An Optimal Control Problem for a Rotating Elastic Crane-Trolley-Load System

In this study we present an extension of a model of an elastic crane transporting a load by means of controlling the crane trolley motion and the crane rotation. In addition to the model considered in Kimmerle et al. (2017), we allow for rotations of the crane and include damping of the trolley and moments of inertia as well. We derive a fully coupled system of ordinary differential equations (ODE), representing the trolley and load (modelled as a pendulum), and partial differential equations (PDE), i.e. the linear elasticity equations for the deformed crane beam. The objective to be minimized is a linear combination of the terminal time, the control effort, the kinetic energy of the load, and penalty terms for the terminal conditions. We show the Frechet-differentiability of the mechanical displacement field with respect to the location of the boundary condition that is moving. This is a crucial point for a further mathematical analysis on the existence of optimal controls and the derivation of necessary optimality conditions. Finally we present first results for the full time-optimal control of the extended model. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.