Avoiding stick-slip through PD control

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Abstract
This note addresses the question of how to achieve steady motion at very low velocities using proportional-derivative (PD) control. Most prior work in control has used friction models which depend only on the current value of velocity. This type of analysis indicates that stick-slip can be avoided only through velocity feedback. The tribology literature, however, indicates that friction also depends on the history of motion. By including this dependence, a second regime of stable motion is revealed which is associated with position feedback gains above a critical value. Two experimentally-based dynamic friction models are compared using a linearized stability analysis. In accord with experiment, as state variable friction model exhibits asymptotically stable motion for any system stiffness (position feedback gain) exceeding a critical value. This property is not exhibited by a time-lag friction model.

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