Optimal control of an elastic crane-trolley-load system - a case study for optimal control of coupled ODE-PDE systems

S.-J. Kimmerle, M. Gerdts and R. Herzog

Mathematical and Computer Modelling of Dynamical Systems, 2018, vol. 24, issue 2, 182-206

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.

Date: 2018
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DOI: 10.1080/13873954.2017.1405046

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