A Comparison of Balanced Truncation Methods for Closed Loop Systems

John R. Singler, Missouri University of Science and Technology
Belinda A. Batten

This document has been relocated to http://scholarsmine.mst.edu/math_stat_facwork/656

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Real-time control of a physical system necessitates controllers that are low order. In this paper, we compare two balanced truncation methods as a means of designing low order compensators for partial differential equation (PDE) systems. The first method is the application of balanced truncation to the compensator dynamics, rather than the state dynamics, as was done in cite{Skelton:1984}. The second method, LQG balanced truncation, applies the balancing technique to the Riccati operators obtained from a specific LQG design. We discuss snapshot-based algorithms for constructing the reduced order compensators and present numerical results for a two dimensional convection diffusion PDE system.