Tuning of optimal fractional-order PID controller using an artificial bee colony algorithm

In this paper, the design of fractional-order PID controller is considered in order to minimize certain performance indices such as integral absolute error, integral square error and integral time absolute error. The design-construction leads to a high-dimensional, multi-modal, complex optimization problem which is difficult to solve analytically. We show that it can be solved heuristically using an artificial bee colony (ABC) algorithm, which is a recently emerged ‘stochastic’ technique inspired from the intelligent foraging behavior of honey bee swarm. For the numerical examples under consideration, we further compare the performance of ABC with a ‘deterministic’ Nelder–Mead simplex algorithm.

[1]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[2]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[3]  YangQuan Chen,et al.  8. Fractional-Order Controller: An Introduction , 2007 .

[4]  Bing-Gang Cao,et al.  Optimization of fractional order PID controllers based on genetic algorithms , 2005, 2005 International Conference on Machine Learning and Cybernetics.

[5]  YangQuan Chen,et al.  Fractional-order [proportional derivative] controller for robust motion control: Tuning procedure and validation , 2009, 2009 American Control Conference.

[6]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[7]  YangQuan Chen,et al.  A fractional order proportional and derivative (FOPD) controller tuning algorithm , 2008, 2008 Chinese Control and Decision Conference.

[8]  Eronini I. Umez-Eronini.  System Dynamics and Control , 1998 .

[9]  I. Podlubny.  Fractional-Order Systems and -Controllers , 1999 .

[10]  Yangquan Chen,et al.  A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments , 2010, IEEE Transactions on Control Systems Technology.

[11]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[12]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[13]  D. Karaboga,et al.  On the performance of artificial bee colony (ABC) algorithm , 2008, Appl. Soft Comput..

[14]  Ameya Anil Kesarkar,et al.  Design of fractional order robust controller for universal plant structure , 2011, 2011 Nirma University International Conference on Engineering.

[15]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .

[16]  Ying Luo,et al.  Fractional order proportional integral (FOPI) and [proportional integral] (FO[PI]) controller designs for first order plus time delay (FOPTD) systems , 2009, 2009 Chinese Control and Decision Conference.

[17]  J Ljubisa Bucanovic,et al.  The fractional PID controllers tuned by genetic algorithms for expansion turbine in the cryogenic air separation process , 2014 .

[18]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[19]  Bing-Gang Cao,et al.  Design of Fractional Order Controller Based on Particle Swarm Optimization , 2006 .

[20]  Duarte Valério,et al.  TUNING-RULES FOR FRACTIONAL PID CONTROLLERS , 2006 .

[21]  Ying Luo,et al.  An analytical design of Fractional Order Proportional Integral and [Proportional Integral] controllers for robust velocity servo , 2009, 2009 4th IEEE Conference on Industrial Electronics and Applications.

[22]  Ameya Anil Kesarkar,et al.  Tuning of robust PIα /PDβ controller for generalized plant structure , 2011, 2011 INTERNATIONAL CONFERENCE ON RECENT ADVANCEMENTS IN ELECTRICAL, ELECTRONICS AND CONTROL ENGINEERING.

[23]  Biplab Satpati,et al.  Robust PID controller design using particle swarm optimization-enabled automated quantitative feedback theory approach for a first-order lag system with minimal dead time , 2014 .

[24]  Dervis Karaboga,et al.  Proportional—Integral—Derivative Controller Design by Using Artificial Bee Colony, Harmony Search, and the Bees Algorithms , 2010 .

[25]  Hung-Cheng Chen,et al.  Tuning of fractional PID controllers using adaptive genetic algorithm for active magnetic bearing system , 2009 .

[26]  Farshad Merrikh-Bayat.  General rules for optimal tuning the PIλDµ controllers with application to first-order plus time delay processes , 2012 .

[27]  Swagatam Das,et al.  Designing fractional-order PIlambdaDµ controller using differential harmony search algorithm , 2010, Int. J. Bio Inspired Comput..

[28]  Ching-Hung Lee,et al.  Fractional-order PID controller optimization via improved electromagnetism-like algorithm , 2010, Expert Syst. Appl..