Underactuated pendulum damping by its length adjustment and passive output selection

Nonlinear passivity-based feedback controller to damp oscillations of the underactuated pendulum-like system via the active modification of the length of the suspension pendulum string is presented here. The structurally rich family of convenient virtual outputs making that system input-output passive will be determined and various asymptotically stabilizing feedback laws will be computed based on them. Among those controllers two qualitatively different cases were tested both in simulations and laboratory real-time experiments. First of them does not require the angular velocity measurement and guarantees that the string length does not exceed the maximum of its initial and its nominal (i.e., the ideal operational) value. The second one, on the contrary, does not require the angle measurement and guarantees that the string length does not go bellow the minimum of its nominal length and its initial value. Both controllers can clearly nicely complement each other in various practical situations if application to a crane with suspended load is considered. Their performances were compared to some previously published approaches as well.