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 μ-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 μ-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.