Considering higher terms of description function for limit cycle generated by friction

In servo systems, there are various nonlinear factors, including friction, backlash and saturation, which will affect the system accuracy, even produce limit cycles. Therefore, the study of the nonlinearity in the system has important theoretical and engineering value. And limit-cycle caused by friction, including its generation and avoiding are focused on. Firstly, the description function for coulomb and viscosity friction model is derived, respectively. Secondly, the effect of numbers of frequency terms considered in description function is discussed. The feature of the phase and amplitude of limit-cycle is studied. Thirdly, a servo system with friction nonlinearity is taken as an example. The simulation results show the correctness of the theoretical deduction.