dynamic response of civil infrastructures subjected to earthquakes or strong winds. The design of liquid dampers for structural vibration control involves the determination of the optimal parameters. This paper presents an optimal design methodology for tuned liquid column dampers (TLCDs) based on the H control theory. A practical structure, Dalian Xinghai Financial Business Building, is used to illustrate the feasibility of the optimal procedure. The model of structure is built by the finite element method and simplified to the lumped mass model. To facilitate the design of TLCDs, the TLCD parametric optimization problem is transferred to the feedback controller design problem. Through the bounded real lemma, an optimization problem with bilinear matrix inequality (BMI) constraints is constructed to design a static output feedback H controller. Iterative linear matrix inequality method is employed and it added some value range constraints to solve the BMI problem. After the TLCD parameters are optimized, the responses of displacement and acceleration in frequency domain and time domain are compared for the structure with and without TLCD. It is validated that the TLCD with the optimized parameters can make the structure satisfy the need for safety and comfort.

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J. Appl. Math., Volume 2014, Special Issue (2013), Article ID 527530, 10 pages.

First available in Project Euclid: 1 October 2014

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Huo, Linsheng; Qu, Chunxu; Li, Hongnan. TLCD Parametric Optimization for the Vibration Control of Building Structures Based on Linear Matrix Inequality. J. Appl. Math. 2014, Special Issue (2013), Article ID 527530, 10 pages. doi:10.1155/2014/527530.

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  • G. W. Housner, L. A. Bergman, T. K. Caughey et al., “Structural control: past, present, and future,” Journal of Engineering Mechanics, vol. 123, no. 9, pp. 897–971, 1997.
  • C.-C. Lin, C.-L. Chen, and J.-F. Wang, “Vibration control of structures with initially accelerated passive tuned mass dampers under near-fault earthquake excitation,” Computer-Aided Civil and Infrastructure Engineering, vol. 25, no. 1, pp. 69–75, 2010.
  • A. S. Pall and C. Marsh, “Response of friction damped braced frames,” Journal of the Structural Division, vol. 108, no. 6, pp. 1313–1323, 1982.
  • J. T. P. Yao, “Concept of structural control,” Journal of Structural Division, vol. 98, no. 7, pp. 1567–1574, 1972.
  • F. Sakai, S. Takaeda, and T. Tamaki, “Tuned liquid column damper-new type device for suppression of building vibrations,” in Proceedings of the International Conference on Highrise Buildings, Nanjing, China, 1989.
  • C. P. Moreno and P. Thomson, “Design of an optimal tuned mass damper for a system with parametric uncertainty,” Annals of Operations Research, vol. 181, pp. 783–793, 2010.
  • U. Mackenroth, Robust Control Systems: Theory and Case Studies, Springer, Berlin, Germany, 2004.
  • J. Rubió-Massegú, F. Palacios-Quiñonero, and J. M. Rossell, “Decentralized static output-feedback ${H}_{\infty }$ controller design for buildings under seismic excitation,” Earthquake Engineering and Structural Dynamics, vol. 41, no. 7, pp. 1199–1205, 2012.
  • A. I. Zečević and D. D. Šiljak, “Design of robust static output feedback for large-scale systems,” IEEE Transactions on Automatic Control, vol. 49, no. 11, pp. 2040–2044, 2004.
  • Y.-Y. Cao, Y.-X. Sun, and W.-J. Mao, “Output feedback decentralized stabilization: ILMI approach,” Systems & Control Letters, vol. 35, no. 3, pp. 183–194, 1998.
  • Y. Wang, “Time-delayed dynamic output feedback ${H}_{\infty }$ controller design for civil structures: a decentralized approach through homotopic transformation,” Structural Control and Health Monitoring, vol. 18, no. 2, pp. 121–139, 2011.
  • M. Kočvara and M. Stingl, “Pennon: a code for convex nonlinear and semidefinite programming,” Optimization Methods & Software, vol. 18, no. 3, pp. 317–333, 2003. \endinput