Vibration Control of an Overhead Crane with Hoisting Motion using Input Shaping Technique

In this paper, an input shaping-based control law is designed for an overhead crane system with time-varying cable length. The proposed method employs a zero vibration (ZV) input shaper. It is well-known that the ZV input shaper is not robust to modeling errors causing by the time-varying dynamics, which leads to the fact that a direct application of ZV input shaper on time-varying systems often results in poor vibration suppression performance. Therefore, we first apply the standard ZV input shaper on an undamped linear time-invariant (LTI) second-order system. This step provides us a reference oscillation function that is exactly zero after the trolley stops. The real control input is then devised to perfectly match the real vibration of the crane system with the reference oscillation, and hence a vibration-free transportation can be achieved. The unshaped command is parameterized and its coefficients are designed to deal with control objectives other than the vibration elimination. The simulation results are provided to validate the efficacy of the proposed approach.