Describing function analysis of a system with friction

This paper discusses different approaches when using the describing function method for the prediction of limit cycles in control systems. The method and friction modeling is briefly reviewed. A simple example showing stick-slip motion is given. Using different friction models the describing function is applied to the example. In particular the author uses it together with a new dynamic friction model. Determining the describing function for the friction nonlinearity itself will not predict existing limit cycles but combining part of the plant with the friction model yields a describing function which captures the behavior of friction for zero velocity. This, however, needs a dual-input describing function which depends on three parameters as compared to the normal two. The results are presented in a three dimensional plot