Optimized input shaping for multi-mode hanging chains using a modal model approach

This work presents a study on the dynamics and control of a hanging chain suspended from an overhead crane, using modal analysis and input shaping techniques. Two standard input shaping functions, step, and polynomial, are evaluated alongside a piecewise cosine function. The effectiveness of proposed input shaping techniques is evaluated based on their impact on the hanging chain’s various mode shapes contribution. The study introduces a key innovation in solving input coefficients for flexible structures by utilizing the modal model matrix created from the Finite Difference Method in conjunction with Laplace transformations. This approach aims to achieve various solutions for the input functions depending on the number of modes considered in the system. The solution varies depending on the number of modes contributing in the response. This allows for highly precise control and provides insights into their potential applications in dynamic control systems involving flexible structures.