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 (2) 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 A. 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. (C) 2016. IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.