On Stabilization of a Triple Inverted Pendulum via Vibration of a Support Point with an Arbitrary Frequency

Resumo

The stabilization of the upper statically unstable position of a triple inverted pendulum via parametric excitation of the support has been studied. The presented results were obtained by the multiple scale method and the Floquet theory. The stability diagrams in the excitation parameters space (amplitude and frequency of the support excitation) are plotted. It is shown that stabilization is possible for low, medium, and high excitation frequencies. The influence of system parameters on stabilization zones of the upper unstable position of the pendulum is analyzed.