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

Gal Berkooz; Thomas C. Corke; Mark N. Glauser; Mark Psiaki; Mani Fischer

doi:10.1117/12.210520

30 May 1995 Design for control of flow instabilities: first principles and an application

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

Proceedings Volume 2494, Sensing, Actuation, and Control in Aeropropulsion; (1995) https://doi.org/10.1117/12.210520
Event: SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, 1995, Orlando, FL, United States

Abstract

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.

Citation Download Citation

Gal Berkooz, Thomas C. Corke, Mark N. Glauser, Mark Psiaki, and Mani Fischer "Design for control of flow instabilities: first principles and an application", Proc. SPIE 2494, Sensing, Actuation, and Control in Aeropropulsion, (30 May 1995); https://doi.org/10.1117/12.210520

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KEYWORDS

Control systems

Dynamical systems

Systems modeling

Nonlinear control

Sensors

Actuators

Filtering (signal processing)

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