Accession Number : AD0821769

Title :   SINGULAR LINES IN THE PARAMETER PLANE.

Descriptive Note : Master's thesis,

Corporate Author : NAVAL POSTGRADUATE SCHOOL MONTEREY CA

Personal Author(s) : Bowie, Douglas John

Report Date : JUN 1967

Pagination or Media Count : 108

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)

Descriptors :   (*CONTROL SYSTEMS, MATHEMATICAL MODELS), SERIES(MATHEMATICS), DAMPING, FEEDBACK, FREQUENCY, MULTIVARIATE ANALYSIS, FUNCTIONS(MATHEMATICS), TABLES(DATA), INTEGRAL EQUATIONS, MATRICES(MATHEMATICS), COMPUTER PROGRAMMING, EQUATIONS, POLYNOMIALS, NONLINEAR SYSTEMS, THESES.

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE