Abstract:
A Gantry Crane is a well-known machine that is used to transport hazardous or large objects from
starting point to another destination. The control problem of gantry cranes has attracted
researchers’ attention because they have a wide application in industrial processes. Being an
underactuated MIMO system and a highly nonlinear system, a crane system has control issues. As
a result, the crane's cart should travel as quickly and accurately as feasible toward its destination
,while the payload swings as minimum as possible. In this paper, we present the modeling and
design of an Adaptive Model Predictive Control (AMPC) system for a three-dimensional (3D)
industrial gantry crane. The goal is to achieve fast and precise positioning while minimizing
payload oscillation. We derived the dynamic model of the system using the most powerful method
called Lagrange, providing an accurate representation of the crane's complex dynamics. To
facilitate controller design, the nonlinear dynamics are linearized around a stable equilibrium
point using the Taylor series expansion and small-angle assumptions, simplifying the complex
dynamics of the crane. The resulting linearized model serves as the foundation for the AMPC,
which optimally adjusts control actions based on real-time feedback to achieve smooth, rapid
positioning of the gantry while minimizing oscillatory motion. The proposed AMPC controller
adaptively adjusts the control parameters in real time to account for changes in system behavior,
ensuring robust performance across varying operating conditions. We evaluated the performance
of the AMPC through extensive simulations in MATLAB/Simulink, demonstrating the controller's
ability to achieve rapid positioning while effectively minimizing payload swing. The simulation
results indicate significant reductions in settling time, minimal overshoot around 0 % , efficient
suppression of oscillations and zero (0) steady state error. The approximate total efficiency of
AMPC compared to MPC is 66.93%, showing that AMPC is significantly more effective in
improving the system's performance. This work introduces the potential of AMPC to enhance the
operational performance of 3D gantry cranes in industrial environments where precise control
and rapid stabilization are essential. Comparative analysis with classical MPC highlights the
advantages of AMPC in handling multi-dimensional control constraints, making it particularly
suitable for industrial applications requiring high precision.
