PID CONTROL IN THE PRESENCE OF STATIC FRICTION - A COMPARISON OF ALGEBRAIC AND DESCRIBING FUNCTION-ANALYSIS

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 Co ulomb + static friction model, dimensional analysis and the study of a ll possible solutions of the equations of motion are used to achieve r igorous and general results for this nonlinear problem. The algebraic prediction of stick-slip for this system is contrasted with prediction s of the describing function. The predictions of the describing functi on are shown to be unreliable for this problem of friction and control . Copyright (C) 1996 Elsevier Science Ltd.