Abstract
This paper paper is devoted to the analysis and control of a simple rigid body mechanical system with dynamic backlash. Contrary to most of the existing work in control literature we explicitly treat all the dynamic and non-linear characteristics of this system. We show that appropriate gains in a PD control scheme can be selected such that the closed-loop system is locally stable around a desired symmetric periodic orbit. Two cases are analyzed: the colocated and the non-colocated controllers. It is shown that both schemes are quite similar, although the non-colocated case yields, as expected, smaller existence and stability regions. This work finds potential application in several areas including the control of kinematic chains with joint clearance and vibro-impact systems.
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