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An analysis of servomechanisms containing a dependent variable nonlinearity

Citation

Anderson, Jack Steele (1953) An analysis of servomechanisms containing a dependent variable nonlinearity. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-04212003-105744

Abstract

A method is developed for obtaining the transient response of an automatic control system containing a nonlinearity in which one dependent variable may be expressed as a unique function of another variable. This method involves obtaining a mathematical expression for the nonlinear characteristic by an expansion in Legendre polynomials, introducing this expression into the equations describing the control system behavior thus obtaining a nonlinear equation in a power series of a dependent variable and solving this nonlinear equation by means of an assumed infinite series solution technique. The rules governing application of the method are discussed.

A saturation type nonlinearity is used to illustrate the application of the method. A second order system is employed to illustrate the accuracy of the method and to present a numerical technique for solving the series of equations arising from the infinite series method of solving the nonlinear system equation. The stability of a fourth order missile control equation with a saturation limit on the control surface is investigated by the method.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering and Applied Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Unknown, Unknown
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1953
Record Number:CaltechETD:etd-04212003-105744
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-04212003-105744
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1431
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:21 Apr 2003
Last Modified:26 Dec 2012 02:38

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