Disturbances and uncertainties are unfavorable elements that always accompany industrial mechatronic systems including cranes. If not fully considered or properly dealt with, they would badly influence the control system performance and degrade the working efficiency. Though traditional sliding mode control (SMC) methods are powerful to address these issues, they are discontinuous and might bring potential damages to the actuating devices. In addition, most existing methods cannot involve such practical constraints as permitted swing amplitudes, maximum velocity, etc. To resolve these problems, we suggest a novel composite antiswing crane control scheme, which involves time-suboptimal analytical trajectory planning and continuous robust tracking control. More precisely, a new analytical suboptimal trajectory planning algorithm is presented, which can generate analytical swing-free smooth trajectories guaranteeing practical constraints. Then, we design a new nonlinear control law to make the crane follow the planned trajectories with continuous control efforts, ensuring stable asymptotic tracking in the presence of perturbations/uncertainties. As far as we know, this is the first crane control scheme that simultaneously achieves state-constrained time-suboptimal trajectory planning and robust control with continuous control efforts. We implement experiments to examine its practical control performance and robustness as well.

References

References
1.
Zhang
,
Y.
, and
Yi
,
J.
,
2010
, “
Dynamic Modeling and Balance Control of Human/Bicycle Systems
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
,
Montreal, Canada
, pp.
1385
1390
.
2.
Wang
,
Z.
,
Chen
,
Y. Q.
, and
Fang
,
N.
,
2004
, “
Minimum-Time Swing-Up of a Rotary Inverted Pendulum by Iterative Impulsive Control
,”
2004 American Control Conference
,
Boston, MA
, pp.
1335
1340
.
3.
Li
,
Y.
, and
Liu
,
Y.
,
2006
, “
Real-Time Tip-Over Prevention and Path Following Control for Redundant Nonholonomic Mobile Modular Manipulators Via Fuzzy and Neural-Fuzzy Approaches
,”
ASME J. Dyn. Syst., Meas., Control
,
128
(
4
), pp.
753
764
.
4.
Lai
,
X.-Z.
,
Pan
,
C.-Z.
,
Wu
,
M.
,
Yang
,
S. X.
, and
Cao
,
W.-H.
,
2014
, “
Control of an Underactuated Three-Link Passive-Active-Active Manipulator Based on Three Stages and Stability Analysis
,”
ASME J. Dyn. Syst., Meas., Control
,
137
(
2
), p.
021007
.
5.
Xin
,
X.
, and
Liu
,
Y.
,
2013
, “
A Set-Point Control for a Two-Link Underactuated Robot With a Flexible Elbow Joint
,”
ASME J. Dyn. Syst., Meas., Control
,
135
(
5
), p.
051016
.
6.
Muske
,
K. R.
,
Ashrafiuon
,
H.
,
Nersesov
,
S.
, and
Nikkhah
,
M.
,
2012
, “
Optimal Sliding Mode Cascade Control for Stabilization of Underactuated Nonlinear Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
134
(
2
), p.
021020
.
7.
Cornejo
,
C.
, and
Alvarez-Icaza
,
L.
,
2012
, “
Passivity Based Control of Under-Actuated Mechanical Systems With Nonlinear Dynamic Friction
,”
J. Vib. Control
,
18
(
7
), pp.
1025
1042
.
8.
Morel
,
Y.
, and
Leonessa
,
A.
,
2003
, “
Adaptive Nonlinear Tracking Control of an Underactuated Nonminimum Phase Model of a Marine Vehicle Using Ultimate Boundedness
,”
IEEE Conference on Decision and Control
,
Maui, HI
, pp.
3097
3102
.
9.
Papadopoulos
,
E.
,
Fragkos
,
I.
, and
Tortopidis
,
I.
,
2007
, “
On Robot Gymnastics Planning With Non-Zero Angular Momentum
,”
IEEE International Conference on Robotics and Automation
,
Roma, Italy
, pp.
1443
1448
.
10.
Vaughan
,
J.
,
Yano
,
A.
, and
Singhose
,
W.
,
2008
, “
Comparison of Robust Input Shapers
,”
J. Sound Vib.
,
315
(
4–5
), pp.
797
815
.
11.
Sorensen
,
K.
, and
Singhose
,
W.
,
2008
, “
Command-Induced Vibration Analysis Using Input Shaping Principles
,”
Automatica
,
44
(
9
), pp.
2392
2397
.
12.
Singhose
,
W.
,
2009
, “
Command Shaping for Flexible Systems: A Review of the First 50 Years
,”
Int. J. Precis. Eng. Manuf.
,
10
(
4
), pp.
153
168
.
13.
Sun
,
N.
,
Fang
,
Y.
,
Zhang
,
X.
, and
Yuan
,
Y.
