A Laboratory Exercise to Illustrate the Describing Function Technique

Many control texts do not provide an adequate insight into the assumptions inherent in the describing function technique for analyzing the stability of nonlinear systems. A laboratory experiment is described which provides this background by investigating the harmonic content of the signals in an analog simulation of a third-order system which incorporates an ideal relay. The paper then proceeds to show how the simulation may be extended to investigate the stability of the system when the relay includes a dead zone or hysteresis. It is shown that under these favorable con ditions, the describing function gives good agreement with the results of the simulation.