Control of Multi-Link Flexible Structures

Abstract

A method of noncollocated controller design for non-uniform flexible structures, governed by the wave equation, is proposed. Exact, infinite dimensional, transfer functions, relating the actuation and measurement points, with general boundary conditions, are derived for the multi-link case. Three modeling methods are presented and discussed. A key element of the model is the existence of time delays, due to the wave motion, which play a major role in the controller design. The design consists of two stages. First an inner rate loop that leads to a finite dimensional plus delay equivalent plant for the outer loop is closed. The outer noncollocated position loop has the structure of an observer-predictor control scheme to compensate for the response delay. The resulting overall transfer function is finite dimensional, with arbitrarily assigned dynamics, plus delay