A spectrum for estimating the maximum control force for passive-base-isolated buildings with LQR control

The combination of passive-base-isolated (PM) and active structural control (ASC) has been employed in many buildings globally to improve control performance. Controllers are mainly designed using the linear-quadratic-regulator (LQR) method, which minimizes the response and control force by using their weights. While the estimation of the required control force is important to select an appropriate actuator to perform ASC, previous approaches utilized trial-and-error because the dependency of the maximum control force on the natural period and the passive damper has not been expressed theoretically. To solve this problem, this paper presents a spectrum, namely a control-force spectrum, to estimate the maximum control force while considering the combination of PBI and ASC. An equivalent model of an ASC system is derived to describe the relationship between the vibration characteristics and the LQR weighting matrices. Using the equivalent model and the control-force spectrum, the maximum control force of an ASC system designed by the LQR method is estimated, and the appropriate maximum control force, natural period, and damping ratio are theoretically determined. This study also develops a design method for PBI construction with ASC that selects the natural period, passive damper, and maximum control force by using spectra without requiring trial-and-error and numerical simulations. A numerical design example validates the design method.