Analysis and Synthesis of Feedback Control Systems in the Parameter Plane III-Nonlinear Systems

The stability and self-excited oscillations of nonlinear feedback control systems are investigated in the parameter plane with respect to both the system parameters and the initial conditions. The proposed analysis procedure is based upon the describing functions defined for both pure and damped sinusoidal signals and, therefore, permits the designer to obtain information about the effects on absolute and relative stability of adjusting system parameters or varying the initial signal level. Control systems with two non-linearities and with amplitude- and frequency-dependent describing functions may be designed advantageously. The method is particularly useful when the describing function appears as a variable pole of relevant transfer functions. The procedure requires no block-diagram manipulations, and it is suitable for the application of computer techniques.