Stability Boundary Locus For Unstable Processes with Time Delay Under Fractional-order PI Controllers

Abstract

Applications of the fractional calculus have recently found a wide area in control theory by means of the advantages fractional derivative order and fractional integrator order provide. As a result, the importance of designing a better fractional-order controller to satisfy the conditions has increased. Because of the difficulties in designing fractional-order controller in the time domain, generally, the frequency domain is used to design controller. Frequency domain parameters as phase margin, gain margin, phase crossover frequency and gain crossover frequency are generally used for designing of the controllers. This paper represents a solution to obtain stability regions to stabilize a first order unstable system plus dead time with fractional-order proportional integrating (PI) controller and aims to show the effects of fractional integrator order, phase margin, and time delay on stability areas by obtaining different stability regions for different fractional integrator order, phase margins and time delays. While the fractional integrator value is varied in a range of [0.1-1], specific values are chosen for phase margin and time delay to observe the alteration in the stability regions. By using stability regions all stabilizing fractional-order Proportional Integrating controllers can be designed.