The controllability function method

Abstract

The paper is devoted to the control problem for the movement of an overhead crane with the use of a dynamic model in the form of "trolley - cargo" mechanical system and the driving force as a control parameter. To solve the system of differential equations, which describe the movement of the system taking into account constraints for the control, the controllability function method is applied. The algorithm for solving the problem is described, a program is developed as well as difficulties, which occur while implementing the method, and ways of its solution are marked. Results of constructing the control and system trajectories are also provided as an example of the program work.