Noncolocated Passivity-Based Control of a 2 DOF Tower Crane with a Flexible Hoist Cable

This paper presents a dynamic model of a two-dimensional tower crane, including a Rayleigh-Ritz discretization of the crane's flexible hoist cable, and proposes a passivity-based control approach for payload trajectory tracking using the mu-tip rate. It is assumed that the crane's payload is massive, which allows for a decoupling of the rigid and elastic system dynamics. It is shown that the crane features a passive input-output mapping from modified force and torque inputs to a modified output formed using the position and velocity tracking errors of the payload. An input strictly passive derivative controller is proposed, which results in the velocity tracking error and the mu-tip position error of the payload converging to zero. A numerical example is presented that demonstrates the controller's performance when the payload is to track an agile trajectory.