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Optimal Control of long cable crane systems
Author(s) -
Vogelsang Jan,
Büskens Christof
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810151
Subject(s) - catenary , piecewise linear function , overhead (engineering) , rack , line (geometry) , piecewise , overhead crane , control theory (sociology) , computer science , function (biology) , engineering , structural engineering , mathematics , control (management) , mechanical engineering , electrical engineering , mathematical analysis , geometry , artificial intelligence , evolutionary biology , biology
Crane systems like overhead cranes used in high–rack warehouses are usually modeled as a multi body system with the cable modeled as a pendulum whose cable is regarded as linear. With cables around 40–50 meters long, it is possible that the description of the cable by a straight line is not sufficient anymore, because the cable is bended slightly. The shape of the cable is more like a curve than a straight line. A more suitable description could be achieved by a chain of piecewise linear links, which is again a multi body system and leads to a differential–algebraic system. Each of these links can be modeled again by a pendulum. Using the example of an overhead crane system used in high–rack warehouses, the conventional model with linearly connected trolley and load is compared to the new model with a piecewise linear connection between trolley and load. The optimal trajectories and controls for both models with respect to the same objective function are analyzed for different cable lengths, loads, transport distances and objective functions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)