For most complex dynamic systems, it is not always possible to measure all system states by a direct measurement technique. 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 (linear as well as nonlinear) with time-periodic coefficients is addressed. It is shown that, for linear periodic systems, 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 a Chebyshev expansion technique where the Floquet multipliers can be placed in the desired locations within the unit circle. For nonlinear time-periodic systems, an observer design methodology is developed using the Lyapunov–Floquet transformation and the Poincaré normal form technique. First, a set of time-periodic near identity coordinate transformations are applied to convert the nonlinear problem to a linear observer design problem. The conditions for existence of such invertible maps and their computations are discussed. Then the local identity observers are designed and implemented using a symbolic computational algorithm. Several illustrative examples are included to show the effectiveness of the proposed methods.
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e-mail: zhangya@auburn.edu
e-mail: ssinha@eng.auburn.edu
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July 2009
Research Papers
Observer Design for Nonlinear Systems With Time-Periodic Coefficients via Normal Form Theory
Yandong Zhang,
Yandong Zhang
Department of Mechanical Engineering, Nonlinear Systems Research Laboratory,
e-mail: zhangya@auburn.edu
Auburn University
, Auburn, AL 36849
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S. C. Sinha
S. C. Sinha
Fellow ASME
Department of Mechanical Engineering, Nonlinear Systems Research Laboratory,
e-mail: ssinha@eng.auburn.edu
Auburn University
, Auburn, AL 36849
Search for other works by this author on:
Yandong Zhang
Department of Mechanical Engineering, Nonlinear Systems Research Laboratory,
Auburn University
, Auburn, AL 36849e-mail: zhangya@auburn.edu
S. C. Sinha
Fellow ASME
Department of Mechanical Engineering, Nonlinear Systems Research Laboratory,
Auburn University
, Auburn, AL 36849e-mail: ssinha@eng.auburn.edu
J. Comput. Nonlinear Dynam. Jul 2009, 4(3): 031001 (10 pages)
Published Online: May 19, 2009
Article history
Received:
January 28, 2008
Revised:
December 23, 2008
Published:
May 19, 2009
Citation
Zhang, Y., and Sinha, S. C. (May 19, 2009). "Observer Design for Nonlinear Systems With Time-Periodic Coefficients via Normal Form Theory." ASME. J. Comput. Nonlinear Dynam. July 2009; 4(3): 031001. https://doi.org/10.1115/1.3124093
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