On the PD regulation of mechanical systems with dynamic backlash

This study concerns the regulation of a simple rigid body mechanical system with dynamic backlash. Contrary to most of the existing works in the control literature we explicitly treat all the non-linear non-smooth characteristics of this system viewed as a rigid body mechanical system with unilateral constraints. We propose a simple PD strategy in order to stabilize the system. For this scheme two cases are analyzed: the colocated and non-colocated controllers. In the colocated scheme we demonstrate the global asymptotic convergence. For the non-colocated control we have proved analytically the existence of cycle limits induced by the control law. This work finds potentials application in several areas including the control kinematic chains with joint clearance and vibro-impact systems.