Data-driven TID controller for double-pendulum overhead crane system with distributed-mass payload

This study proposes a data-driven tilt–integral–derivative (TID) controller for a nonlinear multi-input, multi-output (MIMO) double-pendulum overhead crane system with a distributed-mass payload (DPOC-DMP), in which the controller parameters are tuned using the Safe Experimentation Dynamics Algorithm (SEDA). The main advantage of the proposed data-driven TID controller is its ability to enhance control accuracy and robustness without reliance on an explicit mathematical model. By incorporating a tilt action into the integral–derivative structure, the proposed TID controller significantly improves transient behaviour and suppresses load sway in nonlinear crane dynamics. The tuning of the TID controller parameters is performed using SEDA, which facilitates stable convergence via random but safeguarded perturbations. The effectiveness of the proposed TID controller was evaluated through simulations by analysing tracking errors, sway suppression, control effort, and robustness under external disturbances. Furthermore, the performance of the proposed controller was compared with that of a conventional PID controller. The results demonstrated that the proposed data-driven TID controller achieved superior performance in terms of objective function value, total tracking error, total control input energy, sway suppression capability, and faster recovery under external disturbance conditions. The simulation results show improved transient performance with reduced overshoot and enhanced sway suppression, together with lower control input energy compared with the PID controller. Quantitatively, the proposed method achieved a lower objective function value (310.6951 vs. 326.4870), reduced total tracking error (0.1619 vs. 0.1720), and lower control input energy (3.9647 vs. 4.3902), while maintaining faster recovery under disturbance conditions. In particular, the proposed TID framework improves control accuracy by 2.82% compared with the traditional PID controller, demonstrating its effectiveness in managing complex, nonlinear MIMO crane systems.