PID control in the presence of static friction: A comparison of algebraic and describing function analysis (Q1917127)

By analyzing the time-domain response of a servo with PID position control and Coulomb friction or Coulomb \(+\) static friction, it has been shown that no system with Coulomb friction alone will show a limit cycle in the neighborhood of the origin, and that every system with minimal Coulomb friction and nonzero static friction has such a limit cycle as a possible motion. It is explained that when the Coulomb \(+\) static friction model is valid and the magnitudes of Coulomb and static friction lie in the normal range, there is no combination of PID control parameters that will eliminate stick-slip. The predictions of the describing functions are shown to be unreliable for this problem of friction and control.