Nonlinear Controller Design Via Approximate Normal Forms

Krener, Arthur J.

doi:10.1007/978-1-4684-7095-6_7

Cited by 17 publications

(7 citation statements)

References 15 publications

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“…Still in the context of feedback linearization, methods for increasing the accuracy of a digital implementation of the continuous-time feedback law have been proposed (Lee et al, 1988;Monaco et al, 1986) and a multi-rate method has been studied (Grizzle and Kokotovic, 1988). Similar progress on observer linearization has been reported (Krener, 1986(Krener, , 1989Krener et al, 1987;Phelps and Krener, 1988;Grizzle and Moraal, 1989).…”

Section: Discussionmentioning

confidence: 80%

Sampled-data observer error linearization

Chung

Grizzle

1990

Automatica

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Section: Discussionmentioning

confidence: 80%

Sampled-data observer error linearization

Chung

Grizzle

1990

Automatica

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“…In fact, Theorem 4.5 may be considered as an algebraic realization of the corresponding characterization conditions for a linearizable systems in References [6,7]. (Also refer to References [16,17].)…”

Section: Remarkmentioning

confidence: 99%

Normal form representation of control systems

Cheng

Martin

2002

Intl J Robust & Nonlinear

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SUMMARYThis paper is to investigate the normal form representation of control systems. First, as numerical tools we develop an algorithm for normal form expression and the matrix representation of the Lie derivative of a linear vector "eld over homogeneous vector "elds. The concept of normal form is modi"ed. Necessary and su$cient conditions for a linear transformation to maintain the Brunowsky canonical form are obtained. It is then shown that the shift term can always be linearized up to any degree. Based on this fact, linearization procedure is proposed and the related algorithms are presented. Least square linear approximations are proposed for non-linearizable systems. Finally, the method is applied to the ball and beam example.The e!orts are focused on the numerical and computer realization of linearization process.

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“…Die Existenzbedingungen von Satz 1 seien erfüllt. Wendet man die Transformation (2) auf den Beobachter (35) an, so erhält maṅ z = Aẑ + α(ẑ n , u) + (S (ẑ)) -1 k 0 (S(ẑ)) (z n -ẑ n ) .…”

Section: Approximation Nullter Ordnung Mit Einem High-gain-beobachterunclassified

Entwurf nichtlinearer Beobachter mit linearer und näherungsweise linearer Fehlerdynamik

Röbenack¹

2010

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Zusammenfassung Der Beobachterentwurf mittels exakter Linearisierung ist der Fachwelt seit rund 25 Jahren bekannt. Aufgrund restriktiver Existenzbedingungen bzw. einer aufwendigen Berechnung ist dieser sehr elegante Ansatz in der regelungstechnischen Praxis kaum anzutreffen. Im Beitrag werden zunächst Existenzbedingungen und Berechnungsmethoden rekapituliert. Anschließend geht der Beitrag auf den erweiterten Luenberger-Beobachter ein, welcher auf einer lokalen Taylorlinearisierung basiert und wesentlich leichter zu berechnen ist. Zu diesem Beobachter werden Verallgemeinerungen entwickelt und globale Konvergenzbedingungen angegeben.

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Nonlinear Controller Design Via Approximate Normal Forms

Cited by 17 publications

References 15 publications

Sampled-data observer error linearization

Sampled-data observer error linearization

Normal form representation of control systems

Entwurf nichtlinearer Beobachter mit linearer und näherungsweise linearer Fehlerdynamik

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