Friction and the Inverted Pendulum Stabilization Problem

We consider an experimental system consisting of a pendulum, which is free to rotate $360deg$, attached to a cart. The cart can move in one dimension. We study the effect of friction on the design and performance of a feedback controller, a linear quadratic regulator, that aims to stabilize the pendulum in the upright position. We show that a controller designed using a simple viscous friction model has poor performance—small amplitude oscillations occur when the controller is implemented. We consider various models for stick slip friction between the cart and the track and measure the friction parameters experimentally. We give strong evidence that stick slip friction is the source of the small amplitude oscillations. A controller designed using a stick slip friction model stabilizes the system, and the small amplitude oscillations are eliminated.