Velocity observers for linear mechanical systems subject to single non-smooth impacts

Abstract In this paper, we consider the problem of the velocity estimation from position measurement for linear mechanical systems (with multiple degrees of freedom) subject to single non-smooth impacts, both elastic and inelastic (i.e., with coefficient of restitution e =1 and e ∈(0,1), respectively). Through a simple example, it is shown that a classical Luenberger observer is not able to reproduce instantaneously the jumps in the mass velocities, since it recovers the error induced by such jumps only asymptotically: an infinite sequence of impacts can prevent the estimation error to asymptotically go to zero. A new observer structure is proposed for linear mechanical systems subject to single unilateral constraints, that guarantees that the corresponding error dynamics are exponentially stable, also in presence of an infinite sequence of non-smooth impacts. The observer that we propose switches at the impact times, that can be recognized by position measurements only. To validate the proposed observer, both simulation and experimental tests have been carried out and are briefly reported, pointing out the drawbacks and advantages of the observer.