Robust Control Strategies for a Fixed Bed Chemical Reactor

Citation

Webb, Christopher John (1990) Robust Control Strategies for a Fixed Bed Chemical Reactor. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/h2d4-tq78. https://resolver.caltech.edu/CaltechETD:etd-11132007-110352

Abstract

This thesis addresses the practical application of robust control design to an experimental fixed bed reactor. Controllers are designed using robust control theory, specifically, Structured Singular Value analysis and Internal Model Control theory. These controllers are guaranteed to be stable and have good performance even when there is plant-model mismatch. To understand the sources of model mismatch and how model mismatch affects a fixed bed reactor's control design, an experimental methanation reactor was constructed.

The reactor is non-adiabatic with a constant wall temperature. A series of thermo couples located inside an axial thermowell are used to measure bed temperatures, and a gas chromatograph is used to measure gas concentrations. The pilot plant includes a feed-effluent heat exchanger and a product recycle line for positive feedback of both mass and energy.

A mathematical model of the reactor is developed from first principles. This dynamic model is a three dimensional heterogenous model. It consists of four non-linear coupled partial differential equations. Finite difference methods are used to approximate these equations with a series of ordinary differential equations. The temperature profiles simulated using the model compare favorably with the profiles obtained from the experimental reactor.

Two control configurations are studied: the control of the hot spot temperature using the flow rate of an inert gas, and the control of the outlet concentration and temperature by manipulating the recycle flow rate and power supplied to an inlet heater. For both of these experiments, the control objective is to maintain stability and acceptable performance for a variety of operating conditions. Bounds of the amount of model uncertainty are explicitly incorporated in the controller design.

A new methodology for computing frequency domain uncertainty bounds for single-input single-output systems is presented. This new methodology uses spectral analysis to identify a series of non-parametric frequency domain models and a "regions-mapping" technique to bound the frequency by frequency description of these models in the complex plane. The methodology is compared to existing non-parametric techniques and shown to be superior for identifying the uncertainty bound associated with a nonlinear system. This methodology is then applied to the hot spot temperature identification problem of the fixed bed reactor. A robust controller with a single adjustable parameter is designed for the reactor using Internal Model Control (IMC) theory. The computed uncertainty bounds are experimentally validated using the IMC controller.

A simple procedure is presented for designing a robust controller when one or more of the control variables must be inferred from other process measurements. As part of this procedure, a robust measurement selection scheme determines which process measurements should be used for inference. The measurement selection scheme is based on Structured Singular Value analysis. This procedure is successfully applied to the outlet concentration control for the experimental methanation reactor.

Thesis Files