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Shock and Vibration
Volume 2014 (2014), Article ID 156523, 12 pages
Research Article

LQR Control of Wind Excited Benchmark Building Using Variable Stiffness Tuned Mass Damper

Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India

Received 6 September 2012; Accepted 6 October 2013; Published 8 April 2014

Academic Editor: Jeong-Hoi Koo

Copyright © 2014 S. N. Deshmukh and N. K. Chandiramani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


LQR control of wind induced motion of a benchmark building is considered. The building is fitted with a semiactive variable stiffness tuned mass damper adapted from the literature. The nominal stiffness of the device corresponds to the fundamental frequency of the building and is included in the system matrix. This results in a linear time-invariant system, for which the desired control force is computed using LQR control. The control force thus computed is then realized by varying the device stiffness around its nominal value by using a simple control law. A nonlinear static analysis is performed in order to establish the range of linearity, in terms of the device (configuration) angle, for which the control law is valid. Results are obtained for the cases of zero and nonzero structural stiffness variation. The performance criteria evaluated show that the present method provides displacement control that is comparable with that of two existing controllers. The acceleration control, while not as good as that obtained with the existing active controller, is comparable or better than that obtained with the existing semiactive controller. By using substantially less power as well as control force, the present control yields comparable displacement control and reasonable acceleration control.