MICRO-CHAOS IN DIGITAL-CONTROL

In this paper we analyze a model for the effect of digital control on one-dimensional, linearly unstable dynamical systems. Our goal is to e xplain the existence of small, irregular oscillations that are frequen tly observed near the desired equilibrium. We derive a one-dimensional map that captures exactly the dynamics of the continuous system. Usin g this micro-chaos map, we prove the existence of a hyperbolic strange attractor for a large set of parameter values. We also construct an ' 'instability chart'' on the parameter plane to describe how the size a nd structure of the chaotic attractor changes as the parameters are va ried. The applications of our results include the stick-and-slip motio n of machine tools and other mechanical problems with locally negative dissipation.