Multi-Mode Input Shapers for Oscillation Control of an Overhead Crane with Distributed Mass Payload

Abstract

A crane system with distributed mass payload (DMP) is highly nonlinear and it is a multi-mode system with different oscillation frequencies. The crane dynamics are also largely affected when operating under different cable and payload lengths. This paper investigates robust multi-mode input shapers for effective oscillation control of an overhead crane carrying DMP. Three robust shapers which are Zero Vibration Derivative (ZVD), Extra-Insensitive (EI) and Equal Shaping-Time and Magnitude (ETM) are considered and modified to be multi-mode shapers. These are obtained by convolving two input shapers that are designed separately based on the hook and payload oscillation frequencies. To assess the effectiveness of the shapers, Matlab simulations are performed by using the nonlinear dynamic model of the crane and applied under three distinct cases involving different cable and payload lengths. Simulation results show that the multi-mode EI shaper (MM-EI) has the highest performance in reduction of the hook and payload oscillations, with the lowest maximum transient sway and mean average error. In addition, with 40% errors in the oscillation frequencies, the MM-EI provides the highest robustness by achieving 50% reductions in the payload oscillations as compared to the case with an unshaped input.

Keywords

• distributed mass payload
• double-pendulum
• input shaping
• multi-mode shaper
• overhead crane
• robust shaper