Extended Luenberger observer for non-linear multivariable systems

Birk, J.; Zeitz, Μ.

doi:10.1080/00207178808906138

Cited by 158 publications

(43 citation statements)

References 7 publications

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“…However, the transformation to observer normal form requires the solution of partial differential equations, whose solvability conditions are very strict. The extended Luenberger observer is a modification of the normal form observer, and due to Bestle and Zeitz [1983] and Birk and Zeitz [1988]. This type of observer has a typical Luenberger structure and is based on an extended Jacobian linearization of the error dynamics in coordinates of the observer normal form.…”

Section: Extended Luenberger Observer Theorymentioning

confidence: 99%

“…Since the steerable nips mechanism is a MIMO system, it is necessary to use an extension to the extended Luenberger observer, which is given by Birk and Zeitz [1988]. For a system with output y = h(x) = (h 1 (x), .…”

Section: Extended Luenberger Observers For Mimo Systemsmentioning

confidence: 99%

“…1) to detect the motion of two perpendicular edges of the sheet. These measurements are in term used in a closed-loop extended Luenberger observer, which is based on the work by Bestle and Zeitz [1983] and Birk and Zeitz [1988]. Such an observer is an extension to the normal form observer developed by Krener and Isidori [1983], where some of the conditions required by the latter are relaxed.…”

Section: Introductionmentioning

confidence: 99%

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Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Ergueta

Seifried

Horowitz

et al. 2008

IFAC Proceedings Volumes

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State of the art high speed color printers require sheets being accurately positioned as they arrive to the image transfer station (ITS). This goal has been achieved by constructing a steerable nips mechanism, which is located upstream from the ITS. This mechanism consists of two rollers which not only rotate to advance the paper along the track, but also steer the paper in the yaw direction. A recently developed nonlinear control strategy for the position of the sheet is briefly reviewed. The core of this paper focuses on the addition of a nonlinear observer used to estimate the longitudinal, lateral, and angular positions of a sheet, by detecting its motion along two of its perpendicular sides. The success of the approach presented is corroborated through simulations, in which the estimates from the extended Luenberger observer designed are used on a nonlinear feedback control strategy.

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Section: Extended Luenberger Observer Theorymentioning

confidence: 99%

Section: Extended Luenberger Observers For Mimo Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Ergueta

Seifried

Horowitz

et al. 2008

IFAC Proceedings Volumes

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“…Some observers involve a state dependent correction term L(x), whose design requires extensive symbolic manipulations that might not be feasible for large nonlinear systems [Birk and Zeitz, 1988]. Here, for simplicity, the correction term L is designed independently of the actual states of the system taking a Lyapunov based approach [Gauthier et al, 1992].…”

Section: Observer Designmentioning

confidence: 99%

“…For a detailed discussion of nonlinear observability considering multiple outputs we refer to Birk and Zeitz [1988].…”

Section: Preliminariesmentioning

confidence: 99%

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

Fey¹,

Findeisen

Bullinger³

2008

IFAC Proceedings Volumes

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This version is available at https://strathprints.strath.ac.uk/7337/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.Parameter estimation in kinetic reaction models using nonlinear observers is facilitated by model extensions ⋆ Abstract: An essential part of mathematical modeling is the accurate and reliable estimation of the model parameters. In biology, the required parameters are particularly difficult to measure because of either shortcomings of the measurement technology or a lack of direct measurements. In both cases, parameters must be estimated from indirect measurements, usually in the form of time-series data. Here, we present a novel approach for parameter estimation that is particularly tailored to biological models consisting of nonlinear ordinary differential equations. By assuming specific types of nonlinearities common in biology, such as generalized mass action, Hill kinetics and products thereof, we can take a three step approach: (1) transform the identification into an observer problem using a suitable model extension that decouples the estimation of non-measured states from the parameters; (2) reconstruct all extended states using nonlinear observers; (3) estimate the parameters using the reconstructed states. The actual estimation of the parameters is based on the intrinsic dependencies of the extended states arising from the definitions of the extended variables, and solved via least squares approximation. An important advantage of the proposed method is that it allows us to identify suitable measurements and/or model structures for which the parameters can be estimated. In addition, the proposed identification approach is generally applicable to models of metabolic networks, signal transduction and gene regulation.

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Non-linear multivariable adaptive control of an activated sludge wastewater treatment process

Nejjari¹,

Dahhou²,

Benhammou³

et al. 1999

Int. J. Adapt. Control Signal Process.

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SUMMARYIn this paper a non-linear adaptive feedback-linearizing control is designed for a biological wastewater treatment model. The adaptive control structure is based on the non-linear model of the process and combined with a joint observer estimator which plays the role of the software sensor for the on-line estimation of biological states and parameter variables of interest of the bioprocess. The performances of both estimation and control algorithms are illustrated by simulation results. They demonstrate e!ectiveness and signi"cant robustness against measurement noises and kinetic parameter jumps.

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Extended Luenberger observer for non-linear multivariable systems

Cited by 158 publications

References 7 publications

Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Extended Luenberger Observer for a MIMO Nonlinear Nonholonomic System

Parameter estimation in kinetic reaction models using nonlinear observers facilitated by model extensions

Non-linear multivariable adaptive control of an activated sludge wastewater treatment process

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