Research Papers

Second-Order Sliding Mode Control of a Perturbed-Crane

[+] Author and Article Information
Carlos Vázquez

Department of Applied Physics and Electronics,
Umeå University,
Umeå SE-901 87, Sweden
e-mail: carlos.vazquez@umu.se

Leonid Fridman

Department of Control Engineering and Robotics,
Universidad Nacional Autónoma de México,
Mexico City 04510, Mexico
e-mail: lfridman@unam.mx

Joaquin Collado

Department of Automatic Control CINVESTAV,
Av. IPN 2508,
Mexico City 07360, Mexico
e-mail: jcollado@ctrl.cinvestav.mx

Ismael Castillo

Department of Control Engineering and Robotics,
Universidad Nacional Autónoma de México,
Mexico City 04510, Mexico
e-mail: casism@gmail.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 10, 2014; final manuscript received March 24, 2015; published online April 24, 2015. Assoc. Editor: Hashem Ashrafiuon.

J. Dyn. Sys., Meas., Control 137(8), 081010 (Aug 01, 2015) (7 pages) Paper No: DS-14-1407; doi: 10.1115/1.4030253 History: Received October 10, 2014; Revised March 24, 2015; Online April 24, 2015

A five degrees-of-freedom overhead crane system affected by external perturbations is the topic of study. Existing methods just handle the unperturbed case or, in addition, the analysis is limited to three or two degrees-of-freedom. A wide range of processes cannot be restricted to these scenarios and this paper goes a step forward proposing a control solution for a five degrees-of-freedom system under the presence of matched and unmatched disturbances. The contribution includes a model description and a second-order sliding mode (SOSM) control design ensuring the precise trajectory tracking for the actuated variables and at the same time the regulation of the unactuated variables. Furthermore, the proposed approach is supported by the design of strong Lyapunov functions providing an estimation of the convergence time. Simulations and experiments, including a comparison with a proportional-integral-derivative (PID) controller, verified the advantages of the methodology.

