Type of Document Dissertation Author Evans, Katie Allison Author's Email Address email@example.com 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 AbstractDistributed 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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