Cubic nonlinear oscillation control in the frequency domain
Most strategies in the structural control literature are aimed at improving performance of the primary structural system, but may have limited or even adverse effect on nonstructural components during strong seismic events. In this thesis, we emphasize nonstructural performance using an active controller with cubic nonlinearities. The controller is optimized based on the frequency response functions of a SDOF cubic oscillator. A benchmark base-isolated building is studied as a demonstration and we also compare the performance of the proposed cubic controller with that of a LQG-based semiactive controller and a passive energy dissipation system. The thesis also discusses the fundamental qualitative concepts of control theory—controllability and stability, before addressing the quantitative “optimal” determination of the controller. Thus the thesis presents a comprehensive analysis and design of the cubic control system at a basic level, more advanced aspects are also pointed out in the end.