Reasoning and stability of limit cycle generated by friction in servo system

The phenomenon of limit cycle was observed in low-velocity servo system. With the help of nonlinear analysis tools, this paper analyzes the kinetics of limit cycle and finds out the reasons that induce this phenomenon. First, the Stribeck model was converted to piecewise linearized friction model and the state space model was also obtained. Then, by analyzing the feature of the system balance point and using Poincare-Bendixson theorem, the existence of the limit cycle was proved. The region where the limit cycle occurs was also found. Finally, the stability of the limit cycle was analyzed based on the Poincare map. Simulation and experiment results show that, under low-velocity state, stable limit cycle occurs in the servo system that is disturbed by friction. The reason is that the stability of the equilibrium changes repeatedly. Through the analysis of the system root locus, the measure to eliminate the limit cycle is found.