Transfer functions of distributed parameter systems: A tutorial

In this tutorial article the rich variety of transfer functions for systems described by partial-differential equations is illustrated by means of several examples under various boundary conditions. An important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations, properness, relative degree and minimum phase. It is sometimes possible to design a controller using the irrational transfer function, and several such techniques are outlined. More often, the irrational transfer function is approximated by a rational one for the purpose of controller design. Various approximation techniques and their underlying theory are briefly discussed.