Fuzzy Optimal Control of Uncertain Dynamic Characteristics in Tall Buildings Subjected to Seismic Excitation

Abstract

Analytical investigations have been conducted to suppress vibration of tall building structures in the presence of uncertainty in structural dynamic characteristics. Three control algorithms consisting of probabilistic optimal control, fuzzy logic control and optimal control theories are combined to control system fluctuations and severe seismic excitations. A state-space reduced order model is constructed based on dominant observable and controllable Gramians of Lyapunov equations in order to prevent the control matrix singularity and achieve computational efficiency. Both types of active and semi-active control systems are installed in the buildings to reduce the seismic response. In the case of active control systems, both an active tuned mass damper and active mass driver are installed on the top floor. In the case of semi-active systems, such as electric rheological/magnetic rheological dampers, control devices are installed in selected story units. The class of multi-objective control constraints based on minimum control efforts with respect to stochastics evaluation criteria have been defined and satisfied. The fuzzy rule base matrices and fuzzy inference systems are appropriately constructed corresponding to regular forms of optimal control laws and input-output measured data in the control sequences. The performance and robustness of both active and semi-active control systems are investigated through a series of numerical simulations of a multistory building subjected to a wide range of seismic disturbances.