A Property of Stick-Slip Friction Models which Promotes Limit Cycle Generation

The effects of various "Stick-Slip" friction models on Proportional+Integral+Derivative (PID) controller stability for a simple system are investigated. Some of the more common models lack the ability to produce the limit cycles commonly observed for servos subject to stick-slip friction. A property of stick-slip models is identified which promotes limit cycle generation, and the effects are demonstrated through numerical simulations. This property is shown to be required for a stick-slip friction model to be useful in predicting limit cycle behavior in the simplest systems under PID control. Models lacking this property may lead to the inaccurate prediction of system dynamics.