The wave compensation system can be very useful in several naval applications. It can greatly reduce the relative irregular motion between the two ships when replenishment operations are performed, or between the ship and the offshore platform, which is caused by the waves. It is widely used in offshore operations, offshore cargo transfer, oil and gas exploitation, deep-sea mining, the hoisting and recovery of submersibles, etc. However, when a crane is used in a ship or moving platform, due to the influence of the hull, the crane load movement is similar to a space ball pendulum, which causes the heave displacement to show significant nonlinear motion characteristics. Moreover, the time delay of the detection mechanism and control error could result in untimely compensation, which deteriorates the performance. Consequently, this paper proposes one advanced prediction compensation method, namely Particle Swarm Optimized Model Predictive Trajectory Path controller (PSO−MPTP), which can improve the heave compensation performance. This method, which is based on Model Predictive Control (MPC), is firstly applied to the position servo system and takes into account the heave prediction and control effects simultaneously. The heave displacement of the crane load could be predicted in multiple steps in advance and used as the input of the position loop of the compensation machine. The achieved simulations show that the proposed controller has better prediction ability, higher control accuracy, and stronger robustness.
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