Experimental investigation of micro-chaos

Gergely Gyebrószki, Gábor Csernák, Csaba Budai
8th European Nonlinear Dynamics Conference (2014.07.06-11)
Published at: 
Sunday, July 6, 2014
conference paper

Micro-chaos is a phenomenon when small amplitude chaotic oscillations are inflicted by digital effects (sampling, roundoff and processing delay). In previous works, various digitally controlled unstable linear mechanical systems were analysed; the corresponding micro-chaos maps were derived and the coexistence of several disconnected chaotic attractors was proven. The distance of the farthest attractor from the desired state can be quite large, while the size of these attractors is usually negligible from practical point of view. This is why the phenomenon could be the source of remarkable control error. In this paper, the micro-chaos map of the PD-controlled inverted pendulum – with rounding applied to the calculated control effort, and considering dry friction – is examined by modified Simple Cell Mapping methods and the possibility of constructing an experimental device showing the phenomenon of micro-chaos is analysed. A device having variable control force resolution is presented, and experiments are carried out to verify the theoretical and numerical results.