Input shaper design for double-pendulum planar gantry cranes

Manipulating payload with gantry cranes can be difficult given the inherent system flexibility. Gantry crane dynamics can often be effectively modeled as a single linear flexible mode. However, if the crane is equipped with a large-mass hook and the payload is sufficiently light, then the dynamics can become complicated by double-pendulum effects. This paper presents a method for determining the contribution of the second pendulum mode to the overall dynamic response. Furthermore, an input shaping scheme is developed to reduce residual oscillations. This control method utilizes the double-pendulum dynamics to determine the parameters of the input shaping algorithm.