Nonlinear coupling control laws for a 3-DOF overhead crane system

We consider the regulation control problem for a three-degree-of-freedom (3-DOF), underactuated overhead crane system. Motivated by recent passivity-based controllers for underactuated systems, we design several controllers that asymptotically regulate the planar gantry position and the payload angle. Specifically, utilizing LaSalle´s Invariant 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 two nonlinear controllers that increase the coupling between the planar gantry position and the payload angle