Our aim in the present research study is to develop a systematic natural observer design framework for vector second-order systems in the presence of time-scale multiplicity. Specifically, vector second-order mechanical systems are considered along with fast sensor dynamics, and the primary objective is to obtain accurate estimates of the unmeasurable slow system state variables that are generated by an appropriately designed model-based observer. Within a singular perturbation framework, the proposed observer is designed on the basis of the system dynamics that evolves on the slow manifold, and the dynamic behavior of the estimation error that induces is analyzed and mathematically characterized in the presence of the unmodeled fast sensor dynamics. It is shown, that the observation error generated by neglecting the (unmodeled) fast sensor dynamics is of order , where is the singular perturbation parameter and a measure of the relative speed/time constant of the fast (sensor) and the slow component (vector second-order system) of the overall instrumented system dynamics. Finally, the performance of the proposed method and the convergence properties of the natural observer designed are evaluated in an illustrative example of a two-degree of freedom mechanical system.
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December 2005
Technical Papers
Natural Observer Design for Singularly Perturbed Vector Second-Order Systems
Michael A. Demetriou,
Michael A. Demetriou
Department of Mechanical Engineering,
mdemetri@wpi.edu
Worcester Polytechnic Institute
, Worcester, MA 01609
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Nikolaos Kazantzis
Nikolaos Kazantzis
Department of Chemical Engineering,
nikolas@wpi.edu
Worcester Polytechnic Institute
, Worcester, MA 01609
Search for other works by this author on:
Michael A. Demetriou
Department of Mechanical Engineering,
Worcester Polytechnic Institute
, Worcester, MA 01609mdemetri@wpi.edu
Nikolaos Kazantzis
Department of Chemical Engineering,
Worcester Polytechnic Institute
, Worcester, MA 01609nikolas@wpi.edu
J. Dyn. Sys., Meas., Control. Dec 2005, 127(4): 648-655 (8 pages)
Published Online: December 13, 2004
Article history
Received:
June 11, 2004
Revised:
December 13, 2004
Citation
Demetriou, M. A., and Kazantzis, N. (December 13, 2004). "Natural Observer Design for Singularly Perturbed Vector Second-Order Systems." ASME. J. Dyn. Sys., Meas., Control. December 2005; 127(4): 648–655. https://doi.org/10.1115/1.2101847
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