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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

## Abstract

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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## Figures

Fig. 1

Container crane test stand

Fig. 2

Fig. 3

Control system with state estimation

Fig. 4

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

Fig. 5

Distribution of measurements

Fig. 6

Sketch of camera plane at test stand

Fig. 7

Camera plane

Fig. 8

Estimated and measured states of deflected container

Fig. 9

Error of estimated and measured states of deflected container

Fig. 10

Estimated and measured states of deflected container with standard deviation

Fig. 11

Estimated and measured states of deflected container with modal coupling control

Fig. 12

Estimated and measured states of deflected container with tracking control

Fig. 13

Estimated and measured states of deflected container with reference trajectory

Fig. 14

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

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