Time optimal control of overhead cranes with hoisting of the load
The minimum time transfer of a load, suspended from a trolley by ropes, from an initial pint 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 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.
scientific article; zbMATH DE number 4001981