Modeling and Control of Shipmounted Cranes

Abstract

This thesis presents methods and theory for the mathematical modeling of crane-ship systems and controllers for ship-mounted cranes and crane loads. The thesis contains a collection of four journal papers and one conference paper. In addition, it contains an introduction providing the background for the papers. The thesis presents a method for deriving the equations of motion of a ship with a crane and crane load in wave motions. The method is a Newton-Euler formulation based on Kane’s equations of motion. The dynamic model takes into account that the motion of the crane influences the motion of the ship and vice versa. The wave motion of the ship is modeled with force RAO’s based on the JONSWAP wave spectrum. Two crane control systems are presented. One control system is a linear cascade controller with an inner loop designed to damp out the pendulum motions of the crane load, while the crane tip is controlled by an outer loop. The controller is designed such that the pendulum oscillation motion is controlled with a high bandwidth while the crane tip position is controlled with a lower bandwidth. Additionally, a crane control system is proposed where a crane load can follow a position trajectory with ultimately bounded pendulum motion. The proposed method consists of a Lyapunov-based damping controller in an inner loop, which is designed to damp out the pendulum motions of a crane load, and an outer loop where a nonlinear MPC (Model Predictive Controller) controls the position of the crane load. Two versions of the controller are proposed, one version where the crane tip moves only in the horizontal plane, and one version where the crane tip also moves in the vertical direction and the cable length is controlled. Furthermore, a method for measuring and estimating the pendulum motions of a crane load is presented. The proposed visual measurement system consists of three 2D cameras fixed on a crane king. The cameras are used for tracking two spherical markers attached to the cable and the pendulum oscillation angles are measured by using direct linear triangulation of the image points of the markers. An extended Kalman filter is applied to estimate the pendulum oscillation angles and rates. The thesis also presents a method for estimating the cable length from the crane tip to the center of gravity of the crane load. The proposed solution is a least-squares with projection method. The thesis includes experimental validation of the proposed controllers. Extensive laboratory experiments are performed to demonstrate the performance of the control systems and the methods for estimating the cable length and pendulum motions. Experimental comparisons with existing solutions for crane control are also included.