Robust stabilization of a double pendulum with an elastic joint and uncertain high-frequency dynamics

In this paper we consider an extension of the well- known double pendulum (or pendubot) experiment. The difference is that we add uncertain dynamics to the plant by replacing the rigid motor shaft by an elastic one and by adding an electronic circuit at the input of the pwm amplifier. These additional dynamics make the stabilization problem much harder and basic stabilization methods like pole placement or LQR may lead to bad performance or they may fail at all. Various controllers are designed and compared with respect to their performance and robustness properties: pole placement, LQ, H2, Hinf and mue. If the weighting scheme is suitably chosen, the best results are obtained for a Hinf (resp. a mue) controller. The experiment can serve as a platform for research and education.