SINGULAR LINES IN THE PARAMETER PLANE.

Abstract

The theory of Singular Lines, constant damping ratio-constant undamped natural frequency lines, is derived. A limitation of the parameter plane method for characteristics polynomials whose coefficients are linear functions of two variable parameters which results in undetermined roots is described. The addition of singular lines to the parameter plane diagram specifies these roots allowing solution for all roots of a given polynomial. A general method of solving for singular lines is developed and rules for predicting the existence of such lines are stated. A computer program which solves for and graphically displays singular lines in addition to constant zeta omega, and sigma loci is presented. Singular lines are considered in terms of dominance and macroscopic root sensitivity. A dominant root line in the parameter plane is illustrated. Examples which demonstrate the application of singular line theory to linear, multivariable control systems are presented. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0821769

Entities

People

  • Douglas John Bowie

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Coefficients
  • Computer Programs
  • Computers
  • Control Systems
  • Frequency
  • Polynomials
  • Resonant Frequency

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Dynamics.
  • Linear Algebra