A new continuously differentiable friction model for control systems design

For high-performance engineering systems, model-based controllers are typically required to accommodate for the system nonlinearities. Unfortunately, developing accurate models for friction has been historically challenging. Typical models are either discontinuous and many other models are only piecewise continuous. Motivated by the fact that discontinuous and piecewise continuous friction models are problematic for the development of high-performance continuous controllers, a new model for friction is proposed in this paper. This simple continuously differentiable model represents a foundation that captures the major effects reported and discussed in friction modeling and experimentation. The proposed model is generic enough that other subtleties such as frictional anisotropy with sliding direction can be addressed by mathematically distorting this model without compromising the continuous differentiability