The modeