Modeling dynamic control model of a two-link crane-manipulator

Abstract

The problem of controlling a two-link crane-manipulator depends on the level of complexity of the system. When using a two-link manipulator, two problems need to be solved. The first problem is that you need to define the control parameters in such a way that the given position of the manipulator changes according to the corresponding trajectory. The second problem is that in order to achieve the desired position of the manipulator, it is necessary to correctly parameterized the mathematical model of the control system. One of the problems that affects the accuracy of manipulator control is the correct construction of adequate dynamic control models.
 In this article was propose to consider a direct method of developing a dynamic model of the crane-manipulator. It was propose to apply a mathematical model, which is built on the principles of theoretical mechanics by applying the Lagrange equations of the second kind.
 To modeling a dynamic model of a two-link crane-manipulator, the kinetic and potential energies of the component systems of the manipulator were determined, and on the basis of the Lagrange equation of the second kind, dynamic equations of motion were obtained.
 The dependences between the capturer coordinates and the generalized coordinates were also determined. These dependencies helped to establish the control equations that allow controlling the movement characteristics of the two-link manipulator.