Self-excited Oscillation of Relay Servomechanism with Coulomb Friction and its Graphic Solution

Abstract

In this paper, the authors treat the relay servomechanism containing Coulomb friction as one of the control systems with multiple nonlinearities, and are particularly concerned with the self-excited oscillation of this relay servomechanism, discussing the effect of the Coulomb friction on its performance. In the case where the relay has hysteresis but no dead zone in its characteristics, the self-excited oscillation occurs in the servomechanism and the waveform and the frequency of the oscillation are greatly affected by the Coulomb friction. The output waveform and the freqency in this state are analyzed exactly, using the fact that the Coulomb friction characteristic in a periodic state can be treated as the ideal relay characteristic, and the effects of the Coulomb friction on them are considered. Moreover, the authors develop the graphic method of solving the self-excited oscillation of the relay servomechanism. Using this approximation method, the frequency of the self-excited oscillation can be obtained graphically through the vector locus of the transfer function of the linear part of this servomechanism plotted on a complex plane. The result obtained by this approximation method shows a good agreement with the theoretical one.