Consideration of the transient response is one of the key topics in control system design for time delay systems. In this paper, an efficient method to control the transient response of the first order plus time delay stable (FOPTD) systems using the fractional-order PI (PIλ) controllers is presented. The main characterization of the method is first to construct the global stability region in the (kp, ki)-plane for any fixed value of λ and then to obtain ts and Mp curves corresponding to special settling time and maximum overshoot values in this region. Finally, by intersection of these curves, the Dλ-stability region in the (kp, ki)-plane is found. Changing the value of λ in the range of (0, 2), a set of Dλ-stability regions is obtained. These regions involve the controller parameters providing the closed loop settling time and maximum overshoot specifications together in the acceptable values. Therefore, the designer can easily decide to the selection of suitable values of kp, ki and λ. The simulation results indicate that the presented transient response control method is effective and practically useful in the analysis and control of the stable FOPTD systems by means of fractional-order PI controllers.

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