Type of Document Master's Thesis Author Camp, Katie A.E. Author's Email Address kcamp@vt.edu URN etd-05082001-090500 Title The Search for a Reduced Order Controller: Comparison of Balanced Reduction Techniques Degree Master of Science Department Mathematics Advisory Committee
Advisor Name Title Belinda B. King Committee Chair Jeffrey T. Borggaard Committee Member Robert C. Rogers Committee Member Keywords
- Klein-Gordon Equation
- LQG Balancing
- Reduced Order Feedback Control
- Balanced Truncation
- Balanced Reduction
Date of Defense 2001-05-01 Availability unrestricted Abstract When designing a control for a physical system described by a PDE,it is often necessary to reduce the size of the
controller for the PDE system. This is
done so that real time control can be achieved. One approach often
taken by engineers is to reduce the approximating finite-dimensional
system using a balanced reduction method known as balanced truncation and then
design a control for the lower order system. The unsettling idea
about this method is that it involves discarding information and
then designing a control. What if valuable physical information
were lost that would have allowed a more effective control to be
designed? This paper will explore an alternate balanced reduction
method called LQG balancing. This approach allows for the
designing of a control on the full order approximating system and then
reducing the control. Along the way, the basic ideas of feedback
control design will be discussed, including system balancing and
model reduction. Following, there will be mention of the linear
Klein-Gordon equation and the development of the one-dimensional
finite element approximation of the PDE. Finally, simulations and
numerical experiments are used to discuss the differences between
the two balanced reduction methods.
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