Local and global bifurcations in a simple model of digitally controlled systems

Chaotic vibrations that are originated from the digital implementation of control are known for more than 20 years [1]. The consideration of the effects of sampling and processing delay is a routine procedure among control engineers, but the quantization in the analogue-digital converters is usually neglected. However, this latter effect frequently leads to deterministic but small scale chaotic behaviour – so-called micro-chaos [2, 3] – which is often considered simply as stochastic noise in the practice. In the present contribution a simple but quite general PD-controlled system is considered. It is shown that micro-chaotic oscillations may have a considerable influence on the accuracy and settling time of control systems. We focus on the numerical and analytical examination of global bifurcations since these may lead to the abrupt change of the aforementioned properties of the control system.