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

Effect of time delay on feedback control of a flashing ratchet