There are many industrial processes in which the states, outputs and control variables vary both spatially as well as temporally. These processes are distributed parameter systems (DPS). Currently, most industrial processes are represented by lumped parameter models, which are characterized by ordinary differential equations (ODE's). However, a large number of these processes are actually distributed in nature. Examples such as heat transfer and sheet forming processes, heat exchangers, reactors and bioreactors, are just a few of the many processes where the dependent variables vary in space as well as time.

The natural form of the models that describe distributed parameter systems are partial differential equations (PDE's), integral equations or transcendental transfer functions. For the purpose of this work, we will concentrate on partial differential equation representations of DPS because they stem from fundamental momentum, energy and material balances for a process. More specifically, we will concentrate on one specific type of PDE: parabolic equations.

Conventional approaches for control of DPS are based on spatial discretization of the PDE model, yielding a finite number of ordinary differential equations in time. All the theory available for the control of lumped parameter systems can then be applied to the discretized system of ODE's. Unfortunately, common discretization techniques such as finite difference, finite element and finite volume methods often yield large systems of ODE's, making the problems computationally unattractive. Efforts have been made to reduce the number of ODE's necessary to represent the true distributed parameter system. The approach used in this research is modal analysis. This method is based on the idea that the dynamic behaviour of a system is predominantly determined by the modes associated with the smallest eigenvalues. Modal decomposition uses the technique of eigenfunction expansion to reduce the DPS model to a set of ODE's which are fully decoupled in terms of eigenvalues.

The goal of this research is to combine model predictive control with modal analysis on a parabolic system, and to study the effect of the selection of the number of modes.