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arXiv · 0707.0901

Effect of time delay on feedback control of a flashing ratchet

E. M. Craig·B. R. Long·J. M. R. Parrondo·H. Linke
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Abstract

It was recently shown that the use of feedback control can improve the performance of a flashing ratchet. We investigate the effect of a time delay in the implementation of feedback control in a closed-loop collective flashing ratchet, using Langevin dynamics simulations. Surprisingly, for a large ensemble, a well-chosen delay time improves the ratchet performance by allowing the system to synchronize into a quasi-periodic stable mode of oscillation that reproduces the optimal average velocity for a periodically flashing ratchet. For a small ensemble, on the other hand, finite delay times significantly reduce the benefit of feedback control for the time-averaged velocity, because the relevance of information decays on a time scale set by the diffusion time of the particles. Based on these results, we establish that experimental use of feedback control is realistic.

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E. M. Craig, B. R. Long, J. M. R. Parrondo, H. Linke. 2007-11-09. Effect of time delay on feedback control of a flashing ratchet. https://doi.org/10.1209/0295-5075/81/10002

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