Performance analysis and comparison of fractional-PI controller design methods

Derivative effect of the PID controllers makes the control system sensitive against disturbance effect. Therefore, about 90 percent of the controllers used in the industrial applications consist of PI controllers. Defining as the generalization of the conventional PID controllers, Fractional-order PID controllers came to existence with the application of fractional calculus to the control theory. Fractional-order PID controllers have two extra parameters (fractional integral order-λ and fractional derivative order-μ) with the respect of the classical PID controllers. These parameters make the controller more robust against the disturbances occuring in the control system. Fractional-order PID controller are generally designed in the frequency domain because of the difficulties in the time domain. In the frequency domain, gain margin, phase margin, gain crossover frequency and the phase crossover frequency are the most used parameters in fractional-order PID controller design. Phase margin and gain margin have an important effect on the stability of the system and phase margin is an important parameter for overshoot of the system. Accordingly, phase margin and gain margin are important parameters for controller design in frequency domain. In this study, for integrating systems with dead time and fractional-order unstable system with dead time stability boundary loci are obtained for specific gain and phase margins by adding a Gain-Phase Margin Tester. Additionally, the effect of the process gain (K), time constant (T), fractional system order (α), time delay (ϴ), gain margin (A), phase margin (ϕ) and the fractional integral order (λ) on the stability regions and the critical frequency are investigated. The parameter of the controller are selected from the mid-point of the obtained stability regions and the step responses