Optimal Control of Large Space Structures

Abstract

The author presents a computational spectral factorization method to solve the optimal state feedback control problem for flexible structures that is mathematically rigorous, has a wide range of applicability, is flexible in design, is fast and efficient, and can be used on a minicomputer. This method is applied to the following systems: (1) a membrane, (2) a string, (3) Euler-Bernoulli/Timoshenko beam models, and (4) a beam with structural damping and boundary control. Chapter 1 introduces the topic and includes information on Control of Flexible Spacecraft, Electrostatic Control of Electromagnetic Reflectors, Spectral Factorization versus Riccati Equation Approach, Numerical Simulation of Hyperbolic Partial Differential Equations (PDEs), and a Description of the Algorithm. Chapter 2, The Linear Regulator Problem of a Vibrating Membrane - Mathematical and Computational Framework, contains the following sections: Study of the Hyperbolic System, Study of the Elliptic System, Spectral Factorization, and Gain Computations. Chapter 3, The String Problem, examines Eigenfunction Expansion of the String Equation, Green's Function in the Frequency Domain, the Controllability Question, Localized Control Problems, Approximation of the Identity and Convergence to a Point Control, Multidimensional Point Control-Point Observation, Distributed Control, Control Along a Mode of the System, Multidimensional Control Along Modes of the System, Approximation to the Transfer Function, and Point Control and Numerical Laplace Transforms. Chapter 4, Beam Equations, focuses on the Euler-Bernoulli Beam, Optimal State Feedback Control, Dissipation of Energy, and the Timoshenko Beam Model. Chapter 5, Boundary Control of Beam, looks at Reduction of the Boundary Control Problem of the Beam Problem to a Bounded Input Operator Control, Method of Lines, Reduction of the PDE to a 1st Order System, and Expansion of the Boundary Optimal Control of a Beam with Structure Damping.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA438514

Entities

People

  • Mohamed E. Baraka

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Space

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Artificial Satellites
  • Boundaries
  • Communication Networks
  • Department Of Defense
  • Differential Equations
  • Equations
  • Flexible Structures
  • Frequency Domain
  • Information Operations
  • Large Space Structures
  • Partial Differential Equations
  • Riccati Equation
  • Scientific Research
  • Space Systems
  • Timoshenko Beam

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Robotics and Automation.
  • Structural Dynamics.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers