Analysis of Stability Radius of Inverted Pendulum on a Cart System

Abstract

This paper discusses the concept of stability radius and presents an evaluation of the same for inverted pendulum on a cart system. In a system, robustness can be calculated or determined by using stability radius. It is shown through example that the usual margins (gain and phase margins) may not always present an accurate measure of stability robustness. Simulation results indicate that some parameters in the system may affect the stability radius more than the others. The results also indicate the effect of simultaneous changes in system parameters on the stability radius may be highly nonlinear and non-monotonic. Finally, a design guideline for inverted pendulum mass to length ratio has been derived from the results.