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

This paper presents dynamical modeling and control of the payload swing of the gantry crane. The modeling is done in two dimensions using the Lumped Mass-Model. Two methods are used for the modeling, Newton's Mechanics and Lagrange's Mechanics, and both methods resulted in the same model. The model is linearized and converted to State-Space representation for the implementation of the Linear Quadratic Regulator (LQR). The objective of the controller is to move the payload from its initial position to its final position while minimizing the payload swing angle and vibrations during the movement. Simulation Results in MATLAB proved excellent regulation, fast and smooth convergence of the payload swing angle to a minimum value (close to zero) without causing a delay of the payload to reach its final position.