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.
Bifurcation Control of Nonlinear Systems With Time-Periodic Coefficients
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.
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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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