The H∞ Control for an Inverted-Double Pendulum System Consisting of Elastic Links Connected in Series

A stabilizing control technique for an inverted-double pendulum system consisting of two elastic links connected in series is developed, using a reduced-order model considering only the first vibration mode of the upper elastic beam, and applying an H∞ controller design method for a mixed sensitivity problem that can consider multiplicative perturbations at the input port and is characterized by a settling function. It is found that although the coupling effect of different natural frequencies between the two flexible beams makes the stabilization problem more difficult, it is possible to stabilize the system by a feedback control using only the system’s output signals that include the vibration signal of the upper elastic beam. Furthermore, it is concluded that the more different the lowest natural frequencies of the two elastic beams are, the more easily the system can be stabilized.