Backlash and Friction Reciprocal Effect on Limit Cycle Existence

Backlash and friction reciprocal effect on limit cycle existence is preliminarily investigated for the basic 2nd order servo system with simplified models of Coulomb friction and backlash. By the describing function method, it is shown for this case that the lower boundary for limit cycle existence, in the backlash gap [rad] – dry friction moment [Nm] plane, is a straight line starting in the origin. Besides, a novel condition is formulated for this system to avoid limit cycle excitation for any combinations of dry friction and backlash gap. This condition can be valuable for control systems design with fully unknown or uncertain values of backlash gap and dry friction.