Near Optimal Control Of Flexible Robots

Abstract

This paper deals with an exact state-space dynamic model for a manipulator with a single flexible link. The Bernoulli-Euler beam equations are used to derive the matrix transfer function. This transfer function can be used to describe the link or beam displacement at any position along the beam. A 6th order state model is derived and the opttmal linear regulator controller is determined. It is shown that using a "raised cosine" reference command signal yields a smooth yet quick response. Finally unmodeled modes are added to the plant making it 8th order. The controller and observer are based on the 6th order model. In the performance degrades significantly; however the addition of a very simple law pass filter operating on the control signal restores the behavior to excellent quality.