Many processes are Distributed Parameter Systems (DPS) in which states vary in both time and space (e.g., fixed-bed reactors, polymer extrusion, fibre spinlines, and sheet coating processes). Mathematical description of such systems, generally obtained by applying conservation laws, often takes the form of Partial Differential Equations (PDEs). The commonly used techniques of controlling DPS approximate the systems with a lumped parameter model and apply the available control techniques for Lumped Parameter Systems (EPS). It is generally recognized that such approximation approaches may lead to poor control performance. The research on the control methods that directly use the PDE models has been motivated with the expectation of improved performance, and a variety of feedback control laws have been proposed in the literature.

The objective of this thesis is to exploit the geometric properties of the PDEs used to model DPS and to develop geometric-based control methods to achieve high performance control with tractable computation. The thesis will focus mainly on hyperbolic models for DPS, and, as a result, extensive use will be made of the Method of Characteristics. The Method of Characteristics, a differential geometric approach of constructing integral surfaces for hyperbolic PDEs, is used in the formulation of characteristics-based control methods for DPS in this thesis. A feedback control method is developed such that the hyperbolic systems are driven towards the desired behavior along the characteristic direction. The resulting controller possesses a simple form and provides significantly improved performance. However, studies have shown that, for PDE models, feedback control performance is limited by the time-horizon that is considered within the control calculations. Model Predictive Control (MPC), which takes the long-term process behavior into consideration, is a natural candidate for overcoming the “shortsightedness” of the standard feedback control methods. An extensive effort is made to develop a characteristics-based MPC for various PDE systems. Simulation studies are conducted to illustrate the strength and weakness of the proposed predictive controller, and extensions to parabolic systems are investigated. The research from this thesis shows that the characteristic-based control is a promising novel approach for DPS because of its efficient computation and high performance.