### 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.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Editors | James D. Paduano |

Publisher | Society of Photo-Optical Instrumentation Engineers |

Pages | 70-86 |

Number of pages | 17 |

Volume | 2494 |

ISBN (Print) | 081941848X |

State | Published - 1995 |

Externally published | Yes |

Event | Sensing, Actuation, and Control in Aeropropulsion - Orlando, FL, USA Duration: Apr 17 1995 → Apr 18 1995 |

### Other

Other | Sensing, Actuation, and Control in Aeropropulsion |
---|---|

City | Orlando, FL, USA |

Period | 4/17/95 → 4/18/95 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 2494, pp. 70-86). Society of Photo-Optical Instrumentation Engineers.

**Design for control of flow instabilities : first principles and an application.** / Berkooz, Gal; Corke, Thomas; Glauser, Mark N; Psiaki, Mark; Fischer, Mani.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of SPIE - The International Society for Optical Engineering.*vol. 2494, Society of Photo-Optical Instrumentation Engineers, pp. 70-86, Sensing, Actuation, and Control in Aeropropulsion, Orlando, FL, USA, 4/17/95.

}

TY - GEN

T1 - Design for control of flow instabilities

T2 - first principles and an application

AU - Berkooz, Gal

AU - Corke, Thomas

AU - Glauser, Mark N

AU - Psiaki, Mark

AU - Fischer, Mani

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0029213306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029213306&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0029213306

SN - 081941848X

VL - 2494

SP - 70

EP - 86

BT - Proceedings of SPIE - The International Society for Optical Engineering

A2 - Paduano, James D.

PB - Society of Photo-Optical Instrumentation Engineers

ER -