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Research Papers

Stabilization of Unstable Fixed Points of Fractional-Order Systems by Fractional-Order Linear Controllers and Its Applications in Suppression of Chaotic Oscillations

[+] Author and Article Information
Mohammad Saleh Tavazoei

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran 11155-9363, Irantavazoei@sina.sharif.edu

Mohammad Haeri

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran 11155-9363, Iranhaeri@sina.sharif.edu

This point is valid when the pseudostate vector x is available. But in using the controller of Sec. 4 if we need to estimate the states by an observer, the complexity of the set of controller and the observer may not be less than that of the controller structure introduced in Sec. 3.

J. Dyn. Sys., Meas., Control 132(2), 021008 (Feb 04, 2010) (7 pages) doi:10.1115/1.4000654 History: Received June 03, 2008; Revised September 22, 2009; Published February 04, 2010; Online February 04, 2010

In this paper, two fractional-order linear controllers are proposed to stabilize unstable equilibrium points of a chaotic fractional-order system. The first controller is based on the dynamic output feedback control idea and requires detectability of the linearized model of the fractional-order system on the equilibrium point. The second controller is a dynamic state feedback controller and requires observability of the linearized model. In both considered cases, the stabilizability of the model is assumed. The number of inner states in the second controller is one and therefore its structure is much simpler than the first controller. To illustrate the applicability, these controllers are applied to control chaos in the fractional-order Chen system. Numerical simulations results are presented to evaluate the performance of the proposed controllers.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Stability region of fractional-order linear time invariant system with order 0<α≤1

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Figure 2

Simulation result of example 1

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Figure 3

Simulation result of example 2

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