Describing function method of servomechanism analysis applied to most commonly encountered nonlinearities

Most of the literature dealing with the analysis and synthesis of servomechanisms confines itself to treating only linear systems in which all relationships can be expressed mathematically in the form of ordinary differential equations. However, in actual practice many systems are encountered containing elements which exhibit marked nonlinearities. The principal reason for ignoring such nonlinearities in much of the analysis and design of feedback-control systems is mathematical expediency. There is no simple mathematical method available to cope with nonlinear systems. There are certain types of nonlinear differential equations which are solvable, and techniques such as step-by-step solutions exist for more general nonlinear differential equations. Even to use these, however, involves so much tedious labor that the effort is rarely justifiable.1