Simulation Toolboxes of Dynamic Systems for Optimized Fractional Linear Order Controllers

Today, there is a growing utilization of fractional order systems in the modeling of various phenomena. Furthermore, the capabilities and performance of fractional order controllers in the analysis and design of fractional order systems are of interest to many researchers. In the present research, the most important toolboxes developed for analyzing and designing fractional-order systems were introduced and their capabilities and performance in the analysis and design of fractional order controllers compared. In this regard, the basic features and capabilities of the four different toolboxes were examined. The advantages and disadvantages of each were listed. Then, with the help of three toolboxes, the performance of two fractional-order proportional, integral, and derivative (FOPID) controllers optimized with a meta-heuristic algorithm to stabilize the synchronous generator voltage regulation system and brushless DC motor were simulated. The simulation results showed that the performances of these toolboxes depend to a large extent on their employed algorithms. Thus, the results of Fractional-order Transfer Function (FOTF) and Fractional-order Modelling and Control (FOMCON) toolboxes were very similar and non-integer (NINTEGER) toolbox results were significantly different.