PID control in the presence of static friction: exact and describing function analysis

PID position control in the presence of static friction is shown to lead to a frictional limit cycle for all stabilizing combinations of P, I and D parameters. An idealized Coulomb+static friction model, dimensional analysis and the study of all possible solutions to the differential equations are used to achieve analytic results for this nonlinear problem. Three theorems establishing the predictions of the describing function are also presented.