An extension of the original Ott-Grebogy-Yorke control scheme is used on a simple double pendulum. The base point of the double pendulum moves in both horizontal and vertical directions which leads to rather complicated behavior.A delay coordinate is used to reconstruct the attractor. The required dimension is determined by the False Nearest Neighbor analysis. A newly developed Fixed Point Transformation method is used to identify the unstable periodic orbit (UPO). Two different system parameters are used to control the motion. Minimum parameter constraints are studied. The use of discrete values for parameter changes is also investigated. Based on these investigations, a new on-off control scheme is proposed to simplify the implementation of the controller and minimize the delay in applying the control. / Ph. D.