The problem of designing controllers for nonlinear time periodic systems via feedback linearization is addressed. The idea is to find proper coordinate transformations and state feedback under which the original system can be (exactly or approximately) transformed into a linear time periodic control system. Then a controller can be designed to guarantee the stability of the system. Our approach is designed to achieve local control of nonlinear systems with periodic coefficients desired to be driven either to a periodic orbit or to a fixed point. The system equations are represented by a quasi-linear system containing nonlinear monomials with periodic coefficients. Using near identity transformations and normal form theory, the original close loop problem is approximately transformed into a linear time periodic system with unknown gains. Then by using a symbolic computation method, the Floquet multipliers are placed in the desired locations in order to determine the control gains. We also give the sufficient conditions under which the system is feedback linearizable up to the th order.
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e-mail: zhangya@auburn.edu
e-mail: ssinha@eng.auburn.edu
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April 2007
Research Papers
Development of a Feedback Linearization Technique for Parametrically Excited Nonlinear Systems via Normal Forms
Yandong Zhang,
Yandong Zhang
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering,
e-mail: zhangya@auburn.edu
Auburn University
, Auburn, AL 36849
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S. C. Sinha
S. C. Sinha
Fellow ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering,
e-mail: ssinha@eng.auburn.edu
Auburn University
, Auburn, AL 36849
Search for other works by this author on:
Yandong Zhang
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering,
Auburn University
, Auburn, AL 36849e-mail: zhangya@auburn.edu
S. C. Sinha
Fellow ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering,
Auburn University
, Auburn, AL 36849e-mail: ssinha@eng.auburn.edu
J. Comput. Nonlinear Dynam. Apr 2007, 2(2): 124-131 (8 pages)
Published Online: December 8, 2006
Article history
Received:
April 26, 2006
Revised:
December 8, 2006
Citation
Zhang, Y., and Sinha, S. C. (December 8, 2006). "Development of a Feedback Linearization Technique for Parametrically Excited Nonlinear Systems via Normal Forms." ASME. J. Comput. Nonlinear Dynam. April 2007; 2(2): 124–131. https://doi.org/10.1115/1.2447190
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