Nature-inspired algorithms for optimizing fractional order PID controllers in time-delayed systems

Time-delayed systems frequently appear, especially in sectors such as fluid flow processes, chemical procedures, and the food industry. This paper addresses the optimization of parameters for a fractional order PID (FOPID) controller, which is used to control a time-delayed system, using five distinct algorithms inspired by nature. These algorithms are NewBAT, Cuckoo search (CS), Firefly (FF), Gray Wolf Optimizer (GWO), and Whale optimization algorithm (WOA). The FOPID controller parameters, namely K-P, K-I, K-D,K- lambda and mu, have been optimized using these algorithms. During the optimization process, the integral of the time absolute error (ITAE) was considered as the primary measurement criterion. In addition to this value, the maximum overshoot, settling time, time to reach the maximum value, and error values were examined. Simulations conducted with the obtained parameters tested the system's resilience to disturbances introduced at the output, and the controller responses were also evaluated during these tests. The reactions of the determined parameters to different reference inputs were analyzed, and the results are presented in graphs and tables. The efficiency and reliability of the optimization algorithms were substantiated by comprehensive statistical analyses. These analyses play a critical role in algorithm selection and objective evaluation of the results. Simulation studies were conducted in the Matlab and Simulink environments. The FOMCON Toolbox was used for fractional-order processes.