Stability analysis of dual-mode servomechanisms

Dual-mode servomechanisms have several advantages such as light weight and simplicity, but a serious study of the stability problems encountered in such devices has not appeared in the literature. An analytical method is presented here for determining the stability of dual-mode servomechanisms by an extension of the describing function method of analysis. The method is illustrated with examples, and laboratory data are presented. Analysis by describing functions shows that a dual-mode system may be unstable even though its linear and relay modes of operation are stable as systems by themselves, and the mode-switching circuitry is perfect. It is also shown that for certain mode boundary shapes the describing function is a function of frequency as well as amplitude.