A GBMO-based PIλDμ controller for vibration mitigation of seismic-excited structures

The advantages of fractional-order proportional-integral-derivative (FOPID) controllers in terms of flexibility, robustness against model uncertainties and good disturbance rejection, are good motivations to use them for vibration mitigation of seismic-excited structures. The application of the FOPID controller for adjusting the control force of an active tuned mass damper (ATMD) for seismic control a building is studied in this paper. Gases Brownian motion optimization (GBMO) algorithm is employed for optimal tuning of parameters of the FOPID and PID controllers. Evaluation of the frequency responses of the structure for uncontrolled and controlled cases shows that PID and FOPID controllers are very effective for the seismic control of structures. For further investigation, the performance of the FOPID controller in the reduction of seismic responses of the building in four well-known earthquake excitations is compared with those provided by the PID, linear-quadratic regulator (LQR) and fuzzy logic control (FLC). Simulation results show that the PID and LQR controllers provide the same performance in reducing the maximum top floor displacement of the structure. Moreover, the FLC and FOPID controllers demonstrate a superior performance in seismic control of the structure. The FLC is able to reduce the maximum displacements of all stories for all studied earthquakes. However, the proposed FOPID controller is able to provide a better performance in comparison with the FLC. In average, the FOPID controller mitigates the seismic responses of the structure as much as 29%, 27% and 15% better than the LQR, PID controller and FLC.