Minimizing Cable Swing in a Gantry Crane Using the IDA-PBC Methodology

Precise payload positioning by an overhead crane is difficult due to the fact that the payload can exhibit a pendulum-like swinging motion. The stabilization of loads that are carried by cranes is tedious, and the lack of truly efficient control strategies implies a large economical loss due to the additional time involved in the process. From a control theoretical point of view, cranes are underactuated mechanical systems which give rise to challenging control issues. Motivated by the desire to achieve fast and precise payload positioning while minimizing swinging motion, several researchers have developed various controllers for overhead crane systems. In this paper, we apply a controller design technique called interconnection and damping assignmentpassivity based control (IDA-PBC), that achieves stabilization for underactuated mechanical systems invoking the physically motivated principles of energy shaping and damping injection. IDA-PBC endows the closed-loop system with a Hamiltonian structure with a desired energy function that qualifies as a Lyapunov function for the desired equilibrium. The success of this method relies on the possibility of solving a set of partial differential equations (PDEs) that identify the energy functions that can be assigned to the closed-loop. In this paper, we use a partial feedback-linearization innerloop for explicit solution of these PDEs.