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

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.