A Method for the Determination of a Differential Equation Model for Simple Nonlinear Systems

A method is described for the establishment of a nonlinear differential equation which acts as a model for an actual physical system. It is assumed initially that the actual system contains only a single nonlinear element and that this element may be represented in the differential equation model by a single-valued nonlinear function of a single variable. The method is then extended to systems which contain several nonlinear elements. It is assumed that the system may be excited by a specified periodic input and that neither the input nor the output of the system is significantly corrupted by noise. An experimental criterion is given for the range of periodic inputs which permit satisfactory determination of the differential equation model.