PID position control in the presence minimal Coulomb friction and non-zero 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 of the equations of motion are used to achieve rigorous and general results for this nonlinear problem. The algebraic prediction of stick-slip for this system is contrasted with predictions of the describing function. The predictions of the describing function are shown to be unreliable for this problem of friction and control.