Model selection: From LTI to switched-LPV

A practical problem for control engineers is the selection of the most adequate model of a physical plant in order to design a controller which should achieve a desired performance level. For this selection the required performance, the resulting model uncertainty and a well-established robust controller design methodology play important roles. They determine the structure and complexity of the desired model, i.e. higher performance and low uncertainty levels require higher model complexity in general. Hence an identification procedure focused on the desired performance, rather than on a good mimic of the system dynamics, could prove useful. Here we present an open discussion on this problem illustrated by two examples, both described by nonlinear equations: a Diabetes Mellitus glucose-insulin dynamics and a 2DOF magnetic bearing system. The first may be described as an LTI model plus uncertainty and the second needs to be described as a switched-LPV model in order to guarantee the required performance.