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Journal of Control Science and Engineering
Volume 2012, Article ID 478346, 8 pages
Research Article

Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine

Faculty of Electrical and Computer Engineering, Babol Noshirvani University of Technology, Babol 47148-71167, Iran

Received 6 January 2012; Revised 27 April 2012; Accepted 18 May 2012

Academic Editor: Peilin Fu

Copyright © 2012 S. J. Sadati et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO) time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order 𝑃 𝐼 πœ† 𝐷 πœ‡ controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of 𝑃 𝐼 πœ† 𝐷 πœ‡ controller with respect to a traditional optimized PID controller.