Boundary control of container cranes from the perspective of controlling an axially moving string system

The control objectives in this paper are to move the load of a container crane to its target position and to suppress the transverse vibration of the load. Owing to the fact that the load is hoisted up and down, the crane is modeled as an axially moving string system. The dynamics of the moving string are derived using Hamilton’s principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, where the Lyapunov function candidate takes the form of the total mechanical energy of the system. The boundary control law utilizes the hoisting speed as well as the sway angle of the rope at the gantry side. Through experiment, the effectiveness of the proposed control law is demonstrated particularly in the lift-up process of the load.

[1]  Yoshiyuki Sakawa,et al.  Optimal control of container cranes , 1981, Autom..

[2]  Kamal A. F. Moustafa,et al.  Nonlinear Modeling and Control of Overhead Crane Load Sway , 1988 .

[3]  Kyoung Kwan Ahn,et al.  Robust force control of a hybrid actuator using quantitative feedback theory , 2007 .

[4]  Hyun Cheol Cho,et al.  Adaptive control and stability analysis of nonlinear crane systems with perturbation , 2008 .

[5]  Hyun Cheol Cho,et al.  Lyapunov theory based robust control of complicated nonlinear mechanical systems with uncertainty , 2008 .

[6]  F. Boustany,et al.  Adaptive control of non-completely controlled mechanical systems using dynamic feedback linearization and estimation design , 1992 .

[7]  Seong Wook Lee,et al.  An experimental analysis of the effect of wind load on the stability of a container crane , 2007 .

[8]  Brigitte d'Andréa-Novel,et al.  Feedback stabilization of a hybrid PDE-ODE system: Application to an overhead crane , 1994, Math. Control. Signals Syst..

[9]  H. Troger,et al.  Time optimal control of overhead cranes with hoisting of the load , 1987, Autom..

[10]  Lanfeng Yu.  Calculation method and control value of static stiffness of tower crane , 2008 .

[11]  K. Hong,et al.  Robust adaptive boundary control of an axially moving string under a spatiotemporally varying tension , 2004 .

[12]  W. D. Zhu.  CONTROL VOLUME AND SYSTEM FORMULATIONS FOR TRANSLATING MEDIA AND STATIONARY MEDIA WITH MOVING BOUNDARIES , 2002 .

[13]  Darren M. Dawson,et al.  Asymptotically Stabilizing Angle Feedback for a Flexible Cable Gantry Crane , 1999 .

[14]  Giorgio Bartolini,et al.  Second-order sliding-mode control of container cranes , 2002, Autom..

[15]  Brigitte d'Andréa-Novel,et al.  Exponential stabilization of an overhead crane with flexible cable via a back-stepping approach , 2000, Autom..

[16]  A. A. Renshaw,et al.  Energy and Conserved Functionals for Axially Moving Materials , 1998 .

[17]  K. Hong,et al.  A Feedback Linearization Control of Container Cranes: Varying Rope Length , 2007 .

[18]  Ho-Hoon Lee.  A new approach for the anti-swing control of overhead cranes with high-speed load hoisting , 2003 .

[19]  Jianqiang Yi,et al.  Dynamics and GA-Based Stable Control for a Class of Underactuated Mechanical Systems , 2008 .

[20]  Warren E. Dixon,et al.  Nonlinear coupling control laws for an underactuated overhead crane system , 2003 .

[21]  Fumitoshi Matsuno,et al.  Energy-based control of axially translating beams: varying tension, varying speed, and disturbance adaptation , 2005, IEEE Transactions on Control Systems Technology.

[22]  Weidong Zhu,et al.  Active Control of Translating Media With Arbitrarily Varying Length , 2001 .

[23]  Jean Lévine,et al.  Control of a Reduced Size Model of US Navy Crane Using Only Motor Position Sensors , 2001 .

[24]  Ö. Morgül,et al.  On the stabilization of a cable with a tip mass , 1994, IEEE Trans. Autom. Control..

[25]  Rong-Fong Fung,et al.  Exponential stabilization of an axially moving string by linear boundary feedback , 1999, Autom..

[26]  Keum-Shik Hong,et al.  Exponential Stabilization of an Axially Moving Tensioned Strip by Passive Damping and Boundary Control , 2002 .

[27]  Seonghun Park,et al.  Modeling of a hydraulic engine mount for active pneumatic engine vibration control using the extended Kalman filter , 2009 .

[28]  Rainer Nordmann,et al.  Active vibration μ-synthesis-control of a hydrostatically supported flexible beam , 2007 .

[29]  Dong-Seop Han,et al.  Structural optimization for a jaw using iterative Kriging metamodels , 2008 .

[30]  J. Levine,et al.  A simple output feedback PD controller for nonlinear cranes , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).