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TECHNICAL PAPERS

Controlling Chaos by Hybrid System Based on FREN and Sliding Mode Control

[+] Author and Article Information
C. Treesatayapun

Department of Electrical Engineering, Chiang Mai University, Chiang Mai 50200, Thailandchidentree@northcm.ac.th,tree471@yahoo.com

S. Uatrongjit

Department of Electrical Engineering, Chiang Mai University, Chiang Mai 50200, Thailand

J. Dyn. Sys., Meas., Control 128(2), 352-358 (May 24, 2005) (7 pages) doi:10.1115/1.2194071 History: Received April 01, 2003; Revised May 24, 2005

This paper presents a direct adaptive controller for chaotic systems. The proposed adaptive controller is constructed using the network called fuzzy rules emulated network (FREN). FREN’s structure is based on human knowledge in the form of fuzzy rules. Parameter adaptation algorithm based on the steepest descent method is presented to fine tune the controller’s performance. To improve the system stability, the modified sliding mode algorithm is applied to estimate the upper and lower bounds of the control effort. The suitable control effort is generated by FREN and kept within these bounds. Some computer simulations of using the controller to control the Hénon map have been performed to demonstrate the performance of the proposed controller.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Structure of FREN

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Figure 2

Examples of membership functions (MF)

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Figure 3

Examples of linear consequences (LC)

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Figure 4

Control system using FREN

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Figure 5

State trajectory of uncontrolled Hénon map

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Figure 6

(a) Initial and (b) final setting of MF and LC for Henon map

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Figure 7

Time response of y(k), u(k), and its bounds, and E(K) of Henon map before parameter adaptation

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Figure 8

Time response of y(k), u(k), and its bounds, and E(K) of Henon map after parameter adaptation

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Figure 9

Time response of y(k), u(k), and its bounds, and E(K) of Henon map in the case of sine wave reference signal

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Figure 10

Time response of y(k), u(k), and its bounds, and E(K) of Henon map when xd is sine wave form and u(K) are not kept within stable bound

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