Title page for ETD etd-12012003-114553


Type of Document Dissertation
Author Evans, Katie Allison
Author's Email Address evanska@engr.orst.edu
URN etd-12012003-114553
Title Reduced Order Controllers for Distributed Parameter Systems
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
King, Belinda B. Committee Chair
Borggaard, Jeffrey T. Committee Member
Burns, John A. Committee Member
Herdman, Terry L. Committee Member
Rogers, Robert C. Committee Member
Zietsman, Lizette Committee Member
Keywords
  • Balanced Truncation
  • Central Control Design
  • Euler-Bernoulli beam
  • Klein-Gordon Equation
  • Cable Mass System
  • LQG Balancing
Date of Defense 2003-11-21
Availability unrestricted
Abstract
Distributed parameter systems (DPS) are systems defined on infinite dimensional

spaces. This includes problems governed by partial differential equations (PDEs)

and delay differential equations. In

order to numerically implement a controller for a physical system we often first

approximate the PDE and the PDE controller using some finite dimensional scheme.

However, control design at this level will typically give rise to controllers that

are inherently large-scale. This presents a challenge since we are interested in

the design of robust, real-time controllers for physical systems. Therefore, a

reduction in the size of the model and/or controller must take place at some point.

Traditional methods to obtain lower order controllers involve reducing the model from

that for the PDE, and then applying a standard control design technique. One such model

reduction technique is balanced truncation. However, it has been argued that this type

of method may have an inherent weakness since there is a loss of physical information

from the high order, PDE approximating model prior to control design. In an attempt to

capture characteristics of the PDE controller before the reduction step, alternative

techniques have been introduced that can be thought of as controller reduction methods

as opposed to model reduction methods. One such technique is LQG balanced truncation.

Only recently has theory for LQG balanced truncation been developed in the infinite

dimensional setting. In this work, we numerically investigate the viability of LQG

balanced truncation as a suitable means for designing low order, robust controllers

for distributed parameter systems. We accomplish this by applying both balanced reduction

techniques, coupled with LQG, MinMax and central control designs for the low order

controllers, to the cable mass, Klein-Gordon, and Euler-Bernoulli beam PDE systems.

All numerical results include a comparison of controller performance and robustness

properties of the closed loop systems.

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