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.

中文翻译：

---

水平驱动的倒立摆

倒立摆可以用手或通过底端的高频正弦垂直振荡或如果在底端施加水平力则通过反馈控制来稳定。如果在底端沿水平方向施加正弦力，则摆锤不稳定。本文表明，当倒立摆以小角度落下后，如果在底端施加低频水平力使倒立摆恢复正常，则可以使倒立摆稳定。该技术需要测量坠落角度，但对实际坠落角度不敏感。该技术代表了反馈控制的简单示例，并且比底端的垂直振荡更容易理解。