Control of a Virtically-Driven Inverted Pendulum

Periodic stimulation sometimes stabilizes mechanical systems dynamically. we have investigated a virtically-driven inverted pendulum from a view point of such a dynamic stabilization. First, the stability of the pendulum by the period input is analyzed, and it is shown that the system becomes the parametric excitation system, when period input which modulated the amplitude is added. Next, it is theoretically shown that the pendulum can be asymptotically stabilized, when the amplitude of the input is modulated in the timing which suppresses the parametric excitation. This timing can be realized by modulating the amplitude by the nonlinear feedback which consists of angle and anagular velocity of the pendulum in period doubling of the motion of the pendulum. Finally, the result of verifying the effectiveness by the real machine is shown.