Abhishek Kumar; Sudeep Sharma; R. Mitra

Design of Type-2 Fuzzy Controller based on LQR Mapped Fusion Function

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Author(s)

Abhishek Kumar ^1,* Sudeep Sharma ¹ R. Mitra ¹

1. Electronics & Computer Engineering Department, Indian Institute of Technology Roorkee, Uttarakhand, India

* Corresponding author.

DOI: https://doi.org/10.5815/ijisa.2012.08.03

Received: 17 Oct. 2011 / Revised: 21 Feb. 2012 / Accepted: 3 May 2012 / Published: 8 Jul. 2012

Index Terms

Fusion Function, Fuzzy Control, Linear Inverted Pendulum (LIP), LQR Control, T2FS, Uncertainty

Abstract

“Rule number explosion” in fuzzy controller and “uncertainty” in the model are two main issues in the design of fuzzy control systems. To overcome these problems, we have applied a method in which a linear sensory fusion function has been used to reduce the number of dimensions of fuzzy controller’s inputs and simultaneously use the features of LQR control. Since, in type-2 fuzzy control, the degree of fuzziness increased and it can better handle the uncertainty in the model compared to conventional fuzzy, so the method of sensory fusion with type-2 fuzzy control scheme has been combined to make the controller more robust w.r.t. the parameter variation, perturbance and uncertainty in the model. Performance criteria like IAE, ISE and ITAE have been used to compare the control performance obtained from conventional fuzzy and type-2 fuzzy controller.

Cite This Paper

Abhishek Kumar, Sudeep Sharma, R. Mitra, "Design of Type-2 Fuzzy Controller based on LQR Mapped Fusion Function", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.8, pp.18-29, 2012. DOI:10.5815/ijisa.2012.08.03

Reference

[1]J. Morales, O. Castillo, and J. Soria “Stability on Type-1 and Type-2 Fuzzy Logic Systems,” springer-verlag, Soft Computing for Hybrid Intel. Systems, vol.154, pp. 29-51, 2008.

[2]L. A. Zadeh, “The Concept of a Linguistic Variable and Its Application to Approximate Reasoning–1,” Information Sciences, vol. 8, pp. 199-249, 1975.

[3]N. N. Karnik and J. M. Mendel, “Operations on Type-2 Fuzzy Sets,” Fuzzy Sets and Systems, vol. 122, pp. 327-348, 2001.

[4]Q. Liang and J. M. Mendel, “Interval type-2 fuzzy logic systems theory and design,” IEEE Transactions on Fuzzy Systems, vol. 8, no. 5,pp. 535–550, 2000.

[5]J. M. Mendel, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions, Prentice-Hall, Upper-Saddle River, NJ, 2001.

[6]Raju, G. V. S., J. Zhou, and R. A. Kisner, “Hierarchical fuzzy control,” Int.J. Contr., vol. 54, no. 5, 1991, pp. 1201-1216.

[7]Raju, G. V. S. and Jun Zhou, “Adaptive Hierarchical Fuzzy Controller,” IEEE trans. on systems, man and cybernetics, vol. 23, no. 4, Jul. Aug.1993, pp. 973-980

[8]Moon G. Joo, “A method of converting conventional fuzzy logic system to 2 layered hierarchical fuzzy system,” The IEEE International Conference on Fuzzy Systems, vol. 2, pp.1357-1362, 2003.

[9]Ledeneva, Y. (2006a), “Automatic Estimation of Parameters to Reduce Rule Base of Fuzzy Control Complex Systems,” Master thesis, INAOE Mexico.

[10]Ledeneva, Y., Reyes Garcia, C. A. (2006b). “Automatic Estimation of Fusion Method Parameters to Reduce Rule Base of Fuzzy Control Complex Systems”. In: Gelbukh A., et al. (Eds.): MICAI 2006, Springer-Verlag Berlin Heidelberg, LNAI 4293, pp. 146-155.

