A robustness approach to linear control of mildly nonlinear processes

Schweickhardt, Tobias; Allgöwer, Frank

doi:10.1002/rnc.1163

Cited by 8 publications

(4 citation statements)

References 43 publications

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“…Therefore, the usual small gain condition for robust stability does not apply. If the set is characterized by the maximal amplitude of the signals it contains, a possible remedy is the introduction of artificial saturation in the control system [41], [31], [42].…”

Section: Discussionmentioning

confidence: 99%

On System Gains, Nonlinearity Measures, and Linear Models for Nonlinear Systems

Schweickhardt

Allgöwer

2009

IEEE Trans. Automat. Contr.

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This article is concerned with the assessment and derivation of (best) linear models for nonlinear systems. We introduce a general framework reminiscent of uncertainty descriptions in linear robust control theory in order to define a family of six model quality indices for linear models of nonlinear systems. Each quality index corresponds to the gain of an error system, where the nonlinear system can be represented as the interconnection of a nominal linear model and this error system. For an analysis in a certain region of operation, these gains are considered over a specified signal set. A best linear model is a linear model that minimizes the quality index and the minimal quality index serves at the same time as a measure of nonlinearity of the nonlinear system. We show that the model quality indices and nonlinearity measures can be defined under very weak assumptions, and we give conditions that guarantee the existence of optimal linear models. We discuss the structure of the problem of computing the nonlinearity measures. We show that the local linearization of a state space system is a best linear model for the limiting case of a vanishing operating range for one of the measures. We show the relation between the steady-state behavior of a system and its gain and nonlinearity measures. Furthermore we give linear models and upper bounds for nonlinearity measures for systems composed of a linear dynamic and a nonlinear static part. In the case of scalar (SISO) systems, these bounds are given by the sector bounds of the nonlinearity. Finally, it is shown that a lower bound on the nonlinearity measures can be derived using harmonic analysis. Several small examples serve to illustrate the results and the underlying ideas.

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Section: Discussionmentioning

confidence: 99%

On System Gains, Nonlinearity Measures, and Linear Models for Nonlinear Systems

Schweickhardt

Allgöwer

2009

IEEE Trans. Automat. Contr.

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“…En particulier, dans [SA07] les auteurs se sont penchés sur le cas de systèmes «faiblement» non linéaires : leur objectif étant de les commander par des correcteurs linéaires stationnaires. La démarche consiste à approcher de façon optimale le système non linéaire par un système linéaire stationnaire pour lequel un correcteur linéaire stationnaire est mis au point.…”

Section: Chapitreunclassified

“…• notre méthode permet d'obtenir un modèle réduit dépendant seulement d'une partie de l'ensemble des paramètres (ou, ce qui revient au même dans le contexte non linéaire, seulement de certaines non linéarités) tandis que dans [SA07] le modèle réduit est nécessairement linéaire. Par extension, cette méthode peut être utilisée pour obtenir un modèle d'une complexité réduite quelconque.…”

Section: Chapitreunclassified

Robust Control of Nonlinear Systems

Lin

2007

Robust Control Design

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“…But it can be seen that for this simple system already the proposed procedure not only guarantees stability, but also leads to a better performance when compared to the conventional approach. More details on the approach and more complex worked out examples can be found in (Schweickhardt and Allgöwer, 2006).…”

Section: Linear Control Of Nonlinear Systems -A Small Gain Approachmentioning

confidence: 99%