A solution of a problem of optimal crane control using the controllability function method

Abstract

Productivity, reliability, as well as ease of crane operation largely depends on the vibrations
of cargo suspended on a flexible rope. One of the main reserves to improve the crane efficiency is
transient mode optimization of the trolley movement (acceleration/deceleration). A "trolley – cargo"
movement model that represents operation of an overhead crane in tasks of optimal control are
considered. It is shown that an initial task of cargo movement from a certain initial point to a given
point, at which the system would be at the quiescent state by a finite time and with control
constraints, is equivalent to a task of local zero-controllability for this system. A practical solution
of this task is presented by using the inertial control synthesis method, that is evolution of the
controllability function method. The task of receiving bounded control that transfers a system from
one given point to another are studied. Results of application in the form of several different
algorithms for solving the task using the controllability function method, as well as results of
programs implementing these algorithms, and an analysis of emerging difficulties and ways of its
overcoming are presented and discussed.