[11]Ledeneva, Y., Reyes Garcia, C. A. (2007a). “Automatic Estimation of Parameters for the Hierarchical Reduction of Rules of Complex Fuzzy Controllers”. In: Proceedings of ICINCO, France, pp. 398–401.

[12]Ledeneva, Y., Reyes Garcia, C.A., Gelbukh, A., Garcia Hernandez, R.A. (2007b). “Genetic Optimization of the Parameters of Fuzzy Control Complex Systems”. In: Torres S. et al (Eds.): CORE 2007, Research in Computing Science ISSN: 1870-4069, pp. 37–48.

[13]Lin Wang, Shifu Zheng, Xinping Wang and Liping Fan, “Fuzzy Control of Double Inverted Pendulum Based on Information Fusion,” IEEE International Conference on Intelligent Control and Information, Aug. 2010, pp. 327–331.

[14]Wang Luhao, Sheng Zhanshi, “LQR-Fuzzy Control for Double Inverted Pendulum,” IEEE Conference on Digital Manufacturing & Automation 2010, vol.1, pp. 900-903.

[15]Zheng Fang, Naixu Song and Liangyong Wang, “Design and Implementation of a Novel Fuzzy Controller with DSP for Rotary Inverted Pendulum,” IEEE Chinese Control and Decision Conference (CCDC) june 2009, pp.6122-6127.

[16]M. Jamshidi. Fuzzy Control Systems. Springer-Verlag, chapter of Soft Computing, pp. 42-56, 1997

[17]Yulia Ledeneva, Rene Garcia Hernandez and Alexander Gelbukh, “Automatic Estimation of Parameters of Complex Fuzzy Control Systems,” New Developments in Robotics, Automation and Control KG, Croatia publication, ISBN 978-953-7619-20-6, 2008, pp. 475-504.

[18]John H. Lily “Fuzzy control and Identification” 2010 John Wiley & Sons,Ltd. ISBN 978-1-118-09781-6 (ebk),pp.54-56,235-239.

[19]Jan Jantzen “Foundations of Fuzzy Control”, 2007 John Wiley & Sons, Ltd. ISBN: 0-470-02963-3.

[20]J. Krishen, V.M. Becerra, “Efficient Fuzzy Control of a Rotary Inverted Pendulum Based on LQR Mapping,” Proceedings of IEEE International Symposium on Intelligent Control, pp:2701 – 2706, Oct. 2006.

[21]H. Liu, F. Duan, Y. Gao, “Study on Fuzzy Control of an Inverted Pendulum System in the Simulink Environment,” Proceedings of IEEE on Mechatronics and Automation, pp:937 – 942, Aug. 2007.

[22]Googol Technology, GT-400-SV Inverted Pendulum User’s Manual, 2002.

[23]Jang, J.-S.R.; Chuen-Tsai Sun, “Neuro Fuzzy Modelling and Control,” IEEE Proc., vol.83, pp. 378-406, March1995.

[24]The Mathworks, Using Matlab version 7.10.0, The Mathworks, R2010a.

[25]Yazmin Maldonado, Oscar Castillo and Patricia Melin, “Optimal Design of Type-2 Fuzzy Controllers with a Multiple Objective Genetic Algorithm for FPGA Implementation,” IEEE 2011.

[26]Oscar Castillo and Patricia Melin, “Type-2 Fuzzy Logic: Theory and Applications” Studies in Fuzziness and Soft Computing, springer verlag, Volume 223, 2008 ISBN 978-3-540-76283-6,pp.42-80, 128,144-155.

[27]J. M. Mendel, H. Hagras and Robert I. John, “Standard background material about interval type-2 fuzzy logic systems that can be used by all authors,” www.ieee-cis.org/_files/standards

[28]Fuzzy type-2 toolbox, commercialized by juan Ramon Castro Baja California autonomous university, mexico.

International Journal of Intelligent Systems and Applications (IJISA)