Time optimal control of overhead cranes with hoisting of the load

• Published in: Automatica (Oxford) Vol. 23; no. 4; pp. 437 - 447
• Main Authors: Auernig, J.W., Troger, H.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1987; Elsevier
• Subjects: Applied sciences; boundary value problems; control constraints; cranes; Exact sciences and technology; Hoisting and lifting gears; load hoisting; Material handling, hoisting. Storage. Packaging; materials handling; mathematical models; maximum principle; mechanical handling equipment; Minimum time control; optimal control; overhead crane; ship unloader; state constraints; load hoisting; control constraints; materials handling; Minimum time control; overhead crane; state constraints; maximum principle; ship unloader; Optimal control; Lifting gear; Pontryagin principle; Gantry crane; Maximum principle; Time; Crane; Optimization
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/0005-1098(87)90073-2

The minimum time transfer of a load, suspended from a trolley by ropes, from an initial point at rest to a terminal point where it is required to be at rest again, is investigated by controlling both the traversing motion of the trolley and the hoisting motion of the load. Special care is given to the modelling of the mechanical and electrical features of the system. Mathematically, a boundary value problem with constraints both in the control and state variables is given. Necessary and sufficient conditions for time optimal solutions are derived using an extension of the Pontryagin maximum principle. The nonlinear control problem is solved analytically and a detailed discussion of the solutions is given. Numerical results are presented which apply to ship unloaders.