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.
Propositional dynamic logic (PDL) provides a natural setting for semantics of means-end relations involving non-determinism, but such models do not include probabilistic features common to much practical reasoning involving means and ends. We alter the semantics for PDL by adding probabilities to the transition systems and interpreting dynamic formulas α ϕ as fuzzy predicates about the reliability of α as a means to ϕ. This gives our semantics a measure of efficacy for means-end relations.
Designing an effective controller for shipboard cranes by means of analytical methods is too complex, because of their highly nonlinear equations of motion.In this work we formulate the swinging suppression problem for a new structure of shipboard crane designed by Maryland research group. Then a feedforward control law to greatly decrease the load sway will be introduced. This feedforward control counteracts the effect of ship rolling on load sway based on measurements of ship rolling angle at each instant. The measurement errors and also sways caused by other disturbance sources are not taken into account by this feedforward control. Next, we describe the Model Predictive Control (MPC) based nonlinear controller that is designed for this problem. The proposed controller uses an optimizer to find an open loop solution at each sampling interval for a given horizon, based on a model of the plant and an appropriately defined objective function. MPC acts as a feedback control that will compensate for shortcomings of the feedforward control. Details of the controller, the design process and the simulation results are presented.
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