Limit Cycle Existence Condition in Control Systems with Backlash and Friction

Backlash and friction effect on limit cycle existence is preliminarily investigated for the basic one-mass, 2nd order and two-mass non-linear servo systems with simplified models of Coulomb friction and backlash. By the describing function method, it is shown 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.