FRACTAL DIMENSION AS MEASURE OF CONTROL TIME

Abstract

The nonlinearity caused by the application of digital control may lead to chaotic behaviour. There are several cases, when these chaotic oscillations disappear suddenly. This phenomenon is referred to as transient chaos. In the present paper, we analyse a simple model of a digitally controlled mechanical system, which may perform transient chaotic vibrations, and propose a new procedure for the estimation of the duration of these transients. The relation between the mean lifetime and the so-called escape rate is also examined. As a result, a new formula is introduced, whose reliability is validated with the help of the new lifetime estimation method.