Limit cycle analysis of electro-hydraulic control systems with friction and transport delay

A graphical prediction method is developed to effectively predict the possibilities of the existence of limit cycles for a widely used electro-hydraulic control system subject to nonlinear friction force. The nonlinearity is linearized by its corresponding describing function. Then the stability equation method accompanied by a parameter plane method provides a useful tool for the establishment of necessary conditions to sustain a limit cycle. Further, the stability analysis for systems subject to an uncertain transport delay time is considered. Simulations verify the accuracy of the prediction method.