Development of Robust Boundary Layer Controllers
Final rept. 15 Feb 2000-29 Nov 2002
CALIFORNIA UNIV LOS ANGELES DEPT OF MECHANICAL AND AEROSPACE ENGINEERING
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In this study, control system analysis and design techniques were developed to control turbulent and convective boundary layers. The design was dependant solely on the linearized governing equations of a channel flow and a layer of heated fluid. The three-dimensional Navier-Stokes equations of channel flow, linearized about a Poisueille profile, and Oberbeck-Boussinesq equations of a layer of fluid, linearized about the no motion state, were decomposed by a spectral decomposition involving a two-dimensional Fourier expansion and a Chebyshev Calcrkin projection. The resulting temporal state space model, composed of the coefficients of this decomposition, allowed for a multivariable feedback design combining an array of sensors to an array of actuators. In particular, this spectral decomposition decouples the dynamical equations into a parallel architecture, where each wave number pair sub-system could he handled individually Linear Quadratic Guassian LQC multivariable synthesis and model reduction techniques are applied to a few select wave number pair sub-systems, reducing the required computational bandwidth. Controller performance was tested on direct numerical simulations. Even with a limited number of controlled wave number pairs and a drastic reduction in state space size, the controllers have proven remarkably effective.
- Fluid Mechanics