Describing functions representing the effect of inertia, backlash, and coulomb friction on the stability of an automatic control system - I

A first study is presented of the effect of backlash and coulomb friction upon the stability of an automatic feedback control system. The system consists of a mechanical linkage in which the load member is subjected to a restraining force. Describing functions that represent the load response for finite values of inertia, backlash, and coulomb friction between the load and an external surface are derived analytically. An example illustrates the conditions under which nonlinearities cause sustained oscillations in a given system, and how the Nyquist criterion can be used to obtain frequency and amplitude of the oscillations.