An analysis of servomechanisms containing a dependent variable nonlinearity

[摘要] 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.

[发布机构] University:California Institute of Technology;Department:Engineering and Applied Science

[关键词] Electrical Engineering and Physics