  We study the threshold control protocol for a collective flashing ratchet. In
particular, we analyze the dependence of the current on the values of the
thresholds. We have found analytical expressions for the small threshold
dependence both for the few and for the many particle case. For few particles
the current is a decreasing function of the thresholds, thus, the maximum
current is reached for zero thresholds. In contrast, for many particles the
optimal thresholds have a nonzero finite value. We have numerically checked the
relation that allows to obtain the optimal thresholds for an infinite number of
particles from the optimal period of the periodic protocol. These optimal
thresholds for an infinite number of particles give good results for many
particles. In addition, they also give good results for few particles due to
the smooth dependence of the current up to these threshold values.
