On Symbolic Computation of Flat Outputs for Differentially Flat Systems

Antritter, Felix; Verhoeven, Gregor Günther

doi:10.3182/20100901-3-it-2016.00104

Cited by 9 publications

(9 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By this reason, Lévine [2011] developed a 2-step procedure for computing the flat outputs. This procedure has been implemented in Maple by Antritter and Verhoeven [2010]. The goal of this paper is to find the relations (in the discrete-time) between the necessary and sufficient solvability conditions in Lévine [2011] and Aranda-Bricaire et al [1996] as well as the one-forms they depend on.…”

mentioning

confidence: 99%

On Flatness of Discrete-time Nonlinear Systems

Kaldmäe

Kotta

2013

IFAC Proceedings Volumes

View full text Add to dashboard Cite

mentioning

confidence: 99%

On Flatness of Discrete-time Nonlinear Systems

Kaldmäe

Kotta

2013

IFAC Proceedings Volumes

View full text Add to dashboard Cite

“…Our definition of fractional flatness is based on the notion of defining matrices in the spirit of [24,1].…”

Section: Fractional Flatnessmentioning

confidence: 99%

Flatness for linear fractional systems with application to a thermal system

et al. 2015

View full text Add to dashboard Cite

This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs and a simple algorithm to compute them. We also obtain a characterization of the so-called fractionnally 0-flat outputs. We then present an application to a two dimensional heated metallic sheet, whose dynamics may be approximated by a fractional model of order 1/2. The trajectory planning of the temperature at a given point of the metallic sheet is obtained thanks to the fractional flatness property, without integrating the system equations. The pertinence of this approach is discussed on simulations.

show abstract

“…The implementation of the algorithm is rather simple and has therefore been incorporated into the toolbox. This toolbox can be seen as the continuation of our work on the implementation of computer algebra tools for the analysis of linear time varying [12] and nonlinear [13] systems.…”

Section: Introductionmentioning

confidence: 99%

A toolbox for the analysis of linear systems with delays

Antritter

Middeke

2011

IEEE Conference on Decision and Control and European Control Conference

Self Cite

View full text Add to dashboard Cite

This paper considers linear time varying control systems with delays. Roughly speaking, a so called π-flat output of such a system, if it exists, allows to parameterize the states and inputs of the system using derivatives and delays of the π-flat output. Additionally, also predictions of the π-flat output are allowed, which are characterized by a prediction operator π. We present a toolbox for the computer algebra system Maple, which implements the algorithm recently been proposed in [1] for the computation of π-flat outputputs. We also give an equivalent description of hyper-regularity of polynomial matrices using one-sided inverses. This allowed us to replace the transformation to Smith-Jacobson form by the efficient method of row-/column-reduction for checking hyper-regularity. The implementation of the toolbox is illustrated and its application is explained by means of examples.

show abstract

On Symbolic Computation of Flat Outputs for Differentially Flat Systems

Cited by 9 publications

References 38 publications

On Flatness of Discrete-time Nonlinear Systems

On Flatness of Discrete-time Nonlinear Systems

Flatness for linear fractional systems with application to a thermal system

A toolbox for the analysis of linear systems with delays

Contact Info

Product

Resources

About