Nonlinear coupling control laws for an overhead crane system

In this paper, 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, are then design two nonlinear controllers that increase the coupling between the gantry position and the payload position.