Design of Sliding Mode Controller for the 2D Motion of an Overhead Crane with Varying Cable Length

Overhead cranes are under-actuated systems. They have three outputs that need to be controlled, consisting of cargo swing angle, trolley displacement, and suspended cable length, but only two actuators: cargo lifting and trolley driving forces. The main objective of this study is to design a robust controller for an overhead crane that transfers cargo from point to point as fast as possible and, at the same time, keeps the cargo swing angle small during the transfer process and make it completely vanish at the desired cargo destination. The proposed controller must simultaneously carry out three duties: minimize cargo swing, track trolley to the desired destination, and lift/lower cargo to the reference length of cable. The controller is designed based on a sliding mode control technique. To validate the proposed control quality, a stability analysis of the system is discussed and the response analysis is executed with both MATLAB simulation and experimental research. The simulation and experiment results show that the crane system is stable and has the desired behavior. 