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. doi:10.7907/SQ9A-3G13. https://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.

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