Design of Fuzzy Controller Using Single Linear NominalPlant for Mass-Spring-Damper System

Rajesh Tanna*, Alok Kanti Deb**
* Assistant Professor, Department of Electrical and Electronics Engineering, Vignan's Institute of Information Technology, Andhra Pradesh, India.
** Associate Professor, Department of Electrical and Electronics Engineering, IIT Kharagpur, West Bengal, India.
Periodicity:August - October'2015
DOI : https://doi.org/10.26634/jic.3.4.3722

Abstract

This paper gives position and tracking control of Mass-Spring-Damper System. Many methods are available to design controllers for non-linear systems. But, in this framework, a nonlinear system is represented as the fuzzy average of local linear models which are popularly known as Takagi-Sugeno (T-S) Fuzzy Model. Given a nonlinear system, in terms of a T-S Fuzzy Model, the T-S fuzzy model is rewritten in terms of a single nominal plant and rest of the plants are expressed as a disturbance to the nominal plant. The controller is designed such that, the overall system becomes stable in the presence of the disturbance terms. However, the implementation of the controller is constrained by the norm bound of the disturbance term. The control scheme can be designed using the concept of robust control technique. Moreover, the overall fuzzy scheme guarantees that all signals involved are bounded and the output of the closed-loop system will asymptotically track the desired output trajectory. In this paper, the algorithm has been applied to Mass-Spring-Damper System. The simulation is performed on the Mass-Spring-Damper System and the effectiveness of the proposed method is demonstrated.

Keywords

How to Cite this Article?

Tanna, R., Deb, A.K. (2015). Design of Fuzzy Controller Using Single Linear Nominal Plant for Mass-Spring-Damper System. i-manager’s Journal on Instrumentation and Control Engineering, 3(4), 20-27. https://doi.org/10.26634/jic.3.4.3722

References

[1]. Kazuo Tanaka, Takayuki Ikeda, and Hua O Wang, “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, “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]. H. Wang and K. Tanaka, “An LMI-based Stable Fuzzy Control of Nonlinear Systems and its Application to Control of Chaos”, Proceedings of the Fifth IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1433–1438.
[4]. K. Tanaka and M. Sugeno, “Concept of Stability Margin of Fuzzy Systems and Design of Robust Fuzzy Controllers”, Proceedings of 2nd IEEE International Conference on Fuzzy System, Vol. 1, pp. 29–34.
[5]. Kuang-Yow Lian, Hui-Wen Tu, and Jeih-Jang Liou, “Stability Conditions for LMI Based Fuzzy Control from Viewpoint of Membership Functions”, IEEE Transactions on Fuzzy Systems, Vol. 14, No. 6pp. 874 – 884.
[6]. Stanislaw H. Zak, (1999). “Stabilizing Fuzzy System Models Using Linear Controllers,” IEEE Transactions on Fuzzy Systems, Vol. 7, No. 2, pp. 236 – 240.
[7]. P. Prem Kumar, Indrani Kar, and Laxmidhar Behera, (2006). “Variable Gain Controllers for Nonlinear Systems Using the T-S Fuzzy Model”, IEEE Transactions on Fuzzy Systems, Vol. 36, No. 6, pp. 4150 - 4154.
[8]. L.Behera and I.Kar, (2008). Intelligent Systems and Control: Principles and Applications, Oxford, 2008.
[9]. Kazuo Tanaka and Hua O. Wang, (2001). Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach: Wiley.2001.
[10]. Javier Aracil and Francisco Gordillo, (2000). “Stability Issues in Fuzzy Control”.
[11]. 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.
[12]. K. Tanaka and M. Sano, (1994). “A Robust Stabilization Problem of Fuzzy Controller Systems and its Applications to Backing up Control of A Truck-Trailer”, IEEE Transactions on Fuzzy Systems, Vol. 2, pp. 119–134.
[13]. S. Kawamoto et al., (1996). “Nonlinear Control and Rigorous Stability Analysis Based on Fuzzy System for Inverted Pendulum”, Proceedings of IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1427–1432, 1996.
[14]. Wang, H.O., K. Tanaka and M. Griffin, (1995). ”Parallel Distributed Compensation of Nonlinear Systems by Takagi–Sugeno Fuzzy Model”, Proceedings of the Fourth IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 531–538.
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