Time response of fractional automatic control systems

Abstract

*Λ-Fractional Derivative (Λ-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 Λ-Space(Λ-S). According to the definition of Λ-Fractional Derivative and its correspondence to Λ-Space, those Λ-FDs may be viewed as classical Derivatives of transformed new functions and variables in that Space. Firstly the system is analyzed in Λ-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.

Keywords

• Λ-Fractional Derivative
• Λ-Space
• SISO control systems
• PID control systems
• Stability
• Inverse transformation