Reduced-order models for flow control: balanced models and Koopman modes [chapter]

Clarence W. Rowley, Igor Mezić, Shervin Bagheri, Philipp Schlatter, Dan S. Henningson
2009 IUTAM Bookseries  
This paper addresses recent developments in model-reduction techniques applicable to fluid flows. The main goal is to obtain low-order models tractable enough to be used for analysis and design of feedback laws for flow control, while retaining the essential physics. We first give a brief overview of several model reduction techniques, including Proper Orthogonal Decomposition [3], balanced truncation [8, 9] , and the related Eigensystem Realization Algorithm [5, 6] , and discuss strengths and
more » ... eaknesses of each approach. We then describe a new method for analyzing nonlinear flows based on spectral analysis of the Koopman operator, a linear operator defined for any nonlinear dynamical system. We show that, for an example of a jet in crossflow, the resulting Koopman modes decouple the dynamics at different timescales more effectively than POD modes, and capture the relevant frequencies more accurately than linear stability analysis.
doi:10.1007/978-90-481-3723-7_6 fatcat:4yrpl2quzrfihluwam4aydu6dq