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Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers

Lanusse, Patrick and Oustaloup, Alain and Pommier-Budinger, Valérie Stability of closed-loop fractional-order systems and definition of damping contours for the design of controllers. (2012) International Journal of Bifurcation and Chaos (IJBC), vol. 22 (n° 4). ISSN 0218-1274

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Official URL: http://dx.doi.org/10.1142/S0218127412300133

Abstract

Fractional complex order integrator has been used since 1991 for the design of robust control-systems. In the CRONE control methodology, it permits the parameterization of open loop transfer function which is optimized in a robustness context. Sets of fractional order integrators that lead to a given damping factor have also been used to build iso-damping contours on the Nichols plane. These iso-damping contours can also be used to optimize the third CRONE generation open-loop transfer function. However, these contours have been built using non band-limited integrators, even if such integrators reveal to lead to unstable closed loop systems. One objective of this paper is to show how the band-limitation modifies the left half-plane dominant poles of the closed loop system and removes the right half-plane ones. It is also presented how to obtain a fractional order open loop transfer function with a high phase slope and a useful frequency response. It is presented how the damping contours can be used to design robust controllers, not only CRONE controllers but also PD and QFT controllers.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE
Other partners > Université de Bordeaux 1 (FRANCE)
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Deposited By: valerie budinger
Deposited On:31 May 2012 11:50

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