Fractional Order PI Controller Design for Time Delay Systems

This paper aims to look into the fractional PI controller design for a closed loop system having a plant with time-delay. The ultimate frequency of the system is found using a relay auto tuning test and then the parameters of a PI controller are estimated using this frequency in the Ziegler-Nichols (Z-N) tuning formula. These parameters are then used for a fractional order PI controller and the effect of varying the fractional integrator order (λ) of the PI controller on the closed loop step response is examined. Finally, for a given example, the table that includes specifications of the control system for different λ values has been obtained and according to the desired specifications, optimum fractional order PI controller is designed. The presented results are illustrated with some examples.