Quantization in time, like sampling, and quantization in space, like round-off have counter-intuitive effects in time-delay systems. These can be used in a positive way in several simple control strategies to stabilize otherwise unstable equilibria, in spite of the fact, or actually, just because of the fact that delay tends to destabilize steady-states, tends to make bifurcations subcritical and tends to produce chaotic and transient chaotic behavior in the tangle of unstable limit cycles in the infinite dimensional phase spaces. After a brief introduction to the basic models of human and robotic balancing, a couple of models and experiments are discussed where time delay and sensory threshold, or sampling and round-off are relevant. The examples represent that practically satisfactory balancing can be achieved even with slow and inaccurate computers like the brain. Also, the various sensory signals used by the brain during balancing are discussed together with the possible bifurcation phenomena.
Gabor Stepan is professor in Applied Mechanics at Budapest University of Technology and Economics (BME), in Hungary, a position that he has since 1995. His research interests include nonlinear vibrations and time-delay systems with specific applications in mechanical engineering, like nonlinear dynamics of elastic wheels, vibrations and stability of robots, force control, stabilization of unstable equilibria, human and robotic balancing, rehabilitation robotics, machine tool vibrations, traffic dynamics, hardware-in-the-loop experiments.
He has been on the editorial board of Nonlinear Dynamics, Mechanism and Machine Theory, Physica D, and served for decades in the board of Journal of Nonlinear Science, Philosophical Transactions of the Royal Society. He is member of the Hungarian Academy of Sciences (since 2001) and the Academy of Europe (since 2013), honorary professor of Nanjing University of Aeronautics and Astronautics (since 2014) and foreign member of the Estonian Academy of Science (since 2017). He was elected as associate member of the International Academy for Production Engineering (CIRP, 2012) and fellow of the Society for Industrial and Applied Mathematics (SIAM, 2017). He is ERC Advanced Grant holder (2014-2019) and the recipient of the Thomas K. Caughey Dynamics Award of ASME (2015).
Between 1995 and 2018, Prof Gabor Stepan was the head of the Department of Applied Mechanics at BME, also served as the dean of the Faculty of Mechanical Engineering (2008-2012) and as the chairman of the Section of Engineering Sciences at the Hungarian Academy of Sciences (2011-2017). He was a member of the IUTAM Conference committee, he is presently an elected member of the Executive Committee of the Congress Committee of IUTAM and also member of the Scientific Council of the International Centre of Mechanical Sciences (CISM).
Gabor Stepan was organizer of the 6thEuropean Solid Mechanics Conference (ESMC, Budapest 2006), the BIRS Workshop on Noise, Time Delays & Balance (Banff, Canada 2009), the IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments (Budapest 2010), the 9thEuropean Nonlinear Dynamics Conference (ENOC 2017), the 8thCIRP Conference on High Performance Cutting (HPC18, Budapest 2018) and the 14thIFAC Workshop on Time Delay Systems (TDS18, Budapest 2018). He is a member of the ENOC Congress Committee of Euromech.