控制设计起重机海上吊装作业

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控制设计起重机海上吊装作业470 M.P. Spathopoulos and D. Fragopoulos
In terms of measurements the instantaneous position of the load has to be
calculated from the measurements of ship motions， suspension line inclination
and boom angle， and from the geometry of the crane structure as well as the
length of the line. In terms of the ship motions heave， roll and pitch are
assumed measurable for this work.
Consider the 3D model of a pendulum consisting of a point mass attached to
a light inelastic cable with accelerating cable-top， moving in space. When this
model is simplified by the assumption of small angle oscillations， the dynamics
become decoupled so that the system may be described by the dynamics of
two mutually perpendicular vertical planes. The 3D motion of the pendulum
may then be described as the Cartesian combination of the motion in these
two planes. Now since our objective is to contain pendulation， it is indeed
desirable that the cable angle stays close to vertical， within a few degrees.
This observation justifies considering the pendulation problem in one plane
at a time.
In this paper we preset aspects of modeling the crane in both planes using two
type of models， the torque control model and the kinematic (angular velocity
control) model. Using the torque model we apply the Liapunov technique for
controlling the motion in the luffing plane. Linear control design methods，
namely LQG and GPC， are considered for the linearised system based on the
kinematic model. In terms of practical considerations， an important aspect
is the saturation of the actuator both in angle and angular velocity. Another
consideration is that the system needs to operate with different cable lengths
and， since we derive controllers for a fixed length， a scheduling scheme to
cover various cable lengths is needed. The linearised kinematic model can
be used in both planes and the controller is required to provide angular
velocity signals for the slewing and for the motion of the anti-pendulation
arm. Simulation results， design issues and comparisons are included.