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Research Papers

Unscented Kalman Filter for Real-Time Load Swing Estimation of Container Cranes Using Rope Forces

[+] Author and Article Information
Edwin Kreuzer

Mechanics and Ocean Engineering,
Hamburg University of Technology,
Eissendorfer Straße 42,
Hamburg 21073, Germany
e-mail: kreuzer@tu-harburg.de

Marc-André Pick

Mechanics and Ocean Engineering,
Hamburg University of Technology,
Eissendorfer Straße 42,
Hamburg 21073, Germany
e-mail: pick@tu-harburg.de

Christian Rapp

Mechanics and Ocean Engineering,
Hamburg University of Technology,
Eissendorfer Straße 42,
Hamburg 21073, Germany
e-mail: christian.rapp@tu-harburg.de

Julian Theis

Control Systems,
Hamburg University of Technology,
Eissendorfer Straße 40,
Hamburg 21073, Germany
e-mail: julian.theis@tu-harburg.de

Throughout this article, vectors are considered to be n × 1 matrices and represented by bold identifiers (like n × m matrices), which is useful with regard to implementation.

System (6) with sensor (19) is observable with regard to nonlinear analysis. Refer to e.g., Ref. [12] for the formalism of nonlinear observability.

The square root, defined as C=P with CCT= P, of a positive definite covariance matrix Pxx is evaluated by, e.g., the Cholesky decomposition or the singular value decomposition.

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 13, 2012; final manuscript received January 26, 2014; published online April 4, 2014. Assoc. Editor: Rama K. Yedavalli.

J. Dyn. Sys., Meas., Control 136(4), 041009 (Apr 04, 2014) (9 pages) Paper No: DS-12-1080; doi: 10.1115/1.4026602 History: Received March 13, 2012; Revised January 26, 2014

The container crane represents the link between the containership and the port. It dictates the general conditions for the efficiency of container handling from the ship to the land and vice versa. While containers are handled by the crane, load swing reduces the rate of container turnover. In order to reduce load swing control systems are employed. Closed-loop control systems contain devices to track the position of the load with respect to the trolley's position. Accurate tracking of the load's motion during operation requires additionally installed sensors. Alternatively, the principle of state estimation can be employed. The observation of the motion of the container is carried out by a system model in parallel to the real system, taking into account the available rope force sensor information. Both, nonlinear system model and nonlinear sensor model are taken into consideration. An unscented Kalman filter is designed to estimate the states of the motion of the load. The observer is validated at the container crane test stand in order to provide accurate states for load swing control. Results are presented and discussed.

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References

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Julier, S., and Uhlmann, J. K., 1997, “A New Extension of the Kalman Filter to Nonlinear Systems,” Proceedings of AeroSense: The 11th International Symposium on Aerospace/Defense Sensing, Simulation and Controls, Multi Sensor Fusion, Tracking, and Resource Management, pp. 182–193.
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Kreuzer, E., and Rapp, C., 2010, “Modal Coupling for Active Damping of Load Swing of Container Cranes,” Proceedings in Applied Mathematics and Mechanics, Vol. 10, pp. 625–626.
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Theis, J., 2010, “Beobachterentwurf für einen räumlich pendelnden Körper mit steuerbarer Aufhängung,” Bachelor's thesis, Hamburg University of Technology, Hamburg, Germany, (in German).
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Luenberger, D. G., 1964, “Observing the State of a Linear System,” IEEE Trans. Mil. Electron., 8(2), pp. 74–80. [CrossRef]
Kreuzer, E., and Rapp, C., 2011, “Observer Design and Control of an Underactuated Crane System,” Proceedings of 2nd Workshop of Research Training Group Ports for Containerships of Future Generations, Publications of the Institute of Geotechnics and Construction Management of Hamburg University of Technology, pp. 229–241.
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Pick, M.-A., 2009, “Ein Beitrag zur numerischen und experimentellen Untersuchung extremer Schiffsbewegungen,” Ph.D. thesis, Hamburg University of Technology, Hamburg, Germany.
Bockstedte, A., and Kreuzer, E., 2005, “Hoisting Manipulation by Modal Coupling Control for Underactuated Cranes,” Vib. Control Nonlinear Mech. Struct., 1, pp. 121–130.
Sawodny, O., Aschemann, H., Lahres, S., and Hofer, E. P., 1999, “Advances in Manufacturing Systems,” Tracking Control for Automated Bridge Cranes, S.Tzafestas, ed., Springer-Verlag, London, pp. 309–320.

Figures

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Fig. 1

Container crane test stand

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Fig. 2

Trolley-load system

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Fig. 3

Control system with state estimation

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Fig. 4

Numerical results of ideal (left) and estimated (right) container deflection

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Fig. 8

Estimated and measured states of deflected container

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Fig. 5

Distribution of measurements

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Fig. 6

Sketch of camera plane at test stand

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Fig. 9

Error of estimated and measured states of deflected container

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Fig. 10

Estimated and measured states of deflected container with standard deviation

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Fig. 11

Estimated and measured states of deflected container with modal coupling control

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Fig. 12

Estimated and measured states of deflected container with tracking control

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Fig. 13

Estimated and measured states of deflected container with reference trajectory

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Fig. 14

Estimated and measured states of deflected container with reference trajectory and tracking control

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