Input Shaped Control of a Gantry Crane with Inertial Payload

The focus of this work is on the development of a model for a gantry crane transporting a non point-mass payload such as pipes, where besides the payload swinging, includes the twisting motion also, which can be hazardous if not adequately controlled. Euler-Lagrange equations of motion are derived which permit accounting for payloads whose center of mass does not coincide with the hoisting cable attachment. Work-Energy principle is used to ensure that a collocated Proportional-Derivative (PD)-controller is stabilizing and an input shaper is used to shape the reference profile to permit minimal residual vibration of the payload.