Tensor Product Transformation Based Friction Model

Friction is a very old and universal issue in all mechanical systems. Since friction is non-linear, it is an ever challenging problem. Several empirical nonlinear friction models have been proposed in the technical literature. This paper does not propose any new model but it presents a new, tensor product (TP) based representation of the existing friction models which is suitable for control design. The TP model transformation is a relatively new method for transforming certain nonlinear models into polytopic model form. The main advantage of the TP model transformation is that the most of the linear state feedback design methods including Linear Matrix Inequality (LMI) can immediately applied to the resulting polytopic models to yield controllers with guaranteed performance.