The active structural control (ASC) has been applied to base-isolated buildings to achieve a high-damping system. The critical step for designing an ASC system is selecting control parameters and isolation parameters that satisfy the design restrictions. However, the conventional methods are limited in theoretically estimating the maximum control force, which requires great demand for trial-and-error approaches and numerical simulations. This paper constructed the equivalent model of the feedback control system that theoretically expresses the dependence of vibration characteristics (natural period and damping ratio) of the control system on the feedback gain. Then, the control-force spectrum is proposed that estimates the maximum control force for a feedback control system, adjusting both the natural period and damping ratio of the control system. The maximum responses and control force are estimated without additional numerical simulations and trial-and-error approaches using the equivalent model and control-force spectrum. Moreover, a design method was devised for determining the allowance range of the vibration characteristics of structures (damping ratio and natural period) and controllers that satisfy the design limitations (maximum responses and maximum control force). The design method does not require trial-and-error and numerical simulations, thus simplifying the design procedure. Finally, this paper uses numerical examples and a design example to verify the validity of the control-force spectrum and design method.
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