Design of an Online Adaptive Fractional-Order Proportional-Integral-Derivative Controller to Reduce the Seismic Response of the 20-Story Benchmark Building Equipped with an Active Control System

The objective of the present investigation is to introduce a novel adaptive fractional-order proportional-integral-derivative controller, which is characterized by the online tuning of its parameters by utilizing five distinct multilayer perceptron neural networks employing the extended Kalman filter. Utilizing the backpropagation algorithm in training a multilayer perceptron neural network is deemed effective in identifying the structural system and estimating the plant. The controller is applied using the Jacobian derived from the online estimated model. The utilization of adaptive interval type-2 fuzzy neural networks in conjunction with the extended Kalman filter tuning method and feedback error learning strategy results in enhanced stability and robustness of the controller in the face of estimation error, seismic disturbances, and unknown nonlinear functions. The study aims to validate the efficacy of the proposed controller by examining its performance on a 20-story nonlinear building. The numerical results show that including a compensator enhances the performance of the adaptive fractional-order proportional-integral-derivative controller. The results show that the proposed adaptive fractional-order proportional-integral-derivative controller has a better performance than other controllers and that the interstory drift ratio criterion under the El Centro earthquake with a magnitude of 1.5 times experienced an improvement of up to 65% compared to other controllers, and this amount in the Kobe earthquake reached more than 58%. Other criteria have also experienced significant improvement using the proposed controller.