To adjust the contact force of piezoelectric friction dampers for a benchmark base-isolated structure, a self-tuning fuzzy proportional–derivative controller and an adaptive fuzzy proportional–derivative controller are developed. Considering three candidate signals, namely, the isolation displacement, isolation velocity, and roof acceleration, the best feedback signal for the self-tuning fuzzy proportional–derivative controller is selected based on the Pareto-optimal front. The performance of the self-tuning fuzzy proportional–derivative controller during both near-field and far-field earthquakes is enhanced using an adaptive fuzzy proportional–derivative controller, in which the output gain of the self-tuning fuzzy proportional–derivative controller is adaptively tuned according to the kind of entering earthquake. The control objective is to reduce the isolation system deformations without significant increase in superstructure accelerations during far-field and near-field earthquake excitations. Membership functions and fuzzy control rules are simultaneously tuned using a multi-objective cuckoo search algorithm. Considering 14 real-data earthquakes, simulation results show that the proposed controllers perform better than other reported control strategies in terms of simultaneous reduction of the maximum base displacement and superstructure accelerations. Also, they provide acceptable responses in terms of the inter-story drifts, root mean squared of base displacement, and the floor acceleration. Opposite to other reported control strategies, piezoelectric friction dampers controlled by the self-tuning fuzzy proportional–derivative controller and adaptive fuzzy proportional–derivative controller never enter the saturation area.
A Study on the self-tuning of the design variables and gains using Fuzzy PI+D Controller
