Control Design for Quasi-Linear Hyperbolic Systems With an Application to the Heavy Rope

Abstract

This contribution deals with the feed-forward control design for distributed parameter systems governed by quasi-linear hyperbolic equations. This is achieved in two steps: Firstly, the basic ideas underlying existing flatness-based approaches to nonlinear distributed parameter systems are restated in a general form. As a result the control problem is led back to a Cauchy problem w.r.t. space. Second, the solution of this Cauchy problem is discussed for the quasi-linear hyperbolic case using the method of characteristics. This includes the detailed presentation of a numerical integration scheme. The proposed concept is illustrated by means of a quasi-linear model of the heavy rope and, thus, generalizes results for related finite-dimensional and linear infinite-dimensional models of this system.