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An Approach of Non-Linear Systems Through Fuzzy Control Based on Takagi-Sugeno Method

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GeNeDis 2016

Abstract

Today, the advanced technology is a part of the everyday’s life. As a result, most of the applications used require a more complex system in order to achieve a better performance. These systems have a mathematic background indicating the need of a better mathematical tool to increase the reliability of them. One of the most significant problems coming up against these systems is undoubtedly the non-linearity of the equations governing them. Herein, a linearization method is proposed and studied through intelligent control. The transformation of a non-linear system into a linear is based on fuzzy logic and more specifically on Takagi-Sugeno technique. Firstly, it is analyzed in a theoretical level followed by two examples. The fuzzy model was developed through Matlab program. Finally, the efficiency of the above method was investigated setting up various values for the under study variables and comparing the results of them with the “actual” ones. The square error method was used for a better evaluation indicating that this method is a useful technique except from the applications where the high accuracy is mandatory.

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References

  1. Agarwal, N., and R. Mukkamala. 2005. Design of Complex Systems: Issues and Challenges. Twenty fourth digital avionics systems conference, Vol. 2, p. 8. IEEE.

    Google Scholar 

  2. Bajpai, D., and A. Mandal. 2015. Comparative Analysis of t-Sugeno and Mamdani Type Fuzzy Logic Controller for pmsm Drives. International Journal of Engineering Research and General Science 3 (2): 495–507.

    Google Scholar 

  3. Berenji, H. 1990. Neural Networks and Fuzzy Logic in Intelligent Control. Proceedings of the 5th IEEE International Symposium on Intelligent Control, 1990, pp. 916–920. IEEE.

    Google Scholar 

  4. Califano, C., and C.H. Moog. 2014. The Observer Error Linearization Problem via Dynamic Compensation. IEEE Transactions on Automatic Control 59 (9): 2502–2508.

    Article  Google Scholar 

  5. Denaï, M.A., F. Palis, and A. Zeghbib. 2007. Modeling and Control of Non-Linear Systems Using Soft Computing Techniques. Applied Soft Computing 7 (3): 728–738.

    Article  Google Scholar 

  6. Dierks, T., and S. Jagannathan. 2011. Online Optimal Control of Nonlinear Discrete-Time Systems Using Approximate Dynamic Programming. Journal of Control Theory and Applications 9 (3): 361–369.

    Article  Google Scholar 

  7. Jouan, P. 2003. Immersion of Nonlinear Systems Into Linear Systems Modulo Output Injection. SIAM Journal on Control and Optimization 41 (6): 1756–1778.

    Article  Google Scholar 

  8. Wang, H.O., K. Tanaka, and M.F. Griffin. 1996. An Apprach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues. IEEE Transactions on Fuzzy Systems 4 (1): 14–23.

    Article  Google Scholar 

  9. Liu, T., E. Ko, and J. Lee. 1993. Intelligent Control of Dynamic Systems. Journal of the Franklin Institute 330 (3): 491–503.

    Article  Google Scholar 

  10. Tanaka, K., and H.O. Wang. 2004. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley.

    Google Scholar 

  11. Mishra, S., Y. Mishra, F. Li, and Z. Dong. 2009. Ts-Fuzzy Controlled d g Based Wind Energy Conversion Systems. 2009 IEEE Power & Energy Society General Meeting, pp. 1–7. IEEE.

    Google Scholar 

  12. Salimifard, M., and A.A. Safavi. 2013. Nonlinear System Identi Cation Based on a Novel Adative Fuzzy Wavelet Neural Network. 2013 21st Iranian Conference on Electrical Engineering (ICEE), pp. 1–5. IEEE.

    Google Scholar 

  13. Singh, A., and M. Badoni. 2015. Design and Implementation of Takagi-Sugeno Fuzzy Logic Controller for Shunt Compensator. Journal of The Institution of Engineers (India): Series B: 1–11.

    Google Scholar 

  14. Prasad, L.B., H.O. Gupta, and B. Tyagi. 2011. Intelligent Control of Nonlinear Inverted Pendulum Dynamical System with Disturbance Input Using Fuzzy Logic Systems. 2011 International Conference on Recent Advancements in Electrical, Electronics and Control Engineering (ICONRAEeCE), pp. 136–141. IEEE.

    Google Scholar 

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Correspondence to Andreas Giannakis .

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Giannakis, A., Giannakis, K., Karlis, A. (2017). An Approach of Non-Linear Systems Through Fuzzy Control Based on Takagi-Sugeno Method. In: Vlamos, P. (eds) GeNeDis 2016. Advances in Experimental Medicine and Biology, vol 988. Springer, Cham. https://doi.org/10.1007/978-3-319-56246-9_9

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