Quasicontinuous control of a bronze ribbon experiment using time-delay coordinates

Abstract

We investigate quasicontinuous versions of the Ott-Grebogi-Yorke (OGY) control method in a bronze ribbon experiment using time-delay coordinates for the reconstruction of the attractor. We apply as quasicontinuous control methods the local control method and the minimal expected deviation method. As is known for the original OGY method with time-delay coordinates, values of the control parameter at previous times appear in the linearized dynamics. We discuss two possible ways to derive from this linearization feedback control formulas. These are the extended state space approach and a modified control requirement that demands stabilization not in the next time step but after w+1 time steps, where w is the number of preceding parameter dependences of the linearized dynamics. We show theoretically and demonstrate in the experiment that for the quasicontinuous control methods considered in this paper only the modified control requirement shows satisfying results in the control experiment.