Second Order Sliding Mode Control of a 3-Dimensional Overhead-Crane

In this paper the 3-Dimensional Overhead Crane is the subject of study. The note includes the Euler-Lagrange equations of a 5 degrees of freedom, 5DOF, Overhead Crane and the design of a Second Order Sliding Mode Controller in order to ensure the precise load transfer during the load movement despite of model uncertainties and un-modeled dynamics. Moreover, the system is under-actuated and 5DOF should be controlled with 3 control actions. The stability analysis is developed based on Lyapunov second method ensuring the finite time convergence to the desired sliding output. Simulations and Experimental results are presented.