Mismatch and uncertainty in adaptive and optimizing control systems

Experiments indicate the applicability and potential of adaptive systems for chemical process control. Stability results based on ideal conditions show that these systems asymptotically converge to the desired behavior. However, unpredictable behavior can result due to the nonlinear relationships between model uncertainty, operating conditions and the tuneable parameters of adaptive control system.; The purpose of this thesis is to study the effects of model uncertainty on adaptive control systems. Global input-output and local asymptotic stability analyses are used to quantify the range of operating conditions and tuneable parameters which allow good performance for a given degree of model uncertainty. The results are used to develop better adaptive control and optimization algorithms.; A nonlinear adaptive control scheme is developed which combines nonlinear model-based compensation with adaptive estimation techniques, and its stability is analyzed for a specific class of nonlinear systems. Conic sector bounds on the mismatch between the compensator and process nonlinearities are developed which guarantee global input-output stability of the feedback system. A design method is proposed which uses approximate steady-state process models. Distillation column and CSTR simulation studies reveal improved performance which results from the nonlinear compensation scheme.; The concept of coupling nonlinear compensation with adaptive estimation is used to develop a novel approach to optimization based on the construction of a locally valid static relationship from approximate models and local geometric characteristics. Simulations and experiments illustrate the performance of the adaptive extremum controller on a continuous fermentor.; The results from global input-output stability analyses are limited because boundedness properties can be preserved despite poor performance; however, local asymptotic analysis based on linearization and bifurcation theory provides a means of studying the effects of model uncertainty on the performance of adaptive controllers. Two simple examples are analyzed and it is shown that adaptive controllers can perform poorly in the presence of model uncertainty for certain operating conditions and tuneable parameters. Local stability boundaries are computed from the analysis; various routes to global instability and chaos are identified; and design guidelines and algorithmic modifications for a simple class of model-reference adaptive controllers are developed.