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Mathematical Problems in Engineering
Volume 2015, Article ID 825608, 11 pages
Research Article

Fractional Order Controller Designing with Firefly Algorithm and Parameter Optimization for Hydroturbine Governing System

Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei 430072, China

Received 25 June 2015; Revised 5 August 2015; Accepted 6 August 2015

Academic Editor: Hiroyuki Mino

Copyright © 2015 Li Junyi and Qijuan Chen. 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 PID (FOPID) controller, which is suitable for control system designing for being insensitive to the variation in system parameter, is proposed for hydroturbine governing system in the paper. The simultaneous optimization for several parameters of controller, that is, , , , , and , is done by a recently developed metaheuristic nature-inspired algorithm, namely, the firefly algorithm (FA), for the first time, where the selecting, moving, attractiveness behavior between fireflies and updating of brightness, and decision range are studied in detail to simulate the optimization process. Investigation clearly reveals the advantages of the FOPID controller over the integer controllers in terms of reduced oscillations and settling time. The present work also explores the superiority of FA based optimization technique in finding optimal parameters of the controller. Further, convergence characteristics of the FA are compared with optimum integer order PID (IOPID) controller to justify its efficiency. What is more, analysis confirms the robustness of FOPID controller under isolated load operation conditions.