Session: SYMP 3-2: Advanced Material Systems

Paper Number: 140444

140444 - Multiphysical Design of a Chaos Generator 

Even simple systems, consisting of three energy-storage elements, one nonlinear element and one locally active (negative) resistor, e.g. an amplifier, can exhibit classic chaotic behavior under certain circumstances, as shown by Chua for electronic circuits. In this case, the signals of such a non-linear dynamic system appear unpredictable even though the underlying equations are deterministic. This behavior is referred to as determinate chaotic. Usually, this behavior is not desired and can even lead to catastrophic consequences. Therefore, the knowledge of the situation, where such a behavior can occur, is of importance. Often it would require a tremendous experimental effort to find the operating regime, where this behavior occurs. Based on physics-based mathematical models and analysis techniques, parameter sets leading to chaotic behavior can be identified in a very time-efficient manner without
the need for experimental setups.

In this contribution, an equivalent mechanical chaotic signal generator, based on Chua’s circuit, is analyzed based on the isomorphy between electrical and mechanical elements. The question to be answered is, what are the parameters of a mechanical system leading to a chaotic behavior. Applying the structure-true “2nd” analogy, forces are related to electrical currents, velocities to voltages, masses to capacitors and compliances to inductances. In rotational systems, moments are related to electrical currents, rotational velocities to voltages, rotational masses to capacitors and rotational compliances to inductances. In contrast to the friction element, a negative friction relates velocity and force oppositely, i.e., a tensile force causes a shortening and a compressive force causes an expansion. Such a negative compliance can be, for example, realized with a controlled electrodynamic amplifier in combination with an appropriate mechanism.

Our work focusses on a prediction of the dynamic behavior of such system which is influenced by the system element parameters. The analysis is based on mathematical phase portrait investigations where bifurcations can be identified. Several parameter sets are calculated for which the mechanical system would exhibit chaotic behavior. Within the tolerances, the behavior of the mechanical system can be predicted without performing extensive experiments. For reasonable macro-mechanical elements large elongations results. For micro-electromechanical structures smaller elongations can be predicted at higher frequencies.  The friction element of the chaos generator proved to be a further hurdle. On the one hand, it had to have a very high level of accuracy, but on the other, it still had to be adjustable. An additional problem would have been the coupling of the amplifier, the mechanical Chua diode, which must be virtually frictionless.

As an alternative, an electromechanical system was designed and tested, where the chaotic signal was generated by an electronic Chua’s circuit while a servo motor transformed it into a laser beam movement.

Presenting Author: Uwe Marschner Technische Universitaet Dresden

Presenting Author Biography: Uwe Marschner studied Information Technology and graduated at TU Dresden (PhD 2002, Habilitation 2011). The academic year 1992–1993 he was with the Massachusetts Institute of Technology as a visiting engineer and in 2004 and 2006 with the University of Maryland as researcher within the Alexander von Humboldt Foundation GAFOE follow up program. At the Institute for Semiconductors and Microsystems Technology at the TUD he has established an intelligent sensor design and testing lab. His general interest are intelligent sensors used for indirect measurements and technical diagnosis, with the emphasis on parameter estimation, processing of vibration signals, circuit representation of multi-physical systems and simulation-based microsystems design. He is teaching courses on Microsystems Design and Simulation, Intelligent Medical Implants, Electromechanical Systems, Combined Simulation and Introduction to Electrical Engineering to Mechanical Engineers at TUD and in 2009 Electromechanical Systems Modeling at the University of Maryland. He is a member of IEEE, and ASME Branch Member of the Aerospace Division - Adaptive Structures and Material Systems.

Authors:

Uwe Marschner
Ute Feldmann
Petko Bakardjiev
Gustav Rost