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Observer Design for Nonlinear Systems With Time Periodic Coefficients Via Normal Form Theory

[+] Author Affiliations
Yandong Zhang, S. C. Sinha

Auburn University, Auburn, AL

Paper No. DETC2007-34831, pp. 835-844; 10 pages
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME


For most complex dynamic systems, it is not possible to measure all system states in a direct fashion. Thus for dynamic characterization and controller design purposes, it is often necessary to design an observer in order to get an estimate of those states which cannot be measured directly. In this work, the problem of designing state observers for free systems with time periodic coefficients is addressed. For linear time-periodic systems, it is shown that the observer design problem is the duality of the controller design problem. The state observer is constructed using a symbolic controller design method developed earlier using the Chebyshev expansion technique. For the nonlinear time periodic systems, the observer design is investigated using the Poincaré normal form technique. The local identity observer is designed by using a set of near identity coordinate transformations which can be constructed in the ascending order of nonlinearity. These observer design methods are implemented using a symbolic computational algorithm and several illustrative examples are given to show the effectiveness of the methods.

Copyright © 2007 by ASME



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