Effect of time delay on feedback control of a flashing ratchetE. M. Craig1, B. R. Long1, J. M. R. Parrondo2 and H. Linke1
1 Department of Physics, Materials Science Institute, University of Oregon - Eugene, OR 97403 USA
2 Departamento de Física Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid 28040 Madrid, Spain
received 15 June 2007; accepted in final form 24 October 2007; published January 2008
published online 19 November 2007
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 the experimental use of feedback control is realistic.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.30.Yy - Control theory.
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