Overhead Crane Control Under Constraints: A Comparative Study of Linear and Nonlinear Models

This study presents a control system for an overhead crane using an NMPC control approach to stabilise the cable angle θ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and payload angle θ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> under state and control input constraints. The control strategy, implemented in a MATLAB/Simulink environment, is designed to minimise oscillations and improve the stability and safety of the crane system. The constraints ensure that the angles and control inputs remain within predefined bounds, addressing practical limitations for real-world applications. Both linear and nonlinear system dynamics were analysed, with the results demonstrating the algorithm's effectiveness in stabilising the crane system in both cases. The nonlinear model captures more realistic dynamics, whereas the linear model achieves faster stabilisation. The proposed approach exhibits robustness and accuracy in maintaining stability under constraints.