LPV and LFR modelling of elastic robots for controller synthesis

A quasi linear parameter varying (LPV) model of a 3-DOF robot with elastic joints for controller synthesis is described. As the LPV controller synthesis based on linear fractional representation (LFR) models does not grid the parameter space, an LFR model is also derived. The models described in this paper include a high nonlinear mass inertia, which can vary in a huge range due to the relative movements of the different mass points. For the same reason the nonlinear Coriolis and centrifugal moments are also included in the models. As the models are designed for controller synthesis, they have to be of low complexity. This is achieved by an appropriate choice of the model structure and the scheduling parameters. The proposed approach can be easily adapted to other (not only mechanical) systems based on second order differential equations.