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Abdel-Rahman, E. M., Nayfeh, A. H., and Masoud, Z. N., 2003, “Dynamics and Control of Cranes: A Review,” J. Vib. Control, 9(7), pp. 863–908. [CrossRef]
Ngo, Q. H., and Hong, K.-S., 2012, “Dynamics of the Container Crane on a Mobile Harbor,” Ocean Eng., 53, pp. 16–24. [CrossRef]
Tomczyk, J., Cink, J., and Kosucki, A., 2014, “Dynamics of an Overhead Crane Under a Wind Disturbance Condition,” Autom. Constr., 42, pp. 100–111. [CrossRef]
Sun, N., and Fang, Y., 2014, “Nonlinear Tracking Control of Underactuated Cranes With Load Transferring and Lowering: Theory and Experimentation,” Automatica, 50(9), pp. 2350–2357. [CrossRef]
Vázquez, C., Collado, J., and Fridman, L., 2014, “Super Twisting Control of a Parametrically Excited Overhead Crane,” J. Franklin Inst., 351(4), pp. 2283–2298. [CrossRef]
Vázquez, C., Collado, J., and Fridman, L., 2013, “Control of a Parametrically Excited Crane: A Vector Lyapunov Approach,” IEEE Trans. Control Syst. Technol., 21(6), pp. 2332–2340. [CrossRef]
Singhose, W., Porter, L., Keninson, M., and Kriikku, E., 2000, “Effects of Hoisting on the Input Shaping Control of Gantry Cranes,” Control Eng. Pract., 8(10), pp. 1159–1165. [CrossRef]
Blackburn, D., Lawrence, J., Danielson, J., Singhose, W., Kamoi, T., and Taura, A., 2010, “Radial-Motion Assisted Command Shapers for Nonlinear Tower Crane Rotational Slewing,” Control Eng. Pract., 18(5), pp. 523–531. [CrossRef]
Hong, K., Huh, C., and Hong, K.-S., 2003, “Command Shaping Control for Limiting the Transient Sway Angle of Crane Systems,” Int. J. Control Autom. Syst., 1(1), pp. 43–53.
Ngo, Q., and Hong, K.-S., 2009, “Skew Control of a Quay Container Crane,” J. Mech. Sci. Technol., 23(12), pp. 3332–3339. [CrossRef]
Shah, U., and Hong, K.-S., 2014, “Input Shaping Control of a Nuclear Power Plants Fuel Transport System,” Nonlinear Dyn., 77(4), pp. 1737–1748. [CrossRef]
Fang, Y., Ma, B., Wang, P., and Zhang, X., 2012, “A Motion Planing-Based Adaptive Control Method for an Underactuated Crane System,” IEEE Trans. Control Syst. Technol., 20(1), pp. 241–248.
Todd, M. D., Vohra, S. T., and Leban, F., 1997, “Dynamical Measurement of Ship Crane Load Pendulation,” Proceedings of Oceans MTS/IEEE, pp. 1230–1236.
Kim, Y.-S., Hong, K.-S., and Sul, S.-K., 2004, “Anti-Sway Control of Container Cranes: Inclinometer, Observer, and State Feedback,” Int. J. Control Autom. and Syst., 2(4), pp. 435–449.
Schaub, H., 2008, “Rate-Based Ship-Mounted Crane Payload Pendulation Control System,” Control Eng. Pract., 16(1), pp. 132–145. [CrossRef]
Björkbom, M., Nethi, S., Eriksson, L. M., and Jäntti, R., 2011, “Wireless Control System Design and Co-Simulation,” Control Eng. Pract., 19(9), pp. 1075–1086. [CrossRef]
Chwa, D., 2011, “Nonlinear Tracking Control of 3-D Overhead Cranes Against the Initial Swing Angle and the Variation of Payload Weight,” IEEE Trans. Control Syst. Technol., 17(4), pp. 876–883. [CrossRef]
Lee, H.-H., 2005, “Motion Planning for the Three-Dimensional Overhead-Cranes With High-Speed Load Hoisting,” Int. J. Control, 78(12), pp. 875–886. [CrossRef]
Park, H., Chwa, D., and Hong, K.-S., 2007, “A Feedback Linearization Control of Container Cranes: Varying Rope Length,” Int. J. Control Autom. Syst., 5(4), pp. 379–387.
Tuan, L. A., Lee, S.-G., Dang, V.-H., Moon, S., and Kim, B., 2013, “Partial Feedback Linearization Control of a Three-Dimensional Overhead Crane,” Int. J. Control Autom. Syst., 11(4), pp. 718–727. [CrossRef]
Utkin, V., Guldner, J., and Shi, J., 2009, Sliding Mode Control in Electromechanical Systems, 2nd ed., Taylor and Francis, London.
Levant, A., 1993, “Sliding Order and Sliding Accuracy in Sliding Mode Control,” Int. J. Control, 58(6), pp. 1247–1263. [CrossRef]
Levant, A., 2003, “High-Order Sliding Modes, Differentiation and Output Feedback Control,” Int. J. Control, 76(9), pp. 924–941. [CrossRef]
Shtessel, Y., Edwards, C., Fridman, L., and Levant, A., 2014, Sliding Mode Control and Observation, Birkhäuser, New York. [CrossRef]
