Geodesic
From fractal robustness to the CRONE approach
Alain Oustaloup1 ; Jocelyn Sabatier1 ; Xavier Moreau1
1 Équipe CRONE - LAP - ENSERB, Université Bordeaux I, 351, cours de la Libération - 33405 Talence cedex, France
ESAIM. Proceedings, Tome 5 (1998), pp. 177-192 Cet article a éte moissonné depuis la source EDP Sciences

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This article deals with the transposition of ''fractal robustness'' to automatic control. The considered dynamic model which governs this phenomenon is a non integer order linear differential equation where the natural frequency and the damping ratio of the oscillatory mode of the solution are determined. A remarkable result is that the damping ratio is exclusively linked to the non integer order of the differential equation. This is the corner stone of the CRONE control. The dynamic behaviour of this control is described in tracking and in regulation. The robustness of the damping ratio and of the resonance ratio is demonstrated. An open loop is defined using closed loop performance specifications. A CRONE regulator is approximated by an integer order transmittance. Finally, the principle of the CRONE suspension, the synthesis method and the performance are developed.
DOI : 10.1051/proc:1998006

Alain Oustaloup 1 ; Jocelyn Sabatier 1 ; Xavier Moreau 1

1 Équipe CRONE - LAP - ENSERB, Université Bordeaux I, 351, cours de la Libération - 33405 Talence cedex, France 
@article{EP_1998_5_a14,
     author = {Alain Oustaloup and Jocelyn Sabatier and Xavier Moreau},
     title = {From fractal robustness to the {CRONE} approach},
     journal = {ESAIM. Proceedings},
     pages = {177--192},
     year = {1998},
     volume = {5},
     doi = {10.1051/proc:1998006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:1998006/}
}
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Alain Oustaloup; Jocelyn Sabatier; Xavier Moreau. From fractal robustness to the CRONE approach. ESAIM. Proceedings, Tome 5 (1998), pp. 177-192. doi: 10.1051/proc:1998006

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