Design for control of flow instabilities: first principles and an application

Gal Berkooz, Thomas Corke, Mark N. Glauser, Mark Psiaki, Mani Fischer

Research output: Chapter in Book/Entry/PoemConference contribution

1 Scopus citations


We demonstrate a control strategy for increasing the mean passage time between 'bursts' of a perturbed heteroclinic attractor. Perturbed heteroclinic attractors were proposed by as a model for the dynamics of coherent structures in the turbulent wall layer. It is observed that most of the turbulent drag is produced by 'bursts' in the dynamics of coherent structures, hence increasing the mean time between bursts corresponds directly to drag reduction. The control is actuated by perturbations of the wall topography. We show how one may derive the form of the control input in dynamical systems phase space from the time-dependent boundary perturbation. This is done through a conformal change of coordinates. Assuming that the magnitude of the control input is small, we formulate a robust strategy for the increase of the passage time close to the hyperbolic fixed points of the attractor. We demonstrate the strategy on a 1D PDE, the Kuramoto-Sivashinsky equation. Initial simulations show an increase of 7% in the mean passage time. Our results are global nonlinear control results for a system exhibiting nontrivial dynamics. We further present initial results on estimation and control using partial system observations. In the application at hand, we will have a limited amount of information derived from wall-mounted sensors, thus requiring estimation models. We show results of control using and extended Kalman filter. The control algorithm used yields excellent results including a complete suppression of bursting when large control forces are introduced.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsJames D. Paduano
PublisherSociety of Photo-Optical Instrumentation Engineers
Number of pages17
ISBN (Print)081941848X
StatePublished - 1995
Externally publishedYes
EventSensing, Actuation, and Control in Aeropropulsion - Orlando, FL, USA
Duration: Apr 17 1995Apr 18 1995

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherSensing, Actuation, and Control in Aeropropulsion
CityOrlando, FL, USA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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