International Journal of Bifurcation and Chaos · 2010 · 27 citations · 12 references
EngineeringMechanical EngineeringDynamical SystemsSystem DynamicsVibrationBifurcation TheoryChaos TheoryControl Loop DynamicsControl SystemsControl TheoryDigital Signal ProcessingChaos ControlChaos In Dynamical SystemsChaos In Mechanical SystemsChaotic DynamicsChaotic MapsLinear ControlLinear Control SystemsPiecewise Linear Maps
In the present paper, we introduce and analyze a mechanical system, in which the digital implementation of a linear control loop may lead to chaotic behavior. The amplitude of such oscillations is usually very small, this is why these are called micro-chaotic vibrations. As a consequence of the digital effects, i.e. the sampling, the processing delay and the round-off error, the behavior of the system can be described by a piecewise linear map, the micro-chaos map. We examine a 2D version of the micro-chaos map and prove that the map is chaotic.
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