EXPERIMENTAL CONTROL OF A CHAOTIC PENDULUM WITH UNKNOWN DYNAMICS USING DELAY COORDINATES

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.