Fuzzy Control of Inverted Pendulum System

Rajesh Tanna*, 0**, Vivek Viswanadh***
*,*** Assistant Professor, Department of Electrical and Electronics Engineering, Vignan Institute of Information Technology, Andhra Pradesh, India.
** Professor & Principal, Vignan Institute of Information Technology, Visakhapatnam, Andhra Pradesh, India.
Periodicity:February - April'2016
DOI : https://doi.org/10.26634/jic.4.2.4879

Abstract

This paper gives the position and tracking control of a nonlinear system. Inverted pendulum is an under actuated, unstable and non-linear system. Therefore, control design of such a system is a challenging task. There are many methods to design a controller, but Takagi-Sugeno (T-S) fuzzy controller is one of the traditional control technique which is applied to a non-linear system to check the performance and stability. In this paper, the non-linear system is represented as a linear system by using sector nonlinearity method. Here, the control objective is to control the system such that, the inverted pendulum is stabilized in the upright position. Simulation is performed on the inverted pendulum system, and the effectiveness of the proposed site is demonstrated and the robustness is also verified. In this paper, the algorithm has been applied to the Inverted pendulum system with eight nonlinearities. The simulations are performed on inverted pendulum system and the effectiveness of the proposed method is demonstrated and also the robustness of the system is verified.

Keywords

Sector Nonlinearity, Lyapunov Stability Methods, PDC Control, LMI (Linear Matrix Inquality), Technique and Pole Placement Technique

How to Cite this Article?

Tanna, R., Mary, K.A., and Viswanadh, V. (2016). Fuzzy Control of Inverted Pendulum System. i-manager’s Journal on Instrumentation and Control Engineering, 4(2), 21-28. https://doi.org/10.26634/jic.4.2.4879

References

[1]. Kazuo Tanaka, Takayuki Ikeda, and Hua O Wang, (1998). “Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI Based Designs”. IEEE Transactions on Fuzzy Systems, Vol. 6, No. 2, pp.250-265.
[2]. Kazuo Tanaka, Hiroshi Ohtake, and Hua O. Wang, (2007). “A Descriptor System Approach to Fuzzy Control System Design via Fuzzy Lyapunov Functions”. IEEE Transactions on Fuzzy Systems, Vol.15, No. 3, pp.333-341.
[3]. Kuang-Yow Lian, Hui-Wen Tu, and Jeih-Jang Liou, (2000). “Stability Conditions for LMI Based Fuzzy Control From Viewpoint of Membership Functions”. IEEE Transactions on Fuzzy Systems, Vol. 14, No. 6, pp.874-884.
[4]. L. Behera and I. Kar, (2008). Intelligent Systems and Control: Principles and Applications. Oxford.
[5]. Kazuo Tanaka and Hua O. Wang, (2001). “Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach ”. IEEE Transactions on Fuzzy Systems, Vol.17, No.4, pp.911-922.
[6]. Javier Aracil and Francisco Gordillo, (2000). Stability Issues in Fuzzy Control. Springer Verlag, New York.
[7]. Stanislaw H. Zak,(1999). “Stabilizing Fuzzy System Models Using Linear Controllers”. IEEE Transactions on Fuzzy Systems, Vol. 7, No. 2, pp.236-240.
[8]. Hua O. Wang, Kazuo Tanak, and Michael F. Griffin, (1996). “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues”. IEEE Transactions on Fuzzy Systems, Vol. 4, No. 1, pp.14-23.
[9]. H. Wang and K. Tanaka, (1996). “An LMI-based stable Fuzzy Control of Nonlinear Systems and its Application to th Control of Chaos”. Proceedings of 5 IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1433–1438.
[10]. K. Tanaka and M. Sugeno, (1993). “Concept of Stability Margin of Fuzzy Systems and Design of Robust Fuzzy th Controllers”. in Proceedings of 5 IEEE International Conference on Fuzzy Systems, San Francisco, CA, Vol. 1, pp. 29–34.
[11]. S. Kawamoto et al., (1996). “Nonlinear Control and Rigorous Stability Analysis Based on Fuzzy System for th Inverted Pendulum”. in Proceedings of 5 IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1427–1432.
[12]. Wang, H.O., K. Tanaka and M. Griffin, (1995). ”Parallel Distributed Compensation of Nonlinear Systems by Takagi–sugeno Fuzzy Model”. IEEE, pp.531–538.
[13]. Rajesh Tanna, and Alok Kanti Deb, (2015). “Takagi- Sugeno Fuzzy Control for Nonlinear Systems”. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 4, No.9, pp.7830- 7839
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Online 15 15

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.