A fractional order controller for seismic mitigation of structures equipped with viscoelastic mass dampers

Abstract

In this paper a fractional order (FO) controller is proposed for solving the vibration suppression problem in civil structures. A laboratory scaled steel structure, with one floor, modeled as a single degree-of-freedom system is used as a case study. Two passive control solutions are proposed: a tuned mass damper (TMD) and a viscoelastic damper (VED), the latter being modeled using fractional derivatives. The simulation results show that the VED is able to further reduce the vibrations induced as forced oscillations or due to seismic excitation inputs, as compared to the passive TMD. The FO controller is then tuned using a new approach based on imposing a magnitude condition for the closed-loop system at the structural resonance frequency. The resulting FO active control strategy, together with the VED, ensures an increased seismic mitigation. Structural modeling errors are also considered, with the proposed active FO control strategy behaving robustly in terms of vibration suppression. The novelty of the paper resides in the tuning approach, as well as in the proposed active control strategy that is based upon combing VEDs, described using an FO model, and an FO controller.