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Nonlinear Model Reduction and Control of Complex Distributed Processes

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Abstract:
While most undergraduate process control courses still deal with dynamics and control of lumped chemical processes using linear transfer function models, key technological needs in growth areas such as semiconductor manufacturing, nanotechnology and biotechnology have motivated extensive research on analysis and control of complex nonlinear distributed processes. Examples include the Czochralski crystallization of high-purity crystals and the chemical vapor deposition of thin films for semiconductor manufacturing, as well as the crystallization of proteins and the aerosol-based production of nanoparticles. From a control point of view, the distinguishing feature of complex distributed processes is that they give rise to nonlinear control problems that involve the regulation of highly distributed control variables by using spatially-distributed control actuators and measurement sensors. Thus, complex distributed processes cannot be effectively controlled with control methods which assume that the state, manipulated and to-be-controlled variables exhibit lumped behavior or with linear control algorithms derived on the basis of linear/linearized distributed models. We have pioneered the development of a general and practical framework for the synthesis of practically implementable nonlinear feedback controllers for complex distributed processes based on fundamental models that accurately predict their behavior. The philosophy behind this ``model-based'' approach is that the synthesis of efficient control systems should exploit the ability of a fundamental model to predict the behavior of a process and the fundamental knowledge of the underlying physico-chemical phenomena that the model contains. The key difficulty in developing model-based control methods for distributed chemical processes lies in the ``infinite-dimensional'' nature of the distributed process models, which prohibits their direct use for control system synthesis. We have developed nonlinear order reduction techniques for deriving low-dimensional approximations that accurately reproduce the dynamics and solutions of distributed process models. We have used these approximate models for the synthesis of nonlinear feedback controllers via geometric methods and Lyapunov techniques. The controllers can be readily implemented in practice and enforce the desired control objectives in the infinite-dimensional closed-loop system. We will present applications of the theoretical results to: a) a rapid thermal chemical vapor deposition reactor, b) a Czochralski crystal growth process, c) a fluid dynamic system, d) a continuous crystallizer, and e) a titania aerosol reactor.

Type of Seminar:
Public Seminar
Speaker:
Prof. Panagiotis D. Christofides
Department of Chemical Engineering University of California, Los Angeles Los Angeles CA 90095 USA
Date/Time:
May 08, 2001   17:15
Location:

ETH Zentrum, ETZ E 6, Gloriastrasse 35, 8006 Zurich
Contact Person:

Prof. M. Morari
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Biographical Sketch:
Panagiotis D. Christofides was born in Athens, Greece, in 1970. He received the Diploma in Chemical Engineering degree, in 1992, from the University of Patras, Greece, the M.S. degrees in Electrical Engineering and Mathematics, in 1995 and 1996, respectively, and the Ph.D. degree in Chemical Engineering, in 1996, all from the University of Minnesota. Since July 1996 he has been an Assistant Professor in the Department of Chemical Engineering at the University of California, Los Angeles. His theoretical research interests include nonlinear, robust and optimal control, singular perturbations, and model reduction, optimization and control of nonlinear distributed parameter systems, with applications to chemical processes, advanced materials and semiconductor processing, particle technology, biotechnology and fluid flows. He has published over 80 articles and one research monograph. Professor Christofides has received the Teaching Award from the AIChE Student Chapter of UCLA in 1997, a Research Initiation Award from the Petroleum Research Fund in 1998, a CAREER award from the National Science Foundation in 1998, the Ted Peterson Student Paper Award from the Computing and Systems Technology Division of AIChE in 1999, the O. Hugo Schuck Best Paper Award from the American Automatic Control Council in 2000, and a Young Investigator Award from the Office of Naval Research in 2001.