Optimal control of an elastic crane-trolley-load system - a case study for optimal control of coupled ODE-PDE systems. Issue 2 (4th March 2018)

• Record Type: Journal Article
• Authors: Kimmerle, S.-J.; Gerdts, M.; Herzog, R.
• Is Part Of: Mathematical and computer modelling of dynamical systems. Volume 24:Issue 2(2018)
• Page Start: 182
• Page End: 206
• Publication Date: 2018-03-04
• Subjects: Crane-trolley-load system -- ODE-PDE-constrained optimization -- optimal control of ODE -- coupled ODE-PDE system -- projected gradient method -- FEM for moving boundary conditions; Engineering -- Mathematical models -- Periodicals; Computer simulation -- Periodicals; 515.39
• DOI: 10.1080/13873954.2017.1405046
• Languages: English
• ISSNs: 1387-3954

Abstract

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.