RESUMO
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.
RESUMO
Fractional order PID (FOPID) controllers are introduced as a general form of classical PID controllers using fractional calculus. As this controller provides good disturbance rejection and is robust against plant uncertainties it is appropriate for the vibration mitigation in structures. In this paper, an FOPID controller is designed to adjust the contact force of piezoelectric friction dampers for semi-active control of base-isolated structures during far-field and near-field earthquake excitations. A multi-objective cuckoo search algorithm is employed to tune the controller parameters. Considering the resulting Pareto optimal front, the best input for the FOPID controller is selected. For seven pairs of earthquakes and nine performance indices, the performance of the proposed controller is compared with those provided by several well-known control techniques. According to the simulation results, the proposed controller performs better than other controllers in terms of simultaneous reduction of the maximum base displacement and story acceleration for various types of earthquakes. Also, it provides acceptable responses in terms of inter-story drifts, root mean square of base displacements and floor acceleration. In addition, the evaluation of robustness for a stiffness uncertainty of ±10% indicates that the proposed controller gives a robust performance against such modeling errors.
