Tuning fractional PID controllers for a Steward platform based on frequency domain and artificial intelligence methods

• Authors: Cosmin Copot , Yu Zhong , Clara Ionescu , Robin Keyser
• Languages of publication: EN

Abstracts

EN

In this paper, two methods to tune a fractional-order PI
λ
D
μ controller for a mechatronic system are presented. The first method is based on a genetic algorithm to obtain the parameter values for the fractionalorder PI
λ
D
μ controller by global optimization. The second method used to design the fractional-order PI
λ
D
μ controller relies on an auto-tuning approach by meeting some specifications in the frequency domain. The real-time experiments are conducted using a Steward platform which consists of a table tilted by six servo-motors with a ball on the top of the table. The considered system is a 6 degrees of freedom (d.o.f.) motion platform. The feedback on the position of the ball is obtained from images acquired by a visual sensor mounted above the platform. The fractional-order controllers were implemented and the performances of the steward platform are analyzed.

Keywords

EN

Steward platform; fractional-order; PID control; genetic algorithm; frequency domain

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 6
• Pages: 702-713

Dates

published

1 - 6 - 2013

online

9 - 10 - 2013

Contributors

author

Cosmin Copot

• Department of Electrical energy, Systems and Automation, Ghent University, Technologiepark 913, 9052, Gent, Belgium

author

Yu Zhong

• Department of Electrical energy, Systems and Automation, Ghent University, Technologiepark 913, 9052, Gent, Belgium

author

Clara Ionescu

• Department of Electrical energy, Systems and Automation, Ghent University, Technologiepark 913, 9052, Gent, Belgium

author

Robin Keyser

• Department of Electrical energy, Systems and Automation, Ghent University, Technologiepark 913, 9052, Gent, Belgium

