Control of a flexible inverted pendulum

Abstract

This study treats the control problem of an inverted pendulum with a flexible structure. Controlling an inverted pendulum is a fundamental of stabilizing unstable systems such as walking robots. Furthermore, consideration of the flexibility is essential for controlling light-weight mechanical systems with quick motion. The controlled system in this study consists of a wire-driven carrier, a flexible beam hinged to the carrier, and a weight fixed on the other side of the beam. Linear quadratic control was applied to the system using a personal computer, but resulted in a steady vibration due to the Coulomb friction. The characteristics of the relaxation-type vibration were well explained by the analysis using the method of averaging. A simple recursive algorithm was employed to estimate the amount of Coulomb friction. With on-line estimation and compensation of the friction, linear quadratic control was successfully applied to stabilizing the system.