Passivity-Based Adaptive Control of a 5-DOF Tower Crane

This paper presents a passivity-based adaptive control law for the payload trajectory tracking control of a three-dimensional tower crane with five degrees of freedom. The proposed method extends upon a two-dimensional tower crane control method in the literature by accounting for the additional nonlinearities that arise due to the rotation of the crane's jib. An adaptive control input ensures the tower crane features a passive input-output mapping. A novel approach is developed to bound the time derivative of the system's mass matrix, which is key to the proof of passivity. Robust closed-loop input-output stability is proven using the Passivity Theorem. Numerical simulations are performed, showing the effectiveness of the control law on the three-dimensional tower crane.