NDLI: Control and sensitivity reduction for a viscous Burgers' equation

Content Provider	IEEE Xplore Digital Library
Author	Allen, E. Burns, J.A. Gilliam, D.S.
Copyright Year	2012
Description	Author affiliation: Virginia Tech University, Blacksburg, USA (Burns, J.A.) \|\| Mathematics and Statistics, Texas Tech University, Lubbock, USA (Allen, E.; Gilliam, D.S.)
Abstract	The problem of designing and numerically implementing a controller for a fluid flow system at the boundary of the flow domain is complicated by the facts that the basic model is truly nonlinear and the flow is usually highly sensitive to boundary conditions. High sensitivity to small changes in the boundary such as wall roughness or dynamic excitations can trigger transition to undesirable states. One approach to preventing or delaying a transition is to introduce a simple control loop along the boundary to reduce the sensitivity. In this work we demonstrate the aforementioned idea for a system governed by the one dimensional Burgers' equation. In particular, we focus on the initial boundary value problem for a viscous Burgers' equation which is known to be is extremely sensitive with respect to a small perturbation in a Neumann boundary condition. We use this model to illustrate how this sensitivity can generate erroneous numerical solutions and “transitions” to these states. In particular, for a fixed viscosity and certain initial data the numerical solution z(x; t) of Burgers' equation with a Neumann boundary condition zx(0; t) = 0 converges to a (large) solution that satisfies zx(0; t) = −α for a number α > 0 less than machine precision zero. Thus, the solution of the Burgers' equations for this problem exhibits an extreme sensitivity to the boundary perturbation α and this sensitivity can produce unexpected and undesired dynamic behavior. We use a continuous sensitivity equation method to compute these sensitivities and show that the sensitivity can be eliminated by introducing a very simple proportional error boundary feedback mechanism.
Starting Page	967
Ending Page	972
File Size	1060730
Page Count	6
File Format	PDF
ISBN	9781467320658
ISSN	07431546
e-ISBN	9781467320665
e-ISBN	9781467320641
DOI	10.1109/CDC.2012.6427074
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-12-10
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Sensitivity Boundary conditions Equations Mathematical model Closed loop systems Numerical models
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Modeling and Simulation

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Semiglobal stabilization of a boundary controlled viscous Burgers' equation

Model predictive control of Burgers equation based on Galerkin models

Boundary stabilization of the inviscid Burgers equation using a Lyapunov method

Turbulent behavior for a boundary controlled Burgers' equation

Marcum Q-functions and explicit feedback laws for stabilization of constant coefficient 2 × 2 linear hyperbolic systems

Moment matching based controller reduction for linear systems

New approaches for ℋ∞ performance preserving controller reduction

Global boundary stabilization and regularization of Burgers' equation

Turbulent drag reduction by streamwise traveling waves

Control and sensitivity reduction for a viscous Burgers' equation

Similar Documents

Semiglobal stabilization of a boundary controlled viscous Burgers' equation

Model predictive control of Burgers equation based on Galerkin models

Boundary stabilization of the inviscid Burgers equation using a Lyapunov method

Turbulent behavior for a boundary controlled Burgers' equation

Marcum Q-functions and explicit feedback laws for stabilization of constant coefficient 2 × 2 linear hyperbolic systems

Moment matching based controller reduction for linear systems

New approaches for ℋ∞ performance preserving controller reduction

Global boundary stabilization and regularization of Burgers' equation

Turbulent drag reduction by streamwise traveling waves

Control and sensitivity reduction for a viscous Burgers' equation