Adaptive autobalancing boundary control for a flexible rotor

We design a control strategy for a spinning rotor with an unbalanced disk attached to its free end. The control strategy is composed of a boundary torque applied to the clamped end, and two boundary forces and two boundary torques applied to the free-end. At the clamped-end, the boundary torque ensures that the rotor tracks a desired angular velocity trajectory, while at the free-end, the boundary forces and torques ensure that the rotor displacement is regulated at every point along the length of the rotor. Under the assumption of exact model knowledge, we first develop a model-based control law which exponentially achieves the control objectives. We then illustrate how the model-based control law can be redesigned as an adaptive controller which asymptotically achieves the same control objectives while compensating for parametric uncertainty associated with unbalanced operation