Design of Fractional-order PI controller for linear unstable systems

This paper presents a new strategy for designing of Fractional-order proportional integral (FOPI) controller for a linear unstable systems. The open loop transfer function is compared with the standard fractional-order (FO) transfer function whose closed loop response is always stable and comparison is done in frequency domain i.e. to match magnitude and phase response of the system with the standard FO transfer function. The slope of the Nyquist plot of the standard FO transfer function is also compared with the given open loop system with FOPI controller. The properly tuned FOPI controller´s results are better than its integer order PI and PID counter-part.