Kimmerle, Sven-Joachim; Gerdts, Matthias; Herzog, Roland
Dokumenttyp:
Zeitschriftenartikel / Journal Article
Titel:
Optimal Control of an Elastic Crane-Trolley-Load System
Untertitel:
A Case Study for Optimal Control of Coupled ODE-PDE Systems
Zeitschrift:
Mathematical and Computer Modelling of Dynamical Systems (MCMDS)
Jahrgang:
24
Heftnummer:
2
Jahr:
2018
Seiten von - bis:
182-206
Sprache:
Englisch
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 BFGS update. «
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 inv... »