Neural Network Tuned Fuzzy Controller for MIMO System

In this paper, a neural network tuned fuzzy controller is proposed for controlling Multi-Input Multi-Output (MIMO) systems. For the convenience of analysis, the structure of MIMO fuzzy controller is divided into single input single-output (SISO) controllers for controlling each degree of freedom. Secondly, according to the characteristics of the system-s dynamics coupling, an appropriate coupling fuzzy controller is incorporated to improve the performance. The simulation analysis on a two-level mass–spring MIMO vibration system is carried out and results show the effectiveness of the proposed fuzzy controller. The performance though improved, the computational time and memory used is comparatively higher, because it has four fuzzy reasoning blocks and number may increase in case of other MIMO system. Then a fuzzy neural network is designed from a set of input-output training data to reduce the computing burden during implementation. This control strategy can not only simplify the implementation problem of fuzzy control, but also reduce computational time and consume less memory.

Authors:

• Seema Chopra
• R. Mitra
• Vijay Kumar

Keywords:

• Fuzzy Control
• Neural Network
• MIMO System
• Optimization of Membership functions.

References:

[1] Kuo-Yang Tu, Tsu-Tian Lee, Wen-Jieh Wang, "Design of a multi-layer
fuzzy logic controller for multi-input multi-output systems," Fuzzy Sets
and Systems, vol. 111, pp 199-214, 2000.
[2] J. M. Dias, A. Dourado, "A self-organizing fuzzy controller with a fixed
maximum number of rules and an adaptive similarity factor," Fuzzy Sets
and Systems, vol. 103, , pp 27-48, 1999.
[3] Steven J. Schroeck and William C. Messner, "On Controller Design For
Linear Time-Invariant Dual-Input Single-Output Systems," Proceedings
of the American Control Conference San Diego, California, June 1999,
pp 4122-4126.
[4] Ra'ul Ord'o˜nez and Kevin M. Passino, "Stable Multi-Input Multi-
Output Adaptive Fuzzy/Neural Control," IEEE Transactions on Fuzzy
Systems, vol. 7, No. 3,, pp 345-353, June 1999.
[5] Ruey-Jing Lian , Shiuh-Jer Huang, "A mixed fuzzy controller for MIMO
systems," Fuzzy Sets and Systems vol. 120, pp 73-93, 2001.
[6] Raul Garduno-Ramirez and Kwang Y. Lee, "Wide Range Operation of a
Power Unit via Feedforward Fuzzy Control," IEEE Transactions on
Energy Conversion, vol. 15, No. 4, December 2000.
[7] L. Ljung, System Identification: Theory for The User, Prentice-Hall,
Englewood Cliffs, NJ, 1987.
[8] R.R.Yager and D.P.Filev, "Generation of fuzzy rules by mountain
clustering," Journal of Intelligent and Fuzzy System, vol.2, pp. 209-
219, 1994.
[9] S.L.Chiu, "Fuzzy model identification based on cluster estimation,"
Journal of Intelligent and Fuzzy System, vol.2, pp. 267-278, 1994.
[10] S. Chiu, "Extracting fuzzy rules from data for function approximation
and pattern classification," in Chapter 9 in Fuzzy Set Methods in
Information Engineering: A Guided Tour of Applications, ed. D. Dubois,
H. Prade, and R. Yager, John Wiley, 1997.
[11] Peter Grabusts, "Clustering Methods In Neuro - Fuzzy Modelling,"
URL:http://www.dssg.cs.rtu.lv/download/publications/2002/Garbusts-
RA-2002.pdf.
[12] Petr Pivonka, "Comparative analysis of Fuzzy PI/PD/PID controller
based on classical PID controller approach,". URL:
http://www.feec.vutbr.cz/~pivonka/.
[13] Chia-Feng Juang and Chin-Teng Lin, "An On-Line Self-Constructing
Neural Fuzzy Inference Network and Its Applications," IEEE trans.
Fuzzy System,vol. 6, No. 2, pp. 13-31, 1999.
[14] Seema Chopra, R. Mitra and Vijay Kumar, "Identification Of Rules
Using Subtractive Clustering With Application To Fuzzy Controllers,"
Proc. of the Third International Conference on Machine Learning and
Cybernetics, Shanghai, August 2004, pp. 4125-4131.
[15] D. Driankov, H. Hellendorn, and M. Reinfrank, An Introduction to
