Differential flatness and defect: an overview

Michel Fliess; Jean Lévine; Philippe Martin; Pierre Rouchon

Banach Center Publications (1995)

  • Volume: 32, Issue: 1, page 209-225
  • ISSN: 0137-6934

Abstract

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We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. We treat an example of non-flat system, the variable-length pendulum. A high frequency control strategy is proposed such that the averaged system becomes flat.

How to cite

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Fliess, Michel, et al. "Differential flatness and defect: an overview." Banach Center Publications 32.1 (1995): 209-225. <http://eudml.org/doc/262868>.

@article{Fliess1995,
abstract = {We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. We treat an example of non-flat system, the variable-length pendulum. A high frequency control strategy is proposed such that the averaged system becomes flat.},
author = {Fliess, Michel, Lévine, Jean, Martin, Philippe, Rouchon, Pierre},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {209-225},
title = {Differential flatness and defect: an overview},
url = {http://eudml.org/doc/262868},
volume = {32},
year = {1995},
}

TY - JOUR
AU - Fliess, Michel
AU - Lévine, Jean
AU - Martin, Philippe
AU - Rouchon, Pierre
TI - Differential flatness and defect: an overview
JO - Banach Center Publications
PY - 1995
VL - 32
IS - 1
SP - 209
EP - 225
AB - We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems' standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. We treat an example of non-flat system, the variable-length pendulum. A high frequency control strategy is proposed such that the averaged system becomes flat.
LA - eng
UR - http://eudml.org/doc/262868
ER -

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