Spring 2014 MnDRIVE Seminar Series
The ability to effectively control a fluid would enable many exciting technological advances, such as the design of quieter, more efficient aircraft. Model-based feedback control is a particularly attractive approach, but the equations governing the fluid, although known, are typically too complex to be useful for control. This talk addresses model reduction techniques, which are used to simplify existing models, to obtain low-order models tractable enough to be used for analysis and control, while retaining the essential physics. In particular, we will discuss two techniques: balanced truncation and Koopman operator methods. Balanced truncation is a well-known technique for model reduction of linear systems, that can significantly outperform more conventional methods such as Proper Orthogonal Decomposition (POD). The Koopman operator is an infinite-dimensional linear operator that describes the full dynamics of a nonlinear system, without resorting to linearization. We show how a recently developed algorithm called Dynamic Mode Decomposition can approximate the Koopman operator, and the spectral analysis of this operator can elucidate coherent structures in examples including a jet in crossflow and the wake of a flat plate.
Clarence Rowley is a Professor in the Mechanical and Aerospace Engineering department at Princeton University. He received his undergraduate degree from Princeton in 1995, and his doctoral degree from Caltech in 2001, both in Mechanical Engineering. He returned to Princeton in 2001 as an Assistant Professor and was appointed Associate Professor in 2007, and Full Professor in 2012. His research interests lie at the intersection of dynamical systems, control theory, and fluid mechanics, and focus on reduced-order models suitable for analysis and control design.