Analytical Models of Experimental Artefacts in an Ill-Posed Nonlinear ODE System

Abstract

We discuss different approaches for the analytical description of a mechanical system used in control theory, aiming at the analytical modelling of experimental artefacts observed in the implementation of ideal searched trajectories. Starting from an established analytical solution, we develop an alternative analytical model for this solution with minimal deviations and then extend this starting point to a more flexible toolbox that incorporates a variety of phenomena that typically occur in real implementations of this mechanical system, thus providing an important step towards bridging the gap between theoretical models and experimental reality.