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Sven-Joachim Kimmerle, Matthias Gerdts, R. Herzog, Mathematical and Computer Modelling of Dynamical Systems |
Abstract:
We present a mathematical model of a crane-trolley-load model, where the crane beam is subject to the partial differential equation (PDE) of static linear elasticity and the motion of the load is described by the dynamics of a pendulum that is fixed to a trolley moving along the crane beam. The resulting problem serves as a case study for optimal control of fully coupled partial and ordinary differential equations (ODEs). This particular type of coupled systems arises from many applications involving mechanical multi-body systems. We motivate the coupled ODE-PDE model, show its analytical well-posedness locally in time and examine the corresponding optimal control problem numerically by means of a projected gradient method with Broyden-Fletcher-Goldfarb-Shanno (BFGS) update.
Reference:
- Kimmerle S.-J., Gerdts M., Herzog R.: Optimal control of an elastic crane-trolley-load system - a case study for optimal control of coupled ODE-PDE systems. Mathematical and Computer Modelling of Dynamical Systems 24:2 (2018), 182-206, DOI: doi.org/10.1080/13873954.2017.1405046.