In this study, a method for the nonlinear bifurcation control of systems with periodic coefficients is presented. The aim of bifurcation control is to stabilize post bifurcation limit sets or modify other nonlinear characteristics such as stability, amplitude or rate of growth by employing purely nonlinear feedback controllers. The method is based on an application of the Lyapunov-Floquet transformation that converts periodic systems into equivalent forms with time-invariant linear parts. Then, through applications of time-periodic center manifold reduction and time-dependent normal form theory completely time-invariant nonlinear equations are obtained for codimension one bifurcations. The appropriate control gains are chosen in the time-invariant domain and transformed back to the original variables. The control strategy is illustrated through the examples of a parametrically excited simple pendulum undergoing symmetry-breaking bifurcation and a double inverted pendulum subjected to a periodic load in the case of a secondary Hopf bifurcation.
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December 2003
Technical Papers
Bifurcation Control of Nonlinear Systems With Time-Periodic Coefficients
Alexandra Da´vid, Graduate Research Assistant, Student Member, ASME,
Alexandra Da´vid, Graduate Research Assistant, Student Member, ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849
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S. C. Sinha, Professor, Fellow ASME
e-mail: ssinha@eng.auburn.edu
S. C. Sinha, Professor, Fellow ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849
Search for other works by this author on:
Alexandra Da´vid, Graduate Research Assistant, Student Member, ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849
S. C. Sinha, Professor, Fellow ASME
Nonlinear Systems Research Laboratory, Department of Mechanical Engineering, Auburn University, Auburn, AL 36849
e-mail: ssinha@eng.auburn.edu
Contributed by the Dynamic Systems, Measurement, and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the ASME Dynamic Systems and Control Division Oct. 18, 1999; final revision May 28, 2003. Associate Editor: Fahrenthold.
J. Dyn. Sys., Meas., Control. Dec 2003, 125(4): 541-548 (8 pages)
Published Online: January 29, 2004
Article history
Received:
October 18, 1999
Revised:
May 28, 2003
Online:
January 29, 2004
Citation
Da´vid, A., and Sinha, S. C. (January 29, 2004). "Bifurcation Control of Nonlinear Systems With Time-Periodic Coefficients ." ASME. J. Dyn. Sys., Meas., Control. December 2003; 125(4): 541–548. https://doi.org/10.1115/1.1636194
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