Reliability of predicting stick-slip in robotics and control using describing function

In designing servo controls for machine tools, position controlled robots, tracking mechanisms and disk drives, stick-slip problems are often encountered. Analysis tools are frequently used during the design and development phase in industry and research to predict the stick-slip caused by the dominant friction contributor. If an analysis tool can correctly predict the stick-slip during the design and development phase then the controller design task can be greatly eased-but the analysis tool must be reliable. Reliability in the context of this discussion means the ability of an analysis tool to correctly predict stick-slip for all possible parameter combinations (PID, mass, Coulomb force, etc.) within the problem space. This paper presents an investigation into the reliability of describing functions as an analysis tool. A PID controller is applied to a plant with friction. The friction is represented by different describing functions. The results of describing function analysis are compared with theoretical results to determine the reliability of describing functions applied to the problem of friction