Control of flexible inverted pendulum.

Abstract

This study treats a particular control problem of an inverted pendulum with flexible structure. An inverted pendulum problem is a fundamental of stabilizing unstable systems such as a walking robot. Furthermore, consideration of the flexibility is essential for control of a light weight mechanical system with quick motion. A controlled system in this study consists of a wire-driven carrier, a flexible beam hinged to the carrier and a weight fixed at the other side of the beam. Linear quadratic control was applied to stabilize the system using a personal computer. However, steady vibration due to the coulomb friction was observed in the system. Characteristics of the nonlinear vibration were well explained by the analysis using the method of averaging. A simple recursive algorithm was employed to estimate the value of the Coulomb friction. With an on-line estimation and compensation of the Coulomb friction, linear quadratic control was successfully applied to stabilize, the system.