Hunting Due to Lost Motion

Abstract

Abstract Hunting of a servosystem, due to lost motion, say, in one of its mechanical links, but in absence of input signals, is considered. If the slack is assumed to be taken up suddenly, the motion is governed by a linear differential equation but with proper discontinuities when the direction of motion in the loose link is reversed. For the case of second-order systems it is shown that, if the characteristic roots are complex, a periodic hunting motion always exists, and that the system, no matter how it is started, will converge to this hunting motion. If the characteristic roots of the second-order system are real, then a periodic hunting motion exists, but depending upon how the system is started, it may converge to this motion or it may converge to a stable position at either end of the lost-motion band. Third and higher-order systems are studied in a similar way and the equations for determination of periodic hunting motion obtained. Second-order systems, in which the system “coasts” as the slack is taken up, are discussed briefly.