A Hybrid Control Strategy for a Gantry Crane with the Concept of Multi-Diffeomorphism

This paper investigates the stabilization problem of a class of nonlinear systems characterized by non-minimum phase behavior within each subsystem, with a focus on an application to a gantry crane system that employs friction to control its swing angle. In practical crane operations, the demand for accelerated system response is critical to improving productivity; however, this often induces significant variations in the swing angle, potentially destabilizing the system. To overcome this challenge, we propose a hybrid control approach that combines the concept of multi-diffeomorphism with symmetry considerations to enhance the smoothness of transient responses. Unlike classical input–output feedback linearization, which typically relies on a single diffeomorphism and may compromise the zero dynamics stability, the proposed method distributes the transformation across multiple diffeomorphisms, ensuring balanced and coordinated transient behavior. The design involves the simultaneous development of subsystem-dependent feedback controllers, which collaboratively guarantee the global stability of the overall closed-loop nonlinear gantry crane system. The Lyapunov stability framework is employed to rigorously demonstrate that the tracking errors converge asymptotically to meet the desired performance specifications. In addition, the simulation results demonstrate that the developed hybrid control approach notably enhances the system’s responsiveness while preserving both symmetry and the stability of the zero dynamics. Specifically, the swing angle decreases by over 90% in less than 2 s, highlighting the method’s efficiency in minimizing oscillations during fast operations. This study highlights the practical benefits of integrating symmetry-aware multi-diffeomorphism techniques into nonlinear control design. Such techniques are found to be particularly effective for underactuated mechanical systems like gantry cranes.