A three-dimensional gantry crane system using proportional-derivative controller with input shaping approach

Abstract

This project presents the development of a dynamic model and an efficient control algorithm of a three-dimensional (3D) gantry crane with payload. A 3D gantry crane with simultaneous travelling, traversing, and hoisting is considered. The dynamic equations of motion of the gantry crane system are derived using the Lagrange’s method and represented in nonlinear differential equations. Simulation is performed using Matlab/Simulink to investigate the dynamic behaviour of the system both in time and frequency domains. System responses including positions of rail, trolley and payload, and payload sway angle are obtained and analysed. For control of the 3D gantry crane, a proportional-derivative controller with input shaping for input tracking and reduction of payload sway is proposed. The performances of the controller are examined in terms of input tracking capability, level of sway reduction, and robustness of the input shaper. Simulation and experimental exercises using a lab-scaled 3D gantry crane show that the proposed controller is capable of minimising the payload sway while achieving satisfactory input tracking performance. The controller is also shown to be robust up to 50 % error tolerance in the sway frequencies. Moreover, with the experimental results, it is demonstrated that the proposed control is practical and easy to implement in real-time.