Describing Function Method

This section is primarily concerned with developing the background of the describing function for a single sinusoidal signal and showing how it can be used in the analysis and possibly the design of a nonlinear feedback system. After the definition of the describing function, its value is obtained for several specific nonlinear characteristics and then it is shown how the information can be used to explore the possibility of limit cycles in a nonlinear feedback loop. It is shown how the stability of any limit cycles may be ascertained and two examples of use of the DF in control systems problems are given. Uses of the DF for evaluating the closed loop frequency response and for designing compensators to eliminate limit cycles are discussed. The latter part of the presentation discusses describing functions for other signals, including those consisting of more than one component, and their possible uses in studying some aspects of feedback loop analysis and design.