Abstract—This paper proposes a parameterized Nominal Characteristic Trajectory Following Proportional-Integral-Derivative (NCTF-PID) controller for nonlinear underactuated Multi-Input Multi-Output (MIMO) systems. Conventional NCTF-based controllers rely on non-parametric nominal characteristic trajectories obtained from open-loop experiments, which makes systematic parameter optimization difficult and limits their application to complex nonlinear MIMO systems. To overcome this limitation, a parameterized NCTF structure is developed and integrated with a PID controller, enabling simultaneous optimization of the trajectory-shaping characteristics and PID gains without requiring an accurate mathematical model. The resulting controller is tuned using the Adaptive Safe Experiment Dynamics (ASED) algorithm based solely on measured input-output data, where the optimization objective balances tracking performance and control effort. The developed NCTF-PID controller is evaluated on a nonlinear gantry crane system and compared with conventional PID and Fuzzy-PID controllers. Simulation results show that it achieves the best overall trade-off among tracking performance, payload swing suppression, and control effort. Compared with the PID and Fuzzy-PID controllers, it reduces the objective function value by approximately 28.7% and 11.0%, respectively, while decreasing the accumulated control effort by 68.1% and 44.2%, with the lowest accumulated tracking error among the three controllers. Additional disturbance-response and repeated optimization experiments further verify its robustness and the repeatability of the optimization results. The NCTF-PID controller provides a parameterized data-driven extension of the conventional NCTF methodology for nonlinear underactuated MIMO systems.

Index Terms—data-driven control, Nominal Characteristic Trajectory Following Proportional-Integral-Derivative (NCTF-PID), adaptive safe experiment dynamics, Multi-Input Multi-Output (MIMO) underactuated systems, trajectory tracking

Cite: Fengtao Zhang, Mohd Riduwan Ghazali, Mohd Ashraf Ahmad, and Mohd Zaidi Mohd Tumari, "A Data-driven NCTF-PID Controller for Gantry Crane System Based on Adaptive Safe Experimentation Dynamics Algorithm," International Journal of Electrical and Electronic Engineering & Telecommunications, vol. 15, no. 5, pp. 394-405, 2026. doi: 10.18178/ijeetc.15.5.394-405

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