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.

Issue Section:
Technical Papers
Keywords:
bifurcation, nonlinear dynamical systems, time-varying systems, periodic control, feedback, nonlinear control systems, pendulums
Topics:
Bifurcation, Pendulums, Control equipment
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