Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T00:50:49.054Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal fuzzy PID controller design for an active magnetic bearing system based on adaptive genetic algorithms†

Published online by Cambridge University Press:  04 September 2014

HUNG-CHENG CHEN
HUNG-CHENG CHEN*
Affiliation:
Department of Electrical Engineering, National Chin-Yi University of Technology, Taichung, Taiwan Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose an adaptive genetic algorithm (AGA) for the multi-objective optimisation design of a fuzzy PID controller and apply it to the control of an active magnetic bearing (AMB) system. Unlike PID controllers with fixed gains, a fuzzy PID controller is expressed in terms of fuzzy rules whose consequences employ analytical PID expressions. The PID gains are adaptive and the fuzzy PID controller has more flexibility and capability than conventional ones. Moreover, it can be easily used to develop a precise and fast control algorithm in an optimal design. An adaptive genetic algorithm is proposed to design the fuzzy PID controller. The centres of the triangular membership functions and the PID gains for all fuzzy control rules are selected as parameters to be determined. We also present a dynamic model of an AMB system for axial motion. The simulation results of this AMB system show that a fuzzy PID controller designed using the proposed AGA has good performance.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 24 , Special Issue 5: Mathematical Method in Intelligent Computing and Automation , October 2014 , e240516
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

This research was supported in part by the National Science Council of the Republic of China, under Grant Number NSC99-2622-E-167-023-CC3.

References

Bennett, S. (1987) Development of the PID Controller. IEEE Control Systems Magazine 13 58–65.Google Scholar
Chambers, L. (2001) The Practical Handbook of Genetic Algorithms: Applications, Chapman and Hall/CRC.Google Scholar
Chen, G. (1996) Conventional and Fuzzy PID Controller: An Overview. International Journal of Intelligent Control Systems 1 235–246.Google Scholar
Chen, S. L. (2011) Nonlinear Smooth Feedback Control of a Three-Pole Active Magnetic Bearing System. IEEE Transactions on Control Systems Technology 19 (3)615–621.Google Scholar
Fan, Y. H., Chen, K. Y., Weng, D. L. and Lee, Y. T. (2008) Design of Adaptive Compensator of Force Imbalance for a Single Active Magnetic Bearings Suspended Rotor System. Journal of Applied Physics 103 (7)935–937.Google Scholar
Haiming, L. and Yen, G. G. (2003) Rank-Density-Based Multiobjective Genetic Algorithm and Benchmark Test Function Study. IEEE Transactions on Evolutionary Computation 7 (4)325–343.CrossRefGoogle Scholar
Harinath, E. and Mann, G. K. I. (2008) Design and Tuning of Standard Additive Model Based Fuzzy PID Controllers for Multivariable Process Systems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 38 (3)667–674.Google Scholar
Khoo, W. K. S., Kalita, K., Garvey, S. D., Hill-Cottingham, R. J., Rodger, D. and Eastham, J. F. (2010) Active Axial-Magnetomotive Force Parallel-Airgap Serial Flux Magnetic Bearings. IEEE Transactions on Magnetics 46 (7)2596–2602.CrossRefGoogle Scholar
Knospe, C. R. (2007) Active Magnetic Bearings for Machining Applications. Control Engineering Practice 15 (3)307–313.Google Scholar
LinL., L, L. L., L, L., Jan, H. Y. and Shieh, N. C. (2003) GA-Based Multiobjective PID Control for a Linear Brushless DC Motor. IEEE Transactions on Mechatronics 8 (1)56–65.Google Scholar
Michalewicz, Z. (1996) Genetic Algorithms + Data Structures = Evolution Programs, Springer–Verlag.Google Scholar
Mohan, B. M. and Sinha, A. (2008) Analytical Structures for Fuzzy PID Controllers? IEEE Transactions on Fuzzy Systems 16 (1)52–60.Google Scholar
Na, M. G. (2001) Auto-Tuned PID Controller Using a Model Predictive Control Method for the Stream Generator Water Level. IEEE Transactions on Nuclear Science 48 (5)1664–1671.Google Scholar
Polajzer, B., Stumberger, G., Ritonja, J. and Dolinar, D. (2008) Variations of Active Magnetic Bearings Linearized Model Parameters Analyzed by Finite Element Computation. IEEE Transactions on Magnetics 44 1534–1537.Google Scholar
Srinivas, M. and Patnaik, L. M. (1994) Adaptive Probabilities of Crossover and Mutation in Genetic Algorithms. IEEE Transactions on Systems, Man and Cybernetics 24 (4)656–667.CrossRefGoogle Scholar
Xiu, Z. and Ren, G. (2004) Optimization Design of TS-PID Fuzzy Controllers Based on Genetic Algorithms. In: Proceedings of the 5th World Congress on Intelligent Control and Automation, Hangzhou, China 2476–2480.Google Scholar
Zhiming, L., Jiliu, Z. and Su, L. (2003) New Adaptive Genetic Algorithm Based on Ranking. Proceedings of the International Conference on Machine Learning and Cybernetics 3 1841–1844.Google Scholar