Active base isolation has been studied in the last few decades to improve the control performance of base isolation. As a two-degree-of-freedom active disturbance-rejection method, the equivalent-input-disturbance (EID) approach shows its validity for structural control. It uses a state observer to estimate the effect of disturbances on a control input channel. However, since the model of a base-isolated building has high degrees-of-freedom, the resulting control system has a high order. Thus, the use of a full-order state observer results in the complexity of a control-system implementation. To solve this problem, this paper presents an EID control system that uses a reduced-order state observer (ROSO) to reduce the expense of control-system implementation and ensure system reliability. First, the condition of using an ROSO in an EID control system is derived, and the configuration of an ROSO-based EID control system is presented. Next, the concept of perfect regulation is used to design the gain of the state observer. A stability condition of the system with prescribed control performance is derived in the form of a linear matrix inequality (LMI) that is used to design the gain of the state feedback. Finally, the seismic control of a base-isolated building demonstrates the validity of the method.

The fractional derivative (FD) model is one kind of numerical model of viscoelastic (VE) damper, which can describe the behavior of the frequency sensitivity of VE damper well with some empirical parameters. However, the FD model is difficult to apply to practice design because of its complex calculation. Compared with the FD model, the integer derivative (ID) models are widely used as the VE damper equipped in the high-rise building. However, ID models lack consideration of frequency sensitivity, which significantly affects their accuracy. To consider frequency sensitivity in the ID model, this study attempted to use the 4-element and 6-element models of ID models to approximate the FD model, easily describing the VE characteristic of the damper. The wind forces of 500-year-return periods were employed to analyze the influence of the frequency sensitivity of the VE damper on wind-induced responses and energy dissipation. The results of this study showed that the 4-element and 6-element models not only matched frequency sensitivities well to the FD model in the low-frequency region of wind excitation but also had good agreements with the FD model in wind-induced responses and energy dissipation. Based on the findings in this study, the 4-element and 6-element models were recommended as numerical models for the wind-resistant design of high-rise buildings with VE dampers. It helps improve the wind-induced behavior simulation of VE dampers considering their frequency sensitivity in high accuracy without massive experimental cost.

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.