A time delay between a change in an input and the corresponding change in output that real dynamic systems often exhibit has a whole host of causes. For mathematical modeling needs, it is aggregated into a total phenomenon called time delay or dead time [3]. In process control, one often encounters systems that can be described by transfer functions with time delays [1]. If a dynamic system with delay is modeled as a time-invariant linear system, its transfer function (rational function) becomes, due to the delay, a transcendent function [3]. For design and analysis purposes, these delays are usually approximated by rational transfer functions [2]. This is usually done using delay approximation methods. The Taylor series expansion, Padé.PI and PID controllers have been at the center of control engineering practice for seventy years [4]. The use of PI or PID controller is ubiquitous in industry. It has been stated, for example, that in process control applications more than 95% of controllers are of the PI or PID type [1, 4, 5]. PID controllers can ensure satisfactory performance with a simple algorithm for a wide range of processes [6, 7]. Internal model control (IMC) provides a progressive, effective, natural, generic, unique, powerful and simple framework for analyzing and summarizing control system performance [8-11]. The simplicity and improved performance of IMC-based optimization rule and analytically derived IMC-PID optimization techniques have attracted the attention of industrial users over the past decade [10, 11]. The well-known IMC-PID optimization rule provides a clear trade-off between closed-loop performance and robustness to model uncertainties and is obtained by only one we... half of the paper... closed-loop responses for SI/SO systems, AIChE Journal, 44, 106–115.[16] Shamsuzzoha, M., & Lee, M. (2008c). Analytical design of an advanced PID filter controller for integrating first-order unstable processes with time delay, Chemical Engineering Science, 63, 2717-2731.[17] Seborg, D. E., Edgar, T. F., & Mellichamp, D. A. (2004). Process Dynamics and Control, 2nd ed. Wiley, New York.[18] Libor Pekar and Eva Kureckova, Rational approximations for time-delayed systems: case studies, mathematical methods and techniques in engineering and environmental sciences, pp. 217-222, ISBN: 978-1-61804-046-6.[19] Jonathan R. Partington, Some frequency-domain approaches to model reduction of delay systems, Annual Reviews in Control 28 (2004) 65–73.[20] C. Battle and A. Miralles, On the approximation of delay elements using feedback, Automatica, vol. 36, number 5, 2000, pp. 659-664.