Adaptive PID Coupling Tracking Control for Double-Pendulum Crane Based on Digital Twin Technology

This article presents an advanced digital twin system constructed for a double-pendulum crane (DPC) with complex dynamic characteristics, aiming to address the pressing need for intelligent control of DPC. The high complexity and underactuated nature of the DPC system make virtual-physical mapping, tracking control, and antiswing control highly challenging. To tackle these issues, this study designs a novel adaptive proportional-integral-derivative (PID) coupling tracking control method with an automatic gain adjustment mechanism, achieving real-time and accurate motion mapping from the physical to the virtual DPC and effectively suppressing the double-pendulum swing, which is a key goal. Particularly, to effectively compensate for different lumped disturbances in both the physical and virtual DPC and improve tracking accuracy, a time-delay control strategy is integrated into the underactuated DPC system, and an adaptive method is employed to estimate the influence of state-dependent time-delay errors online, thereby relaxing conventional boundedness assumptions. Finally, synchronous motion experiments demonstrate the effectiveness and superiority of the proposed virtual-physical tracking control method.