Transfer function modeling of multi-link flexible structures

Abstract

The paper considers the problem of deriving the accurate, infinite dimension, Laplace transfer function matrix of a system consisting of links that are individually governed by a one-dimensional wave equation. The first step is deriving some single input transfer functions, for a single uniform link. The building blocks of those transfer functions are time delays, representing the wave motion, and low-order rational expressions, representing the boundary phenomena. The transfer function approach enables simple yet accurate simulation schemes, exact frequency response for the entire frequency range, finite time analytical solutions, and a good starting point for dedicated control laws. The transfer function provides also an alternative way of obtaining many of the well-known properties of flexible structures. Three methods of modeling multi-link systems are presented. Two of them provide systematic and easy to use approaches for deriving models for systems of any order.