An energy-based adaptive control design technique for multibody-mechanisms with flexible links

In this article, an adaptive control design technique for multibody mechanisms is proposed and described in detail for the case of a planar four-bar flexible-link mechanism. The controller is obtained by superposing a PD position controller, an adaptive proportional vibration controller, and, when the effects of gravity cannot be neglected, an additional term that compensates the (equivalent) gravity torque. The controlled system simple stability is formally proved by means of a model-independent energy-based approach, whereas asymptotic stability is discussed only for the case when no gravity effect needs to be accounted for. The controller performances are tested in simulation in both cases.