The role of the method of characteristics in the solution of estimation and control problems for hyperbolic PDE systems

In this chapter we summarize the use of the Method of Characteristics (MC) in the solution of estimation and control problems for processes whose model is given by First-Order Partial Differential Equations or Hyperbolic systems. First, a dynamical robust observer is built with the MC for a non-isothermal plug flow reactor whose state variables travel along one characteristic line. Then, this observer in its integral equation version is designed for a solid-waste anaerobic digestion process which is described by a set of variables that follow different characteristic lines. In both cases the aim of the observers is to estimate the evolution of certain specific variables which is necessary to monitor but whose measurement becomes difficult either because do not exists the suitable analytical techniques or because such measurement is relatively expensive. Finally, the chapter is closed with an analysis of a robust control law derived with the MC for a heat exchanger in which a time-variant characteristic line is involved. The performance of the observers and the control law is analyzed with simulation experiments obtaining satisfactory results. ©2011 Nova Science Publishers, Inc. All rights reserved