Model Predictive Control of Gantry Crane with Input Nonlinearity Compensation

Authors: Steven W. Su , Hung Nguyen, Rob Jarman, Joe Zhu, David Lowe, Peter McLean, Shoudong Huang, Nghia T. Nguyen, Russell Nicholson, Kaili Weng

Abstract:

This paper proposed a nonlinear model predictive control (MPC) method for the control of gantry crane. One of the main motivations to apply MPC to control gantry crane is based on its ability to handle control constraints for multivariable systems. A pre-compensator is constructed to compensate the input nonlinearity (nonsymmetric dead zone with saturation) by using its inverse function. By well tuning the weighting function matrices, the control system can properly compromise the control between crane position and swing angle. The proposed control algorithm was implemented for the control of gantry crane system in System Control Lab of University of Technology, Sydney (UTS), and achieved desired experimental results.

Keywords: Model Predictive Control, Control constraints, Input nonlinearity compensation, Overhead gantry crane.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1059665

References:

[1] E. Arnold, O. Sawodny, J. Neupert, and K. Schneider. Anti-sway system for boom cranes based on a model predictive control approach. IEEE International Conference on Mechatronics and Automation; Piscataway, NJ, 3:1533--1538, 2005.
[2] Er-Wei Bai. Adaptive dead zone inverses for possibly nonlinear control systems. In Gang Tao and Frank L. Lewis, editors, Adaptive Control of Nonsmooth Dynamic Systems, pages 31--47. Springer, 2001.
[3] Alberto Bemporad, Manfred Morari, and N. Lawrence Ricker. Model Predictive Control Toolbox. The MathWorks, Inc, 1994.
[4] C.E. Garcia, D.M. Prett, and M. Morari. Model predictive control: Theory and practice-a survey. Automatica, 25:335--348, 1989.
[5] A. MacFarlane. Dynamical System Models. Harrap, London, 1970.
[6] L.F. Mendonc, J.M. Sousa, and J.M.G. Sa da Costa. Optimization problems in multivariable fuzzy predictive control. Int. J. Approximate Reasoning, 36:199--221, 2004.
[7] H.T. Nguyen. State-variable feedback controller for an overhead crane. Journal of Electrical and Electronics Engineering, 14(2):75--84, 1994.
[8] H.M. Omar and A.H. Nayfeh. Gantry cranes gain scheduling feedback control with friction compensation. Journal of Sound and Vibration, 281:1--20, 2005.
[9] A.J. Ridout. Anti-swing control of the overhead crane using linear feedback. Journal of Electrical and Electronics Engineering, 9(1/2):17--26, 1989.
[10] A.J. Ridout. Variable damped control of the overhead crane. IECON Proceedings, IEEE, Vol. 2, Los Alamitos, CA, pages 263--269, 1989.
[11] J.A. Rossiter. Model-based Predictive Control. CRC PRESS, London, 2003.
[12] Rastko R. Selmic and Frank L. Lewis. Deadzone compensation in motion control systems using augmented multilayer neural networks. In Gang Tao and Frank L. Lewis, editors, Adaptive Control of Nonsmooth Dynamic Systems, pages 49--81. Springer, 2001.
[13] Gang Tao and Petar V. Kokotovic. Adaptive control of systems with actuator and sensor nonlinearities. Wiley, New York, 1996.
[14] Jung Hua Yang and Kuang Shine Yang. Adaptive coupling control for overhead crane systems. Mechatronics, 17(2-3):143--152, 2007.
[15] J. Yu, F.L. Lewis, and T. Huang. Nonlinear feedback control of a gantry crane. Proc. American Control. Conf., Seattle, pages 4310--4315, June 1995.