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Control of Turbulent and Magnetohydrodynamic Channel Flows

Boundary Stabilization and State Estimation

  • Rafael Vazquez
  • Miroslav Krstic

Part of the Systems&Control: Foundations&Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages I-X
  2. Rafael Vazquez, Miroslav Krstic
    Pages 1-37
  3. Rafael Vazquez, Miroslav Krstic
    Pages 39-54
  4. Rafael Vazquez, Miroslav Krstic
    Pages 71-102
  5. Rafael Vazquez, Miroslav Krstic
    Pages 103-114
  6. Rafael Vazquez, Miroslav Krstic
    Pages 115-133
  7. Rafael Vazquez, Miroslav Krstic
    Pages 135-151
  8. Rafael Vazquez, Miroslav Krstic
    Pages 153-196
  9. Rafael Vazquez, Miroslav Krstic
    Pages 197-198
  10. Back Matter
    Pages 199-207

About this book

Introduction

This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions.

Efforts in flow control over the last few years have led to a wide range of developments in many different directions, but most implementable developments thus far have been obtained using discretized versions of the plant models and finite-dimensional control techniques. In contrast, the design methods examined in this book are based on the “continuum” version of the backstepping approach, applied to the PDE model of the flow. The postponement of spatial discretization until the implementation stage offers a range of numerical and analytical advantages.

Specific topics and features:

* Introduction of control and state estimation designs for flows that include thermal convection and electric conductivity, namely, flows where instability may be driven by thermal gradients and external magnetic fields.

* Application of a special "backstepping" approach where the boundary control design is combined with a particular Volterra transformation of the flow variables, which yields not only the stabilization of the flow, but also the explicit solvability of the closed-loop system.

* Presentation of a result unprecedented in fluid dynamics and in the analysis of Navier–Stokes equations: closed-form expressions for the solutions of linearized Navier–Stokes equations under feedback.

* Extension of the backstepping approach to eliminate one of the well-recognized root causes of transition to turbulence: the decoupling of the Orr–Sommerfeld and Squire systems.

Control of Turbulent and Magnetohydrodynamic Channel Flows is an excellent reference for a broad, interdisciplinary engineering and mathematics audience: control theorists, fluid mechanicists, mechanical engineers, aerospace engineers, chemical engineers, electrical engineers, applied mathematicians, as well as research and graduate students in the above areas. The book may also be used as a supplementary text for graduate courses on control of distributed-parameter systems and on flow control.

 

Keywords

Navier–Stokes equation closed-loop systems convection design electric conductivity flow between co flow control flow stabilization flow state estimation fluid dynamics partial differential equation partial differential equations thermal convection turbulence turbulent flows

Authors and affiliations

  • Rafael Vazquez
    • 1
  • Miroslav Krstic
    • 2
  1. 1.Escuela Superior de Ingenieros Departamento de Ingeniería AeroespacialUniversidad de Sevilla41092 SevillaSpain
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan DiegoU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-4699-8
  • Copyright Information Birkhäuser Boston 2008
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4698-1
  • Online ISBN 978-0-8176-4699-8
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site