The week's pick
Random Articles
Reseach Article
Model Reference based Tuning of PID Controller using Bode's Ideal Transfer Function and Constrained Particle Swarm Optimization
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 71 - Number 17 |
| Year of Publication: 2013 |
| Authors: Anindya Bhattacharyya, N. Murali |
10.5120/12450-9207
|
Anindya Bhattacharyya, N. Murali . Model Reference based Tuning of PID Controller using Bode's Ideal Transfer Function and Constrained Particle Swarm Optimization. International Journal of Computer Applications. 71, 17 ( June 2013), 21-27. DOI=10.5120/12450-9207
Abstract
A new method for designing PID Controllers using Bode's ideal transfer function and constrained Particle Swarm Optimization (PSO) is proposed in this paper. Bode's ideal transfer function is introduced using fractional calculus and Carlsson's approximation is used for converting the transfer function from fractional to integer domain. The PID controller is designed by minimizing a hybrid objective function using PSO. Simulation examples confirming the effectiveness of the resulting controller are also discussed in detail and a performance comparison, highlighting the enhanced capability of PSO over other conventional mathematical optimization approaches, is also made in the paper.
References
- D. Shantanu. , "Functional fractional calculus for system identification & controls. ," Springer, 2008.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, ADVANCES IN FRACTIONAL CALCULUS :Theoretical Developments and Applicationsin Physics and Engineering: Springer, 2007.
- I. Podlubny, Fractional Differential Equations: : An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, New York: Academic Press. 1998
- K. B. Oldham, and J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order, Academic Press New York 1974.
- K. J. Astrom, and T. Hagglund, "PID controller: Theory, design, and tuning. ," Instrument Society of America, 1995.
- A. Visioli, Practical PID Control: Springer-Verlag London Limited 2006.
- A. O'Dwyer, Handbook of PI and PID Controller Tuning Rules: Imperial College Press, 2006 2nd edition.
- M. Araki et. all "Two Degree of Freedom PID Controller" " System,Control and Information, Vol 42, pp. pp 18-25, 1988.
- I. Petras, R. Caponetto, G. Dongola et al. , FRACTIONAL ORDER SYSTEMS:Modeling and Control Applications: World Scientific, 2010.
- J. G. Ziegler, N. B. Nichols, and " "Optimum settings for automatic controllers"," in Trans. ASME, 1942, pp. 433-444.
- R. S. Barbosa, J. A. T. Machado, and I. M. Ferreira, "Tuning of PID Controllers Based on Bode's Ideal Transfer Function," Nonlinear Dynamic"s, Vol. 38, pp. 305–321, 2004.
- H. S. Farhad Farokhi, "A Robust Control-Design Method Using Bode's Ideal Transfer Function. "
- J. Kennedy & R. Eberhart, "Particle Swarm Optimization," 1995.
- R. C. Eberhart, and Y. Shi, ""Comparing Inertia Weights and Constriction Factors in Particle Swarm Optimization"," in Proceedings of the Congress on Evolutionary Computation 2000, pp. 84-88.
- G. E. Carlson, and C. A. Halijak, ""Simulation of the fractional derivative operator ?s and the fractional integral operator 1/?s"," in Central States Simulation Council Meeting on extrapolation of analog computation methods, Kansas State University, July 1961, pp. 1-22.
- B. M. Vinagre, I. Podlubny, A. Hernandez et al. , "Some Approximations Of Fractional Order Operators Used In Control Theory And Applications. " pp. 231–248.
- S. Manabe, "The Non-Integer Integral and its application to Control Systems. " pp. 83-87.
- Y. S. Bijaya Ketan Panigrahi & Meng-Hiot Lim "Handbook of Swarm Intelligence Concepts, Principles and Applications," Springer, 2011.
- M. Clerc et all. "The Swarm And The Queen: Towards A Deterministic And Adaptive Particle Swarm Optimization" in Proceedings of the Conference on Evolutionary Computation, 1999, pp. 1951-1957.
- X. Hui & R. Eberhart, "Solving Constrained Nonlinear Optimization Problem with Particle Swarm Optimization. "
- C. S. Thenehalli, "Design Optimization Using Augmented Lagrangian Particle Swarm Optimization," Faculty of the Graduate School, The University of Texas at Arlington.
- K. E. Parsopoulos & M. N. Vrahatis, "Particle Swarm Optimization Method for Constrained Optimization Problems".
- X. S. Yang, Introduction to Mathematical Optimization From Linear Programming to Metaheurestics: Cambridge International Science Publishing, 2009.
- N. Pillay, "A Particle Swarm Optimization Approach for Tuning Of SISO PID Control Loops" Masters, Department Of Electronic Engineering, Durban University of Technology, 2008.
- "MATLAB optimization toolbox user's guide ,The Mathworks Inc" The Mathworks Inc.
- S. Saha, S. Das, R. Ghosh et al. , "Fractional order phase shaper design with Bode's integral for iso-damped control system," ISA Transactions, vol. 49, pp. 196-206, 2012.
- Clerc. M, Kennedy J. "The particle swarm-explosion, stability, and convergence in a multidimensional complex space". IEEE Trans. Evolutionary Computation 2002, 6, p. 58-73.
Index Terms
Keywords