Stabilization of Nonlinear Feedback Control Systems

Conventional methods for linear systems may be used for determining the operating characteristics of a nonlinear device near equilibrium, provided the differential equations expressing its operation can be expanded in a Taylor series about the equilibrium point. These methods are justified only for variations about equilibrium sufficiently smnall that all second and higher power terms of the expansions can be neglected, thereby reducing the expansions to linear equations. In linear feedback systems the response is independent of the equilibrium point. If a system is inherently nonlinear, it generally will not have this characteristic. It is shown that these systems can be modified so that the response of the output will also be independent of the equilibrium point, except for an amplitude scale factor, for a given incremental input variation from equilibnum.