Seismic structural control using magneto-rheological dampers: A decentralized interval type-2 fractional-order fuzzy...

In this paper, a combination of the interval type-2 fuzzy logic controller (IT2FLC) with the fractional-order proportional-integral-derivative (FOPID) controller, namely optimal interval type-2 fractional-order fuzzy proportional-integral-derivative controller (OIT2FOFPIDC), is developed for enhancing the seismic performance and robustness in seismic structural control applications. Based on the energy concepts, a decentralized framework of the OIT2FOFPIDC is proposed for easy and simple implementation in structures during earthquakes. For this purpose, a coot optimization algorithm (COA), as a powerful optimization algorithm, is also applied to adjust the membership functions (MFs), scaling factors, and the main controller parameters. Three controllers, namely optimal type-1 fuzzy proportional-integral-derivative controller (OT1FPIDC), optimal interval type-2 fuzzy proportional-integral-derivative controller (OIT2FPIDC), and optimal proportional-integral-derivative controller (OPIDC), are also proposed for comparison purposes. The seismic performances of the suggested controllers are examined with the evaluation of nine seismic performance indices and different ground accelerations in a 6-story smart structure equipped with two dampers. The robustness of the four controllers in the presence of the stiffness uncertainties is also compared in this study. On average, a reduction of 25.0%, 18.8%, and 18.5% in peak displacement, inter-story drift, and acceleration of stories is obtained for the OIT2FOFPIDC over the OT1FPIDC, respectively. Similarly, these reductions in comparison with the OIT2FPIDC are 16.3%, 13.3%, and 12.0%. Also, these reductions, in comparison with the OPIDC, are 33.3%, 27.8%, and 25.8%. Furthermore, simulation results show that the OIT2FOFPIDC is more robust than the other proposed controllers against uncertainties due to structural stiffness.