Basis Construction for the Design of Boundary Feedback Controls From Reduced Order Models (Preprint)

Abstract

We develop a reduced basis construction method that allows for separate consideration of baseline and actuated dynamics in the reduced modeling process. A prototype initial boundary value problem, governed by the two-dimensional Burgers equation, is formulated to demonstrate the utility of the method in a boundary control setting. A weak formulation approach, in combination with proper orthogonal decomposition and Galerkin projection, is used to develop a reduced model of the distributed parameter system. Comparisons are done between reduced and full order solutions under open-loop boundary actuation to illustrate advantages gained by separate consideration of actuated dynamics in the reduced modeling process. A tracking control problem is specified for the full order system using a linear quadratic regulator formulation. Comparisons of feedback control effectiveness are done to demonstrate benefits in control effectiveness obtained from separate consideration of actuated dynamics during model reduction.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2006
Accession Number
ADA464776

Entities

People

  • R. C. Camphouse

Organizations

  • Air Force Research Laboratory

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Air Force Facilities
  • Air Force Research Laboratories
  • Aircrafts
  • Boundaries
  • Boundary Value Problems
  • Construction
  • Differential Equations
  • Dynamics
  • Equations
  • Feedback
  • Flow
  • Fluid Flow
  • Governments
  • Military Research
  • Models
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Robotics and Automation.