Design and Analysis of Complex Fractional-order PID Controllers

Abstract

This paper is focused on the design of a complex fractional-order differentiator and integrator for the order $\\alpha+j\\beta$. Furthermore, for these differentiators and integrators practical realization, an approximation using a curve fitting-based iterative algorithm is proposed. The design of various complex fractional PID controllers using the proposed differentiator and integrator has been presented. The simulation study results show that the designed controllers with complex orders have produced a steady behavior equivalent to fractional controllers behavior. The step response characteristics on the process plant also show that the designed controllers performed well in controlling the process.