Fuzzy Control. New York: Springer-Verlag, 1993.
[16] Seema Chopra, R. Mitra and Vijay Kumar, "Identification of Self-
Tuning Fuzzy PI type controllers with reduced rule set," Proc. of the
IEEE International Conference on Networking, Sensing and Control,
Arizona March 2005., pp.537-542.
[17] J. R. Yang, "ANFIS: Adaptive-Network-Based Fuzzy Inference
System," IEEE transactions on systems, man, and cybernetic, vol. 23,
No. 3, pp. 665-685 May/June 1993.
[18] K Tanaka, M Sano and H. Watanabe, "Modelling and Control of Carbon
Monoxide Concentration using a Neurofuzzy technique," IEEE trans.
Fuzzy System., vol 3, No 3, pp. 271-279, August 1999.
[19] T. Takagi, M. Sugeno, "Fuzzy identification of systems and its
application to modeling and control," IEEE Trans. on Systems, Man, and
Cybernetics, vol. 15, 1985, pp. 116-132.
[20] Kevin M.Passino and Stephen Yurkovich, "Fuzzy Control", Addison
Wesley Longman, Inc., California, 1998.
[21] A. Nurnberger, D. Nauck and R Kruse, "Neuro-fuzzy control based on
the Nefcon-model: recent developments," Soft Computing, vol. 2, 1999,
pp. 168-182.
[22] Mohammad Fazle Azeem, Madasu Hanmandlu, Nesar Ahmed,
"Structure identification of Generalized Adaptive Neuro-Fuzzy
Inference Systems," IEEE trans. Fuzzy System., vol 11, No 5, Oct. pp.
666-681, 2003.
[23] Shie-Jue Lee and Chen-Sen Ouyang, "A Neuro-fuzzy system modeling
with Self-Constructing Rule Generation and Hybrid SVD-Based
Learning," IEEE trans. Fuzzy System., vol 11, No 3, pp. 341-353, June
2003.
[24] Chin-Teng Lin and C. S. George Lee, "Reinforcement Structure/
Parameter Learning for Neural Network based Fuzzy Logic Control
Systems," IEEE trans. Fuzzy System., vol 2, No 1, pp. 46-73, February
1994.
[25] G. Castellano and A.M. Fanelli, "Fuzzy inference and rule extraction
and using neural network," URL:
[26] Chin-Teng Lin and Ya-Ching Lu, "A Neural Fuzzy System with fuzzy
supervised learning," IEEE transactions on systems, man, and
cybernetic-Part B, vol. 26, No. 5, pp 744-763, Oct. 1996.
[27] R.K.Mudi and N.R.Pal, "A robust self-tuning scheme for PI and PD type
fuzzy controllers," IEEE trans. Fuzzy System, vol. 7, No. 1, pp. 2-16.,
1999.
[28] Kuhu Pal, Rajani K. Mudi, and Nikhil R. Pal, "A New Scheme for
Fuzzy Rule-Based System Identification and Its Application to Self-
Tuning Fuzzy Controllers," IEEE transactions on systems, man, and
cyberneticsÔÇöpart b: cybernetics, vol. 32, no. 4, August 2002.
[29] Seema Chopra, R. Mitra and Vijay Kumar, "Fuzzy controller -
Choosing an appropriate and smallest rule set," International Journal on
Computational Cognition, vol 3, No. 4, pp 73-79, Dec 2005
[30] Seema Chopra, R. Mitra and Vijay Kumar, "Analysis and Design of
Fuzzy Controller using Neurofuzzy Techniques," Proc. of the
International Conference on Computer Applications in Electrical
Engineering Recent Advances, CERA 2005, Sep 2005, pp 39-43.
[31] Seema Chopra, R Mitra, Vijay Kumar, "Analysis and Design of Fuzzy
models using Fuzzy Curves," Proceedings of the Second Conference on
Intelligent systems & networks, Jagdhari, Feb. 2005, pp. 65-71.
[32] Seema Chopra, R. Mitra and Vijay Kumar, "Analysis of Fuzzy PI and
PD type controllers using subtractive clustering," International Journal
on Computational Cognition, vol 4, No. 2, pp 30-34, June 2006.
[33] Process Explorer - Sysinternals software. Available at URL:
www.sysinternals.com.
[34] Seema Chopra, R. Mitra and Vijay Kumar, "Reduction of Fuzzy Rules
and Membership Functions of Fuzzy PI and PD type Controllers,"
International Journal of Control, Automation, and Systems, vol. 4, no. 4,
pp. 438-447, August 2006,.
[35] Seema Chopra, R. Mitra and Vijay Kumar, "A Neurofuzzy learning and
its Application to Control system," International Journal on
Computational Intelligence, ISSN 1304-4508, vol. 3, no. 1, pp. 72-78,
2006.