Nonlinear input-shaping controller for quay-side container cranes

Mohammed F. Daqaq, Ziyad N. Masoud

Research output: Contribution to journalArticlepeer-review


Input-shaping is one of the most practical open-loop control strategies for gantry cranes, especially those having predefined paths and operating at constant cable lengths. However, when applied to quay-side container cranes, its performance is far from satisfactory. A major source of the poor performance can be linked to the significant difference between the gantry crane model and the quay-side container crane model. Gantry cranes are traditionally modeled as a simple pendulum. However, a quay-side container crane has a multi-cable hoisting mechanism. In this paper, a two-dimensional four-bar-mechanism model of a container crane is developed. For the purpose of controller design, the crane model is reduced to a double pendulum with two fixed-length links and a kinematic constraint. The method of multiple scales is used to develop a nonlinear approximation of the oscillation frequency of the simplified model. The resulting frequency approximation is used to determine the switching times for a bang-off-bang input-shaping controller. The performance of the controller is numerically simulated on the full model of the container crane, and is compared to the performance of similar controllers based on a nonlinear frequency approximation of a simple pendulum and a linear frequency approximation of a constraint double pendulum. Results demonstrate a superior performance of the controller based on the nonlinear frequency approximation of the constraint double pendulum. The effect of the oscillation frequency on the controller performance is investigated by varying the model's frequency around the design value. Simulations revealed that the performance of the controller suffers serious degradation due to small changes in the model frequency. To alleviate the shortcomings of the input-shaping controller, a delayed-position feedback controller is successfully applied at the end of each transfer maneuver to eliminate residual oscillations without affecting the commands of the input-shaping controller.

Original languageEnglish (US)
Pages (from-to)149-170
Number of pages22
JournalNonlinear Dynamics
Issue number1-2
StatePublished - Jul 2006


  • Container cranes
  • Delayed-position feedback control
  • Input-shaping
  • Nonlinear stability
  • Sway control

ASJC Scopus subject areas

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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