Balancing a Stick with Eyes Shut: Inverted Pendulum on a Cart without Angle Measurement

TL;DR

This paper demonstrates that an inverted pendulum on a cart can be stabilized using cart position feedback with an additional feedforward compensator, despite the system's inherent stabilization challenges without angle measurement.

Contribution

It introduces a novel control scheme employing a parallel feedforward loop to stabilize the inverted pendulum without angle sensors, expanding control options for such systems.

Findings

Stabilization achieved with cart position feedback and an added compensator.

Sensitivity to noise is approximately three times higher than with angle feedback.

Discussion of robustness, parameter choices, and comparison with other control methods.

Abstract

We consider linear time-invariant dynamic systems in the single-input, single-output (SISO) framework. In particular, we consider stabilization of an inverted pendulum on a cart using a force on the cart. This system is easy to stabilize with pendulum angle feedback. However, with cart position feedback it cannot be stabilized with stable and proper compensators. Here we demonstrate that with an additional compensator in a parallel feedforward loop, stabilization is possible with such compensators. Sensitivity to noise seems to be about 3 times worse than for the situation with angle feedback. For completeness, discussion is presented of compensator parameter choices, robustness, fragility and comparison with another control approach.