Rj. Dekorte et al., EXPERIMENTAL CONTROL OF A CHAOTIC PENDULUM WITH UNKNOWN DYNAMICS USING DELAY COORDINATES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(4), 1995, pp. 3358-3365
Unstable periodic orbits (UPOs) of an experimental chaotic pendulum we
re stabilized using a semicontinuous control method (SCC), applying co
ntrol actions several times per cycle. One advantage of this method, c
ompared to a one-map-based control method such as the Ott-Grebogi-York
e method [Phys. Rev. Lett. 64, 1196 (1990)], is the applicability to s
ystems with relatively large unstable eigen-values and/or high noise l
evels. Compared to a continuous type of feedback control as was propos
ed by Pyragas [Phys. Lett. A 170, 421 (1992)], the advantage is that t
he controller settings can be measured from experimental data. Because
the control method uses delay coordinates, only one variable has to b
e measured. This paper describes an SCC method using delay coordinates
, the extraction of UPOs from time series, how the effect of the contr
ol parameter can be measured, the effect on the control in case of an
error in the estimate of the UPO, and how this error can be reduced to
obtain more stable control.