This paper devises a new method for estimating the maximum response and maximum control force for high‐rise base‐isolated buildings with active structural control (active base isolation) to simplify the conventional complex design procedure. While active base isolation has emerged as a prominent solution for achieving high control performance, its design process is inherently complex, particularly when applied to high‐rise buildings where wind loads become prominent. To address this problem, we propose a streamlined method inspired by the gust factor methodology widely used in conventional passive wind‐resistant designs. This method estimates the maximum response and maximum control force without the need for numerical simulations. We first construct an equivalent passive model of a multi‐degree‐of‐freedom control system to theoretically compute the dynamics of the system. Based on the constructed equivalent passive model and then propose a method to calculate the mean displacement and mean control force using only the static equilibrium of this model. Furthermore, we extend the conventional gust factor approach to active base isolation to estimate the maximum displacement and maximum control force for active base isolation without the need for numerical simulations. We validate our methods through a series of numerical examples, incorporating key parameters such as feedback gain, aspect ratio of building, return period of wind force, and stiffness of isolation. Numerical verifications show that the mean response and mean control force are estimated by the static equilibrium of the proposed equivalent passive model. Moreover, the maximum response and maximum control force can be estimated by the proposed gust factors. Our methods can be applied for feedback control systems using a given feedback gain.

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.

This paper presents a new design method based on a robust-control strategy in the form of a linear matrix inequality (LMI) approach for a passive tuned mass damper (TMD), which is one of the common passive-control devices for structural vibration control. To apply the robust control theory, we first present an equivalent expression that describes a passive TMD as an active TMD. Then, some LMI-based condition is derived that not only guarantees robust stability but also allows us to adjust the robust H∞ performance. In particular, this paper considers the transfer function from a seismic-wave input to structural responses. Unlike other methods, this method formulates the problem to be a convex optimization problem that ensures a global optimal solution and considers uncertainties of mass, damping, and stiffness of a structure for designing a TMD. Numerical example uses both a single-degree-of-freedom (SDOF) and 10DOF models and seismic waves. The simulation results demonstrated that the TMD that is designed by the presented method has good control performance even if the structural model includes uncertainties, which are the modeling errors.