Feedback Linearization Control of Overhead Cranes with Varying Cable Length

Based on partial feedback linearization technique, a nonlinear controller is proposed for an overhead crane system. The overhead crane is an underactuated mechanical system having three degrees of freedom (trolley displacement, cable length and cargo swing angle) with only two actuators (one is for cargo hoisting and the other is for trolley driving). The main purpose of the proposed controller is tracking the trolley to the desired position, hoisting the cargo up/down to have desired length of cable, and eliminating the cargo swing as fast as possible. To show the effectiveness of the proposed controller, simulation is performed using MATLAB. The simulation results show that the crane system with the proposed controller is asymptotically stable. Furthermore, all state trajectories of the system reach to steady state within a considerably short time even if the inherent structure of system is changed.