Natural Observer Design for Singularly Perturbed Vector Second-Order Systems

[+] Author and Article Information
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 127(4), 648-655 (Dec 13, 2004) (8 pages) doi:10.1115/1.2101847 History: Received June 11, 2004; Revised December 13, 2004

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 O(ε), where ε 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.

Copyright © 2005 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Energy norm, [eT(t)Ke(t)+ėT(t)Mė(t)]1∕2

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Figure 2

Position and velocity outputs for ε1=ε2=0.0

Grahic Jump Location
Figure 3

Position and velocity outputs for ε1=ε2=0.8




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