References

• [1] R. H. Bishop, The Mechatronics Handbook (CRC Press, USA, 2002)
• [2] M. Steinbuch, R. J. E. Merry, M. L. G. Boerlage, M. J. C. Ronde, M. J. G. van de Molengraft, In: W. S. Levin (Ed.), Advanced Motion Control Design, Second edition (CRC Press, USA, 2010) 27–1/25
• [3] M. Steinbuch, G. Schootstra, O. H. Bosgra, In: W. S. Levine (Ed.), Robust control of a compact disc mechanism (CRC Express, London, 2000) 231–237
• [4] K. J. Astrom, T. Hagglund, Advanced PID control (ISA-The Instrumentation, Systems, and Automation Society, Research Triangle Park, USA, 2006)
• [5] B. Stuart, A history of control engineering: 1930–1955 (Peter Peregrinus Ltd., London, 1993)
• [6] A. Oustaloup, La Derivation Non Entiere: Theorie, Synthese et Applications (Hermes, Paris, 1995)
• [7] I. Podlubny, Fraction order systems and PI −λD μ controllers, IEEE T. Automat. Contr. 44, 208 (1999) http://dx.doi.org/10.1109/9.739144[Crossref]
• [8] B. M. Vinagre, C. A. Monje, A. J. Calderon, J. I. Suarez, J. Vib. Control 13, 1419 (2007) http://dx.doi.org/10.1177/1077546307077498[Crossref]
• [9] D. Baleanu, J. A. T. Machado, A. Luo, Fractional Dynamics and Control (Springer, New York, USA, 2012) http://dx.doi.org/10.1007/978-1-4614-0457-6[Crossref]
• [10] R. L. Bagley, R. A. Calico, Fractional-order state equations for the control of viscoelastic damped structures, J. Guid. Control Dynam. 14, 304 (1991) http://dx.doi.org/10.2514/3.20641[Crossref]
• [11] N. M. F. Ferreira, J. A. T. Machado, Fractional-order hybrid control of robotic manipulators (Proceedings of the 11th International Conference on Advanced Robotics, Coimbra, Portugal, 2003) 393
• [12] A. Kailil, N. Mrani, M. M. Touati, S. Choukri, N. Elalami, Low earth-orbit satellite attitude stabilization with fractional regulators, Int. J. Syst. Sci. 35, 559 (2004) http://dx.doi.org/10.1080/00207720412331285878[Crossref]
• [13] H. Delavari, D. M. Senejohnny, D. Baleanu, Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter, Cent. Eur. J. Phys. 10, 1095 (2012) http://dx.doi.org/10.2478/s11534-012-0073-4[Crossref]
• [14] A. Babakhani, D. Baleanu, R. Khanbabaie, Hopf bifurcation for a class of fractional differential equations with delay, Nonlinear Dynam. 69, 721 (2012) http://dx.doi.org/10.1007/s11071-011-0299-5[Crossref]
• [15] A. K. Golmankhaneh, Investigations in Dynamics: With Focus on Fractional Dynamics (Lap Lambert, Academic Publishing, Germany, 2012)
• [16] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Solutions of the fractional Davey-Stewartson equations with variational iteration method, Rom. Rep. Phys. 64, 337 (2012)
• [17] F. Padula, A. Visioli, J. Process Contr. 21, 69 (2011) http://dx.doi.org/10.1016/j.jprocont.2010.10.006[Crossref]
• [18] M. Silva, T. Machado, J. Vib. Control. 12, 1483 (2006) http://dx.doi.org/10.1177/1077546306070608[Crossref]
• [19] J. Villagra, B. Vinagre, I. Tejado, Data-driven fractional PID control: application to DC motors in flexible joints (In IFAC Conference on Advanced in PID Control, 2012)
• [20] M. R. Faieghi, H. Delavari, D. Baleanu, Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control, J. Vib. Control 18, 1366 (2012) http://dx.doi.org/10.1177/1077546311422243[Crossref]
• [21] H. Fan, Y. Sun, X. Zhang, Research on fractional order controller in servo press control system (Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, China, 2007) 934–938
• [22] C. Ma, Y. Hori, Fractional order control and its application of controller for robust two-inertia speed control (Proceedings of the 4th International Power electronics and Motion Control Conference, vol. 3, Xian, China, 2004) 1477–1482.
• [23] N. L. S. Hashim et al., Procedia Engineering 41, 805 (2012) http://dx.doi.org/10.1016/j.proeng.2012.07.247[Crossref]
• [24] C. M. Ionescu, J. T. Machado, R. De Keyser, Computer and Mathematics with Applications 62, 845 (2011) http://dx.doi.org/10.1016/j.camwa.2011.04.021[Crossref]
• [25] Y. Kobayashi, T. Watanabe, T. Ando, M. Seki, M.G. Fujie, Fractional impedance control for reproducing the material properties of muscle and its application in a body weight support system (3rd IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics, 2010) 553–559 http://dx.doi.org/10.1109/BIOROB.2010.5626773[Crossref]
• [26] D. Steward, A platform with six degrees of freedom (Proceedings of the Institution of Mechanical Engineering, vol. 180(1), June, 1965) 371–386
• [27] W. Rekdalsbakken, The use of artificial intelligence in controlling a 6 DOF motion platform (Proceedings of 21st European Conference on Modeling and Simulation, Prague, Czech Republic, 2007) 471–476
• [28] L. Ljung, System identification: theory for the user (Prentice-Hall, USA, 2007)
• [29] J. Kennedy, R. C. Eberhart, Y. Shi, Swarm Intelligence (Morgan Kaufmann, USA, 2001)
• [30] R. C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory (Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, 4th–6th October, 1995) 39–43
• [31] L. Y. Chang, H. C. Chen, Tuning of fractional PID controllers using adaptive genetic algorithm for active magnetic bearing system, WSEAS Transactions on System 8, 226 (2009)
• [32] P. Rai, V. Shekher, O. Prakash, Determination of stabilizing parameter of fractional order PID controller using genetic algorithm, International Journal of Computational Engineering and Management 15, 24 (2012)
• [33] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning. (Addison-Wesley Publishing Company, Inc., Reading, MA, 1989)
• [34] M. Gen, R. W. Cheng, L. Lin, Network Models and Optimization: Multiobjecive Genetic Algorithm Approach (Springer, London, 2008)
• [35] H. Unbehauen, Controller design in time-domain, Control Systems, Robotics and Automation (EOLSS, Oxford, 2009)
• [36] C. A. Monje, Y. Q. Chen, B. M. Vinagre, D. Xue, V. Feliu, Fraction-order System and Controls: Fundamentals and Applications (Springer, London, 2010) http://dx.doi.org/10.1007/978-1-84996-335-0[Crossref]
• [37] D. Y. Xue, C. N. Zhao, Y. Q. Chen, A modified approximation method of fractional order system (Proceedings of IEEE Conference on Mechatronics and Automationm, Luoyang, China, 2006) 1043–1048

Identifiers

DOI

10.2478/s11534-013-0225-1