Nonlinear coupling control laws for an overhead crane system

We consider the regulation control problem for a two-degree-of-freedom (2-DOF), underactuated overhead crane system. Inspired by recently designed passivity-based controllers for underactuated systems, we design several controllers that asymptotically regulate the gantry position and payload position. Specifically, utilizing LaSalle´s invariance set theorem, we first illustrate how a simple proportional-derivative (PD) controller can be utilized to asymptotically regulate the overhead crane system. Motivated by the desire to achieve improved transient performance, we then design a two nonlinear controllers that increase the coupling between the gantry position and payload position