Nonlinear Input-Shaping Controller for Quay-Side Container Cranes

Abstract

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.

A Smooth Wave‐Form Shaped Command with Flexible Maneuvering Time: Analysis and Experiments

“…The denominator equals zero for c = 2 or c = 2 3 . On the other hand, these values would set the numerator to zero, as can be determined by (17). Using l'Hôpital's rule for these two values of c, the limit of (15) approaches to constant values.…”

A Graphical Approach to Input-Shaping Control Design for Container Cranes With Hoist

“…The position vector to the center of mass of the payload of the constrained double pendulum is (8) Using (8), we write the kinetic and potential energies of the constrained double pendulum as (9) To derive the equation of motion that describes the time variation of , we substitute the constraints (6) and (7) into (9) and use the Euler-Lagrange equations given by (10) where . Substituting (9) in (10) In the above linear approximation, we have assumed that .…”

“…Daqaq et al [10] reported that for single-step input shaping, a controller based on a nonlinear frequency approximation of the payload oscillations results in a superior performance when compared to that based on a linear approximation. To check the sensitivity of the proposed double-step controller to frequency approximations, a comparison between the performance of the proposed controller using the linear and nonlinear frequency approximations is illustrated in Fig.…”

“…Daqaq et al [10], however, reported that an input-shaping controller based on a simple pendulum fails when applied to quay-side container cranes. In fact, results showed that such a controller may amplify residual oscillations to large magnitudes.…”

Research of Anti-Swing Control System of Tower Crane Based on EI Input Shaping

“…At present, researches about the bridge crane are popular [2][3][4][5][6][7], however the research of tower crane anti-swing is deficiency, especially during the rotation motion. This paper has constructed the simulation model of tower crane by using the Matlab software based on analysis of kinematics model, and analyzed the anti-swing benefit of the EI input shaper.…”