The application of the fractional-order PID (FOPID) controller is recently becoming a topic of research interest for vibration control of structures. Some researchers have successfully implemented the FOPID controller in a single-input single-output (SISO) control structural system subjected to earthquake excitations. However, there is a lack of research that focuses on its application in multi-input multi-output (MIMO) control systems to implement it in seismic-excited structures. In this case, the cross-coupling of the process channels in the MIMO control structural system may result in a complex design process of controllers so that each loop is independently designed. From an operational point of view, the time delay and saturation limit of the actuators are other challenges that significantly affect the performance and robustness of the controller so that ignoring them in the design process may lead to unrealistic results. According to the challenges, the present study proposed an optimal fractional-order PID control design approach for structural control systems subjected to earthquake excitation. Gases Brownian motion optimization (GBMO) algorithm is utilized for optimal tuning of the controller parameters. Considering six real earthquakes and seven performance indices, the performance of the proposed controller, implemented on a ten-story building equipped with an active tendon system (ATS), is compared with those provided by the classical PID controller. Simulation results indicate that the proposed FOPID controller is more efficient than the PID in both terms of seismic performance and robustness against time-delay effects. The proposed FOPID controller can maintain suitable seismic performance in small time delays, while a significant performance loss is observed for the PID controller.
