Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 102-106). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 133-143).

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The complexity of large industrial engineering systems such as chemical plants has continued to increase over the years. As a result, flexible control systems are required to handle variation in the operating conditions. In the classical approach, first the plant model should be linearized at the nominal operating point and then, a robust controller should be designed for the resulting linear system. However, the performance of a controller designed by this method deteriorates when operation deviates from the nominal point. When the distance between the operating region and the nominal operating point increases, this performance degradation may lead to instability. In the context of traditional linear control, one method to solve this problem is to consider the impact of nonlinearity as “uncertainty” around the nominal model and design a controller such that the desired performance is satisfied for all possible systems in the uncertainty set. As the size of uncertainty increases, conservatism occurs and at some point, it becomes impossible to design a controller that can provide satisfactory performance. One of the methods proposed to overcome the aforementioned shortcomings is the so-called Multiple Model approach. Using Multi-Models, local designs are performed for various operating regions and membership functions or a supervisory switching scheme is used to interpolate or switch among the controllers as the operating point moves among local regions. Since the Multiple Model method is a natural extension of the linear control method, it inherits some benefits of linear control such as simplicity of analysis and implementation. However, all these benefits are valid locally. For example, the multiple model method may be vulnerable when global stability is taken into account. The core objective of this thesis is to develop new tools to study stability of closed-loop nonlinear systems controlled by local controllers in order to improve design of multiple model control systems. For example, one of the aims of this work is to investigate how to determine the region where closed loop system is stable. A secondary objective is to study the effects of the exogenous signals on stability of such systems. / Controls

Nonlinearities exist in all process control systems. The use of linear control techniques is valid only in a narrow range of operation. Therefore, in this thesis, multivariable nonlinear control techniques are considered. The target process is the single effect evaporative process of the liquor burning unit in Alcoa's alumina refinery in Kwinana and the proposed triple effects unit in the Wagerup refinery. Two types of nonlinear control strategies using differential geometry were studied, namely, the input output linearization (Kravaris and Soroush, 1990) and the input state linearization (Hunt et al, 1983a). The research has successfully demonstrated the superiority and simplicity of the nonlinear controller through simulations and plant implementations. An integrated software package using MAPLE V.3 as the computing environment was developed to automate the solution algorithms and to graphically simulate the closed loop dynamics of different processes using the two nonlinear control strategies.The issue of robustness of the nonlinear controller was addressed by developing a procedure called uncertainty vector adjustment. The effectiveness of the new strategy was successfully demonstrated on the simulated liquor burning process. Furthermore, the stability of the adjustment technique was proved and its theoretical bounds were established using Lyapunov function analysis.A comparative study of geometric nonlinear filter and extended Kalman filter was conducted to reduce the requirement of full state feedback necessary for nonlinear control using either input output linearization or input state linearization. The simulation of the single effect evaporation unit of the liquor burning process showed that the geometric nonlinear filter is superior to the extended Kalman filter in terms of nonlinear tracking performances.The plant trials of the input output linearization ++ / in Alcoa's Kwinana alumina refinery demonstrated the practicability and feasibility of implementing nonlinear control in an industrial setting and also fostered a closer gap between academia and industry. The trials established guidelines for implementing a global linearizing controller on site, including conversion of the relevant constraints and the output of an industrial proportional and integral controller to the equivalent proportional and integral action required by the nonlinear controller. The results showed that the performance of the nonlinear controller was better than the current linear controller on site in terms of responsiveness and resistance to disturbances. Hence, the nonlinear control strategy enables the process to settle faster.All in all, efforts have been made in this thesis to minimise the use of abstract mathematical language and, in some cases, simplify the language so that nonlinear control theory can be understood by a wider range of audience, especially industrial practitioners. It is hoped that the insights provided in the dissertation will encourage more industrial implementations of nonlinear controllers and forge more interaction to close the widening gap between academic and industrial practice in process control.Keywords: nonlinear control, differential geometry, symbolic algebra, evaporator process, uncertainty vector adjustment, geometric nonlinear filter.