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An Analysis of Servomechanisms Containing a Dependent Variable Nonlinearity


Anderson, Jack Steele (1953) An Analysis of Servomechanisms Containing a Dependent Variable Nonlinearity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/SQ9A-3G13.


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.))
Subject Keywords:(Electrical Engineering and Physics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • McCann, Gilbert Donald (advisor)
  • Pickering, William Hayward (advisor)
  • Wilts, Charles H. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1953
Additional Information:Title in 1953 Caltech Commencement program varies: Analysis of Non-Linear Servomechanisms
Record Number:CaltechETD:etd-04212003-105744
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1431
Deposited By: Imported from ETD-db
Deposited On:21 Apr 2003
Last Modified:17 May 2023 22:14

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