Modelling and controlling one-degree-of-freedom impacts under elastic/plastic deformations

The paper extends a control structure proposed previously to control one-degree-of-freedom impacts between two bodies, possibly subject to elastic/plastic deformations. First, basic equations describing the motion of the bodies involved in the collision are derived, both for a state of noncontact and for a state of contact, taking into account the possible permanent deformations that can occur if plastic yielding begins. A control scheme is proposed on the basis of an observer that is able to estimate asymptotically the impact-induced forces (if any), to recognise (on the basis of these estimates) if the bodies, when in contact, are subject to elastic or plastic deformations, and to allow asymptotic compensation for the impact-induced forces when the two bodies are in contact. The paper is completed by a simulation test