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Mathematical Problems in Engineering
Volume 2015, Article ID 818353, 22 pages
Research Article

Singularly Perturbation Method Applied To Multivariable PID Controller Design

1Department of Control and Mechatronics Engineering, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia
2Department of Industrial Systems Engineering and Design, Jaume I University of Castello, 12080 Castello de la Plana, Spain
3Department of Industrial Electronics, Faculty of Electronics and Computer Engineering, Universiti Teknikal Malaysia Melaka, 76100 Durian Tunggal, Melaka, Malaysia

Received 8 April 2015; Accepted 4 June 2015

Academic Editor: Herve G. E. Kadji

Copyright © 2015 Mashitah Che Razali 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.


Proportional integral derivative (PID) controllers are commonly used in process industries due to their simple structure and high reliability. Efficient tuning is one of the relevant issues of PID controller type. The tuning process always becomes a challenging matter especially for multivariable system and to obtain the best control tuning for different time scales system. This motivates the use of singularly perturbation method into the multivariable PID (MPID) controller designs. In this work, wastewater treatment plant and Newell and Lee evaporator were considered as system case studies. Four MPID control strategies, Davison, Penttinen-Koivo, Maciejowski, and Combined methods, were applied into the systems. The singularly perturbation method based on Naidu and Jian Niu algorithms was applied into MPID control design. It was found that the singularly perturbed system obtained by Naidu method was able to maintain the system characteristic and hence was applied into the design of MPID controllers. The closed loop performance and process interactions were analyzed. It is observed that less computation time is required for singularly perturbed MPID controller compared to the conventional MPID controller. The closed loop performance shows good transient responses, low steady state error, and less process interaction when using singularly perturbed MPID controller.