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.

References

References
1.
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
.10.1177/1077546303009007007
2.
Ngo
,
Q. H.
, and
Hong
,
K.-S.
,
2012
, “
Dynamics of the Container Crane on a Mobile Harbor
,”
Ocean Eng.
,
53
, pp.
16
24
.10.1016/j.oceaneng.2012.06.013
3.
Tomczyk
,
J.
,
Cink
,
J.
, and
Kosucki
,
A.
,
2014
, “
Dynamics of an Overhead Crane Under a Wind Disturbance Condition
,”
Autom. Constr.
,
42
, pp.
100
111
.10.1016/j.autcon.2014.02.013
4.
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
.10.1016/j.automatica.2014.07.023
5.
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
.10.1016/j.jfranklin.2013.02.011
6.
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
.10.1109/TCST.2012.2233739
7.
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
.10.1016/S0967-0661(00)00054-X
8.
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
.10.1016/j.conengprac.2010.01.014
9.
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
.
10.
Ngo
,
Q.
, and
Hong
,
K.-S.
,
2009
, “
Skew Control of a Quay Container Crane
,”
J. Mech. Sci. Technol.
,
23
(
12
), pp.
3332
3339
.10.1007/s12206-009-1020-1
11.
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
.10.1007/s11071-014-1414-1
12.
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
.
13.
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
.
14.
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
.
15.
Schaub
,
H.
,
2008
, “
Rate-Based Ship-Mounted Crane Payload Pendulation Control System
,”
Control Eng. Pract.
,
16
(
1
), pp.
132
145
.10.1016/j.conengprac.2007.04.011
16.
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
.10.1016/j.conengprac.2011.05.012
17.
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
.10.1109/TCST.2008.2011367
18.
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
.10.1080/00207170500197571
19.
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
.
20.
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
.10.1007/s12555-012-9305-z
21.
Utkin
,
V.
,
Guldner
,
J.
, and
Shi
,
J.
,
2009
,
Sliding Mode Control in Electromechanical Systems
,
2nd ed.
,
Taylor and Francis
,
London
.
22.
Levant
,
A.
,
1993
, “
Sliding Order and Sliding Accuracy in Sliding Mode Control
,”
Int. J. Control
,
58
(
6
), pp.
1247
1263
.10.1080/00207179308923053
23.
Levant
,
A.
,
2003
, “
High-Order Sliding Modes, Differentiation and Output Feedback Control
,”
Int. J. Control
,
76
(
9
), pp.
924
941
.10.1080/0020717031000099029
24.
Shtessel
,
Y.
,
Edwards
,
C.
,
Fridman
,
L.
, and
Levant
,
A.
,
2014
,
Sliding Mode Control and Observation
,
Birkhäuser
,
New York
.10.1007/978-0-8176-4893-0
25.
Boiko
,
I.
,
2009
,
Discontinuous Control Systems: Frequency-Domain Analysis and Design
,
Birkhäuser
,
Boston
.
26.
Bartolini
,
G.
,
Pisano
,
A.
, and
Usai
,
E.
,
2002
, “
Second-Order Sliding-Mode Control of Container Cranes
,”
Automatica
,
38
(
10
), pp.
1783
1790
.10.1016/S0005-1098(02)00081-X
27.
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
.10.1007/s12541-014-0404-z
28.
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
.10.1109/TMECH.2010.2093907
29.
Ngo
,
Q.
, and
Hong
,
K.-S.
,
2012
, “
Adaptive Sliding Mode Control of Container Cranes
,”
IET Control Theory Appl.
,
6
(
5
), pp.
662
668
.10.1049/iet-cta.2010.0764
30.
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
.10.1016/j.automatica.2011.02.012
31.
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
.10.1109/TAC.2006.875008
32.
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
.10.1016/j.jfranklin.2013.12.011
33.
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
.10.1002/rnc.2795
34.
Davila
,
J.
,
2013
, “
Exact Tracking Using Backstepping Control Design and High-Order Sliding Modes
,”
IEEE Trans. Autom. Control
,
58
(
8
), pp.
2077
2081
.10.1109/TAC.2013.2246894
35.
Lee
,
H.-H.
,
1998
, “
Modeling and Control of a Three-Dimensional Overhead Crane
,”
ASME J. Dyn. Syst. Meas. Control
,
120
(
4
), pp.
471
476
.10.1115/1.2801488
36.
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
.10.1109/IROS.1994.407375
37.
Weinmann
,
A.
,
1991
,
Uncertain Models and Robust Control
,
Springer-Verlag
,
New York
.10.1007/978-3-7091-6711-3
38.
Utkin
,
V.
,
2013
, “
On Convergence Time and Disturbance Rejection of Super-Twisting Control
,”
IEEE Trans. Autom. Control
,
58
(
8
), pp.
2013
2017
.10.1109/TAC.2013.2251812
39.
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
.10.1016/j.automatica.2008.07.013
40.
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
.10.1093/imamci/dnr036
41.
Polyakov
,
A.
, and
Fridman
,
L.
,
2014
, “
Stability Notions and Lyapunov Functions for Sliding Mode Systems
,”
J. Frank. Inst.
,
351
(
4
), pp.
1831
1865
.10.1016/j.jfranklin.2014.01.002
42.
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
.10.1016/j.jsv.2004.01.037
43.
Anderson
,
P. M.
, and
Bose
,
A.
,
1983
, “
Stability Simulation of Wind Turbine Systems
,”
IEEE Trans. Power Appar. Syst.
,
102
(
12
), pp.
3791
3795
.10.1109/TPAS.1983.317873
44.
Biagiotti
,
L.
, and
Melchiorri
,
C.
,
2008
,
Trajectory Planning for Automatic Machines and Robots
,
Springer-Verlag
,
Berlin
, p.
194
.
You do not currently have access to this content.