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Finite Dimensional Modeling and Control of Distributed Parameter Systems
Authors:
Daguang
Zheng and Karlene A. Hoo
Department of Chemical Engineering, Texas Tech University, Lubbock, TX
ABSTRACT
Accurate solutions of the DPS may be represented as the sum of an infinite series. Control design however, requires low-order models
primarily due to implementation limitations. As such, developing low-order models of high fidelity is important if the objective is
accurate control of the DPS. When an exact model (system of partial differential equations) of the system is known, this work presents a
method to develop a low-order model that assures convergent and
consistent projection to a finite space. The resulting low-order model can then be used to design finite dimensional controllers. When there
is no available first-principle model of the system, this work introduces a novel system identification method, that combines the
characteristics of singular value decomposition (SVD) and the
Karhunen-Loeve (KL) expansion for DPS to arrive at a low-order model that captures the dominant characteristics of the
system. Here as well, the final model form allows for the synthesis of finite order controllers. Two nonlinear reactor systems that can be
described by systems of partial differential equations (PDEs) are provided to demonstrate the model identification methods. Feedback
controllers are then synthesized based on these models to demonstrate their performance for disturbance rejection.Publication Information:
Download
the introduction - PDF format
Compt.
& Chem. Engng., 26, No, 7-8, p 1049-1076, 2002
Corresponding Author: Karlene A. Hoo
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