A horizontally driven inverted pendulum

An inverted pendulum can be stabilised by hand or by a high frequency sinusoidal vertical oscillation of the bottom end or by feedback control if a horizontal force is applied at the bottom end. The pendulum is unstable if a sinusoidal force is applied in a horizontal direction at the bottom end. It is shown in the present paper that an inverted pendulum can be stabilised if a low frequency horizontal force is applied at the bottom end to right the pendulum after it falls through a small angle. The technique requires a measurement of the fall angle but is not sensitive to the actual fall angle. The technique represents a simple example of feedback control and is more easily understood than vertical oscillation of the bottom end.