Payload trajectory tracking of a 5-DOF tower crane with a varying-length hoist cable: A passivity-based adaptive control approach

This paper presents a passivity-based adaptive control method for a 5 degree-of-freedom (DOF) tower crane that guarantees robust payload trajectory tracking. The 5-DOF tower crane system considered in this work features three actuated degrees of freedom (including a varying-length hoist cable) and two unactuated degrees of freedom in the hoist cable sway. The proposed controller includes an adaptive feedforward-like control input that is used to ensure that the tower crane features an output strictly passive input–output mapping. The Passivity Theorem is invoked to guarantee closed-loop input–output stability for any output strictly passive negative feedback controller. A novel approach is developed to bound the time derivative of the system's mass matrix, which is a critical aspect of the proof of passivity. Experimental tests are performed, which demonstrate the effectiveness of the control law on a small-scale three-dimensional tower crane.