Yu (Yu, C. C. Auto tuning of PID controllers: Relay feedback approach; Springer-Verlag: Berlin, 1999.) introduced the saturation relay feedback test for determining the ultimate gain and ultimate frequency of the system that is required for the design of PI/PID controllers. In the present work, two modifications are proposed to improve the efficiency of the saturation relay feedback test, especially for systems with a large dead time. In the first method, the safety factor is corrected based on the ideal relay feedback test. In the second method, higher order harmonics are included in the analysis of ideal relay. Simulation results are given to show the improvement of the proposed method over that of Yu method for a FOPTD system and a higher order system. The methods proposed by Srinivasan and Chidambaram (Srinivasan K.; Chidambaram, M. Chem. Biochem. Eng. Q. 2003, 18 (3), 249-256.) and Luyben (Luyben, W. L. Ind. Eng. Chem. Res. 2001, 40, 4391-4402.) for identifying FOPTD model parameters are compared. Two example systems are considered for the identification of a FOPTD model. For both the examples, after identification, the IMC tuning method is used for the controller design. The closed loop performances are compared with that of the actual system.