Control of Spatially Inhomogeneous Shear Flows

Abstract

Model-based feedback control of the instabilities arising in a spatially inhomogeneous boundary layer flow is studied. To build a reduced-order model of the problem, where the application of standard tools from control theory become computationally feasible also for fluid flow systems, the main features of the flow behavior are investigated in an input-output framework. The observable, controllable and balanced modes of the system have been identified. The location and structure of these modes reflect the location of sensors/actuators and the perturbation dynamics; i.e. the observable modes are located upstream, where the sensitivity to initial conditions is the largest. The controllable modes, conversely, are located downstream, where the response to the forcing is the largest. The analysis presented here can be closely related to stability analysis, using global modes and optimal disturbances, except that inputs and outputs are taken into account. The quantity one wishes to optimize for is now defined by a sensor output, while perturbations are introduced by the inputs considered in the model. Furthermore, in view of the control application, the formulation of the control objective function as an output is particularly attractive in this input-output setting, since this behavior is well captured by the ROM. Model reduction is achieved by projecting the governing equations on the leading balanced modes of the system. We show that the input-output behavior of the flat-plate boundary layer can be captured accurately with an ROM based on these modes. Finally, the model is used to apply feedback control based on measurements from one upstream sensor and an actuator further downstream. The perturbations growth could be reduced efficiently using the H2 optimal feedback controller.

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Document Details

Document Type
Technical Report
Publication Date
Nov 27, 2009
Accession Number
ADA527290

Entities

People

  • Dan S. Henningson
  • Espen Akervik
  • Luca Brandt
  • Onofrio Semeraro
  • Shervin Bagheri

Organizations

  • Royal Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Ground and Sea Platforms
  • Sensors

DTIC Thesaurus Topics

  • Boundary Layer
  • Boundary Layer Flow
  • Closed Loop Systems
  • Computational Fluid Dynamics
  • Computational Science
  • Control Theory
  • Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Hydrodynamics
  • Hypervelocity Flow
  • Kalman Filters
  • Layers
  • Mathematical Filters
  • Measurement
  • Shear Flow

Readers

  • Computational Modeling and Simulation
  • Control Systems Engineering.
  • Robotics and Automation.