Boiko, I., 2009, Discontinuous Control Systems: Frequency-Domain Analysis and Design, Birkhäuser, Boston.
Bartolini, G., Pisano, A., and Usai, E., 2002, “Second-Order Sliding-Mode Control of Container Cranes,” Automatica, 38(10), pp. 1783–1790. [CrossRef]
Tuan, L., Kim, J.-J., Lee, S.-G., Lim, T.-G., and Nho, L., 2014, “Second-Order Sliding Mode Control of a 3D Overhead Crane With Uncertain System Parameters,” Int. J. Precis. Eng. Manuf., 15(5), pp. 811–819. [CrossRef]
Ngo, Q. H., and Hong, K.-S., 2012, “Sliding-Mode Antisway Control of an Offshore Container Crane,” IEEE/ASME Trans. Mechatron., 17(2), pp. 201–209. [CrossRef]
Ngo, Q., and Hong, K.-S., 2012, “Adaptive Sliding Mode Control of Container Cranes,” IET Control Theory Appl., 6(5), pp. 662–668. [CrossRef]
Chen, W., and Saif, M., 2011, “Actuator Fault Diagnosis for a Class of Nonlinear Systems and Its Application to a Laboratory 3D Crane,” Automatica, 47(7), pp. 1435–1442. [CrossRef]
Castaños, F., and Fridman, L., 2006, “Analysis and Design of Integral Sliding Manifolds for Systems With Unmatched Perturbations,” IEEE Trans. Autom. Control, 51(5), pp. 853–858. [CrossRef]
Ferreira, A., Punta, E., Fridman, L., Bartolini, G., and Delprat, S., 2014, “Nested Backward Compensation of Unmatched Perturbations Via HOSM Observation,” J. Frank. Inst., 351(5), pp. 2397–2410. [CrossRef]
Ferreira, A., Bejarano, F. J., and Fridman, L., 2013, “Unmatched Uncertainties Compensation Based on High-Order Sliding Mode Observation,” Int. J. Robust Nonlinear Control, 23(7), pp. 754–764. [CrossRef]
Davila, J., 2013, “Exact Tracking Using Backstepping Control Design and High-Order Sliding Modes,” IEEE Trans. Autom. Control, 58(8), pp. 2077–2081. [CrossRef]
Lee, H.-H., 1998, “Modeling and Control of a Three-Dimensional Overhead Crane,” ASME J. Dyn. Syst. Meas. Control, 120(4), pp. 471–476. [CrossRef]
Spong, M., 1994, “Partial Feedback Linearization of Underactuated Mechanical Systems,” IEEE/RSJ/GI International Conference on Intelligent Robots and Systems, Munich, Sept. 12–16, Vol. 1, pp. 314–321. [CrossRef]
Weinmann, A., 1991, Uncertain Models and Robust Control, Springer-Verlag, New York. [CrossRef]
Utkin, V., 2013, “On Convergence Time and Disturbance Rejection of Super-Twisting Control,” IEEE Trans. Autom. Control, 58(8), pp. 2013–2017. [CrossRef]
Polyakov, A., and Poznyak, A., 2009, “Lyapunov Function Design for Finite-Time Convergence Analysis: Twisting Controller for Second-Order Sliding Mode Realization,” Automatica, 45(2), pp. 444–448. [CrossRef]
Moreno, J. A., 2012, “A Lyapunov Approach to Output Feedback Control Using Second-Order Sliding Modes,” IMA Journal of Math. Control Inf., 29(3), pp. 291–308. [CrossRef]
Polyakov, A., and Fridman, L., 2014, “Stability Notions and Lyapunov Functions for Sliding Mode Systems,” J. Frank. Inst., 351(4), pp. 1831–1865. [CrossRef]
Omar, H. M., and Nayfeh, A. H., 2005, “Gantry Crane Gain Scheduling Feedback Control With Friction Compensation,” J. Sound Vib., 281(1–2), pp. 1–20. [CrossRef]
Anderson, P. M., and Bose, A., 1983, “Stability Simulation of Wind Turbine Systems,” IEEE Trans. Power Appar. Syst., 102(12), pp. 3791–3795. [CrossRef]
Biagiotti, L., and Melchiorri, C., 2008, Trajectory Planning for Automatic Machines and Robots, Springer-Verlag, Berlin, p. 194.


Grahic Jump Location
Fig. 3

Simulation: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)

Grahic Jump Location
Fig. 4

Velocity estimation: trolley and rope length (m/s) and payload oscillations (deg/s) versus time (s)

Grahic Jump Location
Fig. 5

Experiment: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)

Grahic Jump Location
Fig. 6

Velocity estimation: trolley and rope length (m/s) and payload oscillations (deg/s) versus time (s)

Grahic Jump Location
Fig. 7

PID: trolley position and rope length (m), payload oscillations (deg), control actions (N) versus time (s)



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