D ynamical Modeling and Control of Motion System of the Gantry Crane to Minimize Swing Angle of the Payload

SYSTEM MODEL

We begin by finding the dynamical model of the motion system of a gantry crane using Newton's mechanics, where we find the relationship between the forces causing the motion and their effect on the motion of the crane using Newton's second law and consider the system to be a Lumped Mass Model. It is the common model in the modeling of cranes where it is considered that the suspension rope is negligible mass and the suspended payload is a concentric particle that has a mass m at the endpoint of the rope [6]. Fig. 1. shows the design model of the gantry crane and the shape of the "coplanar" payload swing.


Fig. 1. Design model of the gantry crane.

The gantry crane can be represented by the system shown in Fig. 2. It is a system consisting of the cart, the mass of M (kg) suspended to it a pendulum representing the movement of the payload, the mass of m (kg) and a rope, the length of L (m), which is a system with two degrees of freedom, which means that the number of variables that do not depend on each other and necessary to fully describe the system’s motion is the distance x(t) and the swing angle θ(t).

Fig. 2. Conventional Diagram of the system of the cart and payload.