,
2012
, “
Transportation Task-Oriented Trajectory Planning for Underactuated Overhead Cranes Using Geometric Analysis
,”
IET Control Theory Appl.
,
6
(
10
), pp.
1410
1423
.
14.
Uchiyama
,
N.
,
Ouyang
,
H.
, and
Sano
,
S.
,
2013
, “
Simple Rotary Crane Dynamics Modeling and Open-Loop Control for Residual Load Sway Suppression by Only Horizontal Boom Motion
,”
Mechatronics
,
23
(
8
), pp.
1223
1236
.
15.
Garrido
,
S.
,
Abderrahim
,
M.
,
Giménez
,
A.
,
Diez
,
R.
, and
Balaguer
,
C.
,
2008
, “
Anti-Swinging Input Shaping Control of an Automatic Construction Crane
,”
IEEE Trans. Autom. Sci. Eng.
,
5
(
3
), pp.
549
557
.
16.
Huang
,
J.
,
Xie
,
X.
, and
Liang
,
Z.
,
2015
, “
Control of Bridge Cranes With Distributed-Mass Payload Dynamics
,”
IEEE/ASME Trans. Mechatronics
,
20
(
1
), pp.
481
486
.
17.
Sun
,
N.
,
Fang
,
Y.
,
Zhang
,
Y.
, and
Ma
,
B.
,
2012
, “
A Novel Kinematic Coupling-Based Trajectory Planning Method for Overhead Cranes
,”
IEEE/ASME Trans. Mechatronics
,
17
(
1
), pp.
166
173
.
18.
Fliess
,
M.
,
Lévine
,
J.
, and
Rouchon
,
P.
,
1993
, “
Generalized State Variable Representation for a Simplified Crane Description
,”
Int. J. Control
,
58
(
2
), pp.
277
283
.
19.
Fliess
,
M.
,
Lévine
,
J.
,
Martin
,
P.
, and
Rouchon
,
P.
,
1995
, “
Flatness and Defect of Non-Linear Systems: Introductory Theory and Examples
,”
Int. J. Control
,
61
(
6
), pp.
1327
1361
.
20.
Kolar
,
B.
, and
Schlacher
,
K.
,
2011
, “
Flatness Based Control of a Gantry Crane
,”
9th IFAC Symposium on Nonlinear Control Systems
,
Toulouse, France
, pp.
487
492
.
21.
Boschetti
,
G.
,
Caracciolo
,
R.
,
Richiedei
,
D.
, and
Trevisani
,
A.
,
2014
, “
A Non-Time Based Controller for Load Swing Damping and Path-Tracking in Robotic Cranes
,”
J. Intell. Rob. Syst.
,
76
(
2
), pp.
201
217
.
22.
Wang
,
Z.
, and
Surgenor
,
B. W.
,
2004
, “
A Problem With the LQ Control of Overhead Cranes
,”
ASME J. Dyn. Syst., Meas., Control
,
128
(
2
), pp.
436
440
.
23.
Van den Broeck
,
L.
,
Diehl
,
M.
, and
Swevers
,
J.
,
2011
, “
A Model Predictive Control Approach for Time Optimal Point-to-Point Motion Control
,”
Mechatronics
,
21
(
7
), pp.
1203
1212
.
24.
Raimúndez
,
C.
,
Barreiro
,
A.
, and
Villaverde
,
A. F.
,
2011
, “
Damping Injection by Reset Control
,”
ASME J. Dyn. Syst., Meas., Control
,
134
(
2
), p.
024504
.
25.
Yu
,
W.
,
Moreno-Armendariz
,
M. A.
, and
Rodriguez
,
F. O.
,
2011
, “
Stable Adaptive Compensation With Fuzzy CMAC for an Overhead Crane
,”
Inf. Sci.
,
181
(
21
), pp.
4895
4907
.
26.
Lee
,
L.-H.
,
Huang
,
C.-H.
,
Ku
,
S.-C.
,
Yang
,
Z.-H.
, and
Chang
,
C.-Y.
,
2014
, “
Efficient Visual Feedback Method to Control a Three-Dimensional Overhead Crane
,”
IEEE Trans. Ind. Electron.
,
61
(
8
), pp.
4073
4083
.
27.
O'Connor
,
W. J.
,
2003
, “
A Gantry Crane Problem Solved
,”
ASME J. Dyn. Syst., Meas., Control
,
125
(
4
), pp.
569
576
.
28.
Sarras
,
I.
,
Kazi
,
F.
,
Ortega
,
R.
, and
Banavar
,
R.
,
2010
, “
Total Energy-Shaping IDA-PBC Control of the 2D-Spidercrane
,”
IEEE Conference on Decision and Control
,
Atlanta, GA
, pp.
1122
1127
.
29.
Sun
,
N.
, and
Fang
,
Y.
,
2012
, “
New Energy Analytical Results for the Regulation of Underactuated Overhead Cranes: An End-Effector Motion-Based Approach
,”
IEEE Trans. Ind. Electron.
,
59
(
12
), pp.
4723
4734
.
30.
Liu
,
R.
,
Li
,
S.
, and
Ding
,
S.
,
2012
, “
Nested Saturation Control for Overhead Crane Systems
,”
Trans. Inst. Meas. Control
,
34
(
7
), pp.
862
875
.
31.
Yang
,
J. H.
, and
Shen
,
S. H.
,
2011
, “
Novel Approach for Adaptive Tracking Control of a 3-D Overhead Crane System
,”
J. Intell. Rob. Syst.
,
62
(
1
), pp.
59
80
.
32.
Solihin
,
M.
I
,
Wahyudi
, and
Legowo
,
A.
,
2010
, “
Fuzzy-Tuned PID Anti-Swing Control of Automatic Gantry Crane
,”
J. Vib. Control
,
16
(
1
), pp.
127
145
.
33.
Masoud
,
Z. N.
, and
Nayfeh
,
A. H.
,
2003
, “
Sway Reduction on Container Cranes Using Delayed Feedback Controller
,”
Nonlinear Dyn.
,
34
(
3–4
), pp.
347
358
.
34.
He
,
W.
, and
Ge
,
S. S.
,
2014
, “
Adaptive Control of a Flexible Crane System With the Boundary Output Constraint
,”
IEEE Trans. Ind. Electron.
,
61
(
8
), pp.
4126
4133
.
35.
Sawodny
,
O.
,
Aschemann
,
H.
, and
Lahres
,
S.
,
2002
, “
An Automated Gantry Crane as a Large Workspace Robot
,”
Control Eng. Pract.
,
10
(
12
), pp.
1323
1338
.
36.
Schindele
,
D.
, and
Aschemann
,
H.
,
2011
, “
Fast Nonlinear MPC for an Overhead Travelling Crane
,”
18th IFAC World Congress
,
Milano, Italy
, pp.
7963
7968
.
37.
Trabia
,
M. B.
,
Renno
,
J. M.
, and
Moustafa
,
K. A. F.
,
2008
, “
Generalized Design of an Anti-Swing Fuzzy Logic Controller for an Overhead Crane With Hoist
,”
J. Vib. Control
,
14
(
3
), pp.
319
346
.
38.
Sano
,
H.
,
Sato
,
K.
,
Ohishi
,
K.
, and
Miyazaki
,
T.
,
2012
, “
Robust Design of Vibration Suppression Control System for Crane Using Sway Angle Observer Considering Friction Disturbance
,”
IEEJ Trans. Ind. Appl.
,
132
(
3
), pp.
357
365
.
39.
Blajer
,
W.
, and
Kołodziejczyk
,
K.
,
2011
, “
Improved DAE Formulation for Inverse Dynamics Simulation of Cranes
,”
Multibody Syst. Dyn.
,
25
(
2
), pp.
131
141
.
40.
Chen
,
W.
, and
Saif
,
M.
,
2008
, “
Output Feedback Controller Design for a Class of MIMO Nonlinear Systems Using High-Order Sliding-Mode Differentiators With Application to a Laboratory 3-D Crane
,”
IEEE Trans. Ind. Electron.
,
55
(
11
), pp.
3985
3996
.
41.
Sun
,
N.
,
Fang
,
Y.
, and
Zhang
,
X.
,
2013
, “
Energy Coupling Output Feedback Control of 4-DOF Underactuated Cranes With Saturated Inputs
,”
Automatica
,
49
(
5
), pp.
1318
1325
.
42.
Zhao
,
Y.
, and
Gao
,
H.
,
2012
, “
Fuzzy-Model-Based Control of an Overhead Crane With Input Delay and Actuator Saturation
,”
IEEE Trans. Fuzzy Syst.
,
20
(
1
), pp.
181
186
.
43.
Yu
,
X.
, and
Kaynak
,
O.
,
2009
, “
Sliding-Mode Control With Soft Computing: A Survey
,”
IEEE Trans. Ind. Electron.
,
56
(
9
), pp.
3275
3285
.
44.
Xu
,
J.-X.
,
Guo
,
Z.-Q.
, and
Lee
,
T. H.
,
2014
, “
Design and Implementation of Integral Sliding Mode Control on an Underactuated Two-Wheeled Mobile Robot
,”
IEEE Trans. Ind. Electron.
,
61
(
7
), pp.
3671
3681
.
45.
Liu
,
R.
, and
Li
,
S.
,
2014
, “
Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems
,”
J. Optim. Theory Appl.
,
161
(
3
), pp.
877
904
.
46.
Wang
,
W.
,
Yi
,
J.
,
Zhao
,
D.
, and
Liu
,
D.
,
2004
, “
Design of a Stable Sliding-Mode Controller for a Class of Second-Order Underactuated Systems
,”
IEE Control Theory Appl.
,
151
(
6
), pp.
683
690
.
47.
Bartolini
,
G.
,
Pisano
,
A.
, and
Usai
,
E.
,
2002
, “
Second-Order Sliding-Mode Control of Container Cranes
,”
Automatica
,
38
(
10
), pp.
1783
1790
.
48.
Lee
,
H. H.
,
2004
, “
A New Design Approach for the Anti-Swing Trajectory Control of Overhead Cranes With High-Speed Hoisting
,”
Int. J. Control
,
77
(
10
), pp.
931
940
.
49.
Lee
,
H. H.
,
Liang
,
Y.
, and
Segura
,
D.
,
2006
, “
A Sliding-Mode Antiswing Trajectory Control for Overhead Cranes With High-Speed Load Hoisting
,”
ASME J. Dyn. Syst., Meas., Control
,
128
(
4
), pp.
842
845
.
50.
Ngo
,
Q. H.
, and
K.-S.
Hong
,
2012
, “
Sliding-Mode Antisway Control of an Offshore Container Crane
,”
IEEE/ASME Trans. Mechatronics
,
17
(
2
), pp.
201
209
.
51.
Ngo
,
Q. H.
, and
K.-S.
Hong
,
2012
, “
Adaptive Sliding Mode Control of Container Cranes
,”
IET Control Theory Appl.
,
6
(
5
), pp.
662
668
.
52.
M.-S.
Park
,
Chwa
,
D.
, and
Eom
,
M.
,
2014
, “
Adaptive Sliding-Mode Antisway Control of Uncertain Overhead Cranes With High-Speed Hoisting Motion
,”
IEEE Trans. Fuzzy Syst.
,
22
(
5
), pp.
1262
1271
.
53.
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
.
54.
Tuan
,
L. A.
,
Lee
,
S.-G.
,
Ko
,
D. H.
, and
Nho
,
L. C.
,
2014
, “
Combined Control With Sliding Mode and Partial Feedback Linearization for 3D Overhead Cranes
,”
Int. J. Robust Nonlinear Control
,
24
(
18
), pp.
3372
3386
.
55.
Almutairi
,
N. B.
, and
Zribi
,
M.
,
2009
, “
Sliding Mode Control of a Three-Dimensional Overhead Crane
,”
J. Vib. Control
,
15
(
11
), pp.
1679
1730
.
56.
Moreno
,
J. A.
, and
Osorio
,
M.
,
2012
, “
Strict Lyapunov Functions for the Super-Twisting Algorithm
,”
IEEE Trans. Autom. Control
,
57
(
4
), pp.
1035
1040
.
57.
Shevitz
,
D.
, and
Paden
,
B.
,
1994
, “
Lyapunov Stability Theory of Nonsmooth Systems
,”
IEEE Trans. Autom. Control
,
39
(
9
), pp.
1910
1914
.
58.
Makkar
,
C.
,
Hu
,
G.
,
Sawyer
,
W. G.
, and
Dixon
,
W. E.
,
2007
, “
Lyapunov-Based Tracking Control in the Presence of Uncertain Nonlinear Parameterizable Friction
,”
IEEE Trans. Autom. Control
,
52
(
10
), pp.
1988
1994
.
59.
Xian
,
B.
,
Dawson
,
D.
,
de Queiroz
,
M. S.
, and
Chen
,
J.
,
2004
, “
A Continuous Asymptotic Tracking Control Strategy for Uncertain Nonlinear Systems
,”
IEEE Trans. Autom. Control
,
49
(
7
), pp.
1206
1211
.
60.
Dupree
,
K.
,
Patre
,
P. M.
,
Wilcox
,
Z. D.
, and
Dixon
,
W. E.
,
2011
, “
Asymptotic Optimal Control of Uncertain Nonlinear Euler–Lagrange Systems
,”
Automatica
,
47
(
1
), pp.
99
107
.
61.
Slotine
,
J. J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
62.
Filippov
,
A. F.
,
1964
, “
Differential Equations With Discontinuous Right-Hand Side
,”
Am. Math. Soc. Transl.
,
42
(
2
), pp.
199
231
.
63.
Fischer
,
N.
,
Kamalapurkar
,
R.
, and
Dixon
,
W. E.
,
2013
, “
LaSalle-Yoshizawa Corollaries for Nonsmooth Systems
,”
IEEE Trans. Autom. Control
,
58
(
9
), pp.
2333
2338
.
64.
Paden
,
B.
, and
Sastry
,
S.
,
1987
, “
A Calculus for Computing Filippov's Differential Inclusion With Application to the Variable Structure Control of Robot Manipulators
,”
IEEE Trans. Circuits Syst.
,
CAS-34
(
1
), pp.
73
82
.
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