| The critical-direction theory is extended to include nonlinear elements through the introduction of the describing function and a general definition of the critical perturbation radius. The approach allows the calculation of the nonlinear Nyquist robust stability margin for systems with both structured and unstructured uncertainties, hence providing a conclusive test for robust stability. Finally, analytic expressions for finding the minimizing amplitude are obtained for circular uncertain value sets.; The robustness of predictive controllers is studied for systems with real parametric uncertainties that belong to an ellipsoidal or hyperbox domain. A parametric stability margin is proposed as a quantitative measure of robust stability as well as a robust controller design methodology that involves evaluating the parametric stability margin over a range of values for the predictive control tuning parameters. In addition, the standard predictive control algorithm is also modified to include a disturbance model to help improve regulatory performance. The resulting disturbance predictive control demonstrated improved performance on linear systems. The performance on nonlinear cases is not satisfactory suggesting that further refinements, such as adaptive control schemes, may be necessary to handle such cases.; Two support tools for operating emulsion polymerization reactors are designed and implemented, namely a continuous sampling and dilution system and an online conversion estimator based on a densitometer. The dilution system is fully automated for data acquisition and real-time control. A dynamic first-principles model is developed and found to agree with experimental data. A new approach to estimate conversion on-line is developed through the use of a densitometer and the calculations are improved by the use of an excess-volume model. Both a one and two-parameter excess-volume models are analyzed, and examples are presented to illustrate the effectiveness of these models. |
