Title page for ETD etd-05082001-090500

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
King, Belinda B. Committee Chair
Borggaard, Jeffrey T. Committee Member
Rogers, Robert C. Committee Member
  • Balanced Reduction
  • Klein-Gordon Equation
  • Balanced Truncation
  • Reduced Order Feedback Control
  • LQG Balancing
Date of Defense 2001-05-01
Availability unrestricted
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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