Linear quadratic regulator (LQR) control has been widely demonstrated to be suitable and effective for active base-isolated buildings. However, its application to the buildings equipped with nonlinear dampers remains challenging due to the theoretical and design complexity. This paper presents a simple response-spectra-based design method for LQR control of active base-isolated buildings with bilinear oil dampers (BODs). First, a gain-scheduling-based LQR (GSLQR) control algorithm is presented to accommodate BODs. The GSLQR controller is defined as a total controller composed of BODs as the passive part and a gain-scheduling (GS) controller as the active part. This separates BODs from the plant, thereby transforming the control of a nonlinear system into the control of a linear system. We optimize the total control force using an LQR algorithm considering acceleration, velocity, and displacement. Then, a response-spectra-based design method is presented. We construct an equivalent passive model (EPM) of the system, which enables the estimation of maximum responses on the response spectra. Moreover, a control-force spectrum is presented to estimate the maximum required active control force. Finally, a design procedure is provided and an example is given to show the feasibility of the design method. The results indicate that this method extends LQR control to buildings with BODs and determines the design parameters from the spectra to meet the design requirements, without relying on simulations or trial-and-error procedures. This presents a promising strategy for designing active control systems in buildings equipped with nonlinear dampers.
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