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. 1. Introduction Active control devices, such as the Active Tuned Mass Damper (ATMD), require substantial input power and could also destabilize the system if the controller is improperly designed. On the other hand, passive control devices are less effective in the presence of stochastic disturbances and/or structural property variations. Semiactive control devices do not possess these disadvantages and thus appear to be sound alternatives to active and passive devices [1–4]. Such devices provide control forces by varying their mechanical properties, based on feedback. The variable stiffness damper is a semiactive device with good potential for controlling wind/earthquake generated response. Kobori et al. [5] and Nasu et al. [6] considered an active variable stiffness (AVS) system, comprising an on-off type two ended hydraulic damper, to make the structure nonresonant during an earthquake. Nemir et al. [7] considered a variable stiffness bracing and obtained rapid dissipation by way of energy redistribution to higher modes. Such AVS systems, while effective, cause abrupt switching of stiffness. Yang et al. [8] proposed a sliding mode controller for an AVS system. A resetting control algorithm, involving the release of potential energy of the device followed by a quick
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