In this paper, a fractional order proportional integral controller (FOPI) and Fractional order[Proportional Integral] (FO[PI]) controller is designed for controlling the level of a spherical tank which is modeled as a first order plus dead time system These controllers are designed based on the same set of design specifications which will satisfy the desired given gain cross over frequency and phase margin. The performance of the designed FOPI and FO [PI] controller is compared with the Conventional integer order Proportional Integral (IOPI) controller. The simulations are done in MATLAB simulink.

1. J. G. Ziegler and N. B. Nichols, "Optimum setting for automatic controller," Trans. ASME,vol. 64, pp. 759–768, 1942.
2. K. Bettou. , A. Charef, "Improvement of control performances using fractional PI?D? controllers"
3. Ying Luo, and YangQuan Chen, "Stabilizing and Robust FOPI Controller Synthesis for First Order Plus Time Delay Systems" IEEE Conference on Decision and Control and European Control Conference,2011
4. Y. Q. Chen, D,Xue, and H,Dou, "Fractional Calculus and Biomimetic Control '', IEEE Int. Conf. on robotics and biomimetics (ROBIO 04), Shengang, China, Aug 2004.
5. Chunna Zhao and Dingy¨u Xue, YangQuan Chen,"A Fractional Order PID Tuning Algorithm for A Class of Fractional Order Plants" Proceedings of the IEEE International Conference on Mechatronics & Automation Niagara Falls, Canada • July 2005.
6. K Vaithiyanathan ,P. K. Bhaba," Design and Real Time Implementation of Fractional Order Proportional-Integral Controller (PI ? ) in A Liquid Level System", Modern Applied Science Vol. 5, No. 6; December 2011.
7. Pankaj Rai, Vineet Shekher "Determination of Stabilizing Parameter of Fractional Order PID Controller Using Genetic Algorithm" IJCEM International Journal of Computational Engineering & Management, Vol. 15 Issue 1, January 2012
8. S. Nithya, N Sivakumaran," Model based controller design for a spherical tank process in real time", IJSSST Vol. 9 No. 4, November 2008
9. Radek Matusu "Application of fractional order calculus to control theory",International journal of Maths and Modern applied sciences, Issue 7, Volume 5, 2011
10. Ying Luo, Yang Quan Chen , Chun Yang Wang,"Tuning Fractional order Proportional Integral controllers for Fractional order systems".

Fractional Order Controller Integer Order Controller Spherical Tank First Order Plus Delay Time Systems