Stability of servomechanisms with friction and stiction in the output element

Servomechanisms with friction in the output element are often observed to oscillate, even though the Bode diagram indicates stability. This paper investigates the conditions for this instability and the type of oscillation that can occur. It finds that an overdamped system with a lag equalizer is stable if
L<2 C/C-1
, where
L
is the lag ratio and
C
=static friction÷Coulomb friction; with a lag-lead equalizer it is stable if
\frac{L}{1+a/b}<\frac{2C}{C-1}
, where
a/b
is the ratio of the two zeros of the network. For under-damped systems, the same analysis may be carried out, resulting in only slightly more complicated expressions. Experimental results that correlate with the theory are also included.