Bifurcation control in an underactuated pendulum

In this paper, a Hopf bifurcation is created by means of a state feedback in an actual underactuated pendulum, in order to obtain oscillations of prescribed amplitude. Toward this end, two different nonlinear feedback laws are designed and analyzed. Theoretical conditions for the birth of a Hopf bifurcation are derived, and the dependence of the amplitudes as a function of the feedback gains is obtained via numerical continuation of the periodic solutions. The experimental results are compared with computer simulations.