Nonsmooth active control method for base-smart isolated structures with roller bearings

In applied structural control technology, base-isolated technology has become popular due to its advantage of simple shock absorption, stable performance, and reasonable cost. Currently, base isolation is extensively applied worldwide, and its role in mitigating the seismic response of structures continues to grow. Moreover, it has been proven effective in decreasing seismic response of structures under recent strong earthquakes. However, the displacement at the isolation layer is sometimes large under strong earthquakes, which will decrease the safety of the structure and perhaps lead to the failure of the isolation layer. Therefore, in this study, the base-isolated structure with roller bearings is taken to investigate the seismic response control of structures, and the active control devices are added in the isolation layer of the isolated structure to decrease the seismic displacement at the isolation layer, so that a smart-isolated structure is formed. Nonsmooth control algorithm is introduced in the smart-isolated structure. Based on the feedback of the velocity and displacement of the isolation layer, nonsmooth control algorithm is proposed for designing the smart-isolated structure. Moreover, according to Lyapunov stable theory, the global finite time stability of intelligent control closed-loop system under nonsmooth control is deduced. A six-layer isolated structure with roller bearings is used as an example, and a simulation analysis of seismic response control is performed based on the nonsmooth active control algorithm and linear quadratic Gaussian (LQG) active control algorithm. The results show that the smart-isolated technology can effectively control seismic displacement at the isolation layer, and compared with the passive isolated technology, the superstructure seismic response is significantly decreased. Meanwhile, the results demonstrate that compared with the LQG control algorithm, the nonsmooth control algorithm has a better control effect and can implement feedback control for base-isolated structures by using fewer feedbacks. Furthermore, the nonsmooth control algorithm has great stability.