Time response of fractional automatic control systems

A-Fractional Derivative (K-FD) is the only non-local Derivative satisfying the demands of Differential Topology. Hence, it is most suitable to investigate the stability of simple SISO and PID control systems. Their behavior is compared in real-time Space in the introduced K-Space(K-S). According to the definition of K-Fractional Derivative and its correspondence to K-Space, those K-FDs may be viewed as classical Derivatives of transformed new functions and variables in that Space. Firstly the system is analyzed in K-S. Afterward, the derived results provide us information about the response of the system in the real Space, by the inverse transformation as proposed from the theory. (C) 2020 The Author(s). Published by Elsevier B.V.