Feedforward Control Law For A Shipboard Crane With Maryland Rigging System

A state-space model of the Maryland Rigging shipboard crane is derived from Newton's law under the assumptions of boom stiffness, fully controllable boom motion, no cable elasticity, no damping, and full control authority for changing the length of the rope. A chaotic rolling moment, with a dominant frequency of the same order as the resonance frequency of the shipboard crane, is applied to the ship as an external disturbance. The effect of this disturbance is studied. Since designing a controller by means of analytical methods for this system is too complex, we use a novel approach to this problem that focuses on the equilibrium point. By deriving the equations for calculating the position of the equilibrium point of the load in space, we change the problem to minimizing the change in the position of this point. A feedforward type controller is then designed as to keep the load closest to the “equilibrium point” for the actual roll angle. The controller seeks to suppress the load sway caused by the ship's rolling motion by changing the luffing angle while the friction in the pulley is assumed to be negligible. Changing the luffing angle seems to be the most effective control action in shipboard cranes. The feedforward gain is then optimized by numerical methods. The simulation results for this controller show a huge decrease in the sway magnitude as compared to the cases with no control. The roll angle, luffing angle of the boom, and the length of the rope are changed individually and then the related optimum feedforward gains are numerically obtained. Using these data, the mapping of the optimum gain based on these variables is derived. Scheduling the gain based on this mapping greatly improves the performance of the feedforward controller. This procedure can be repeated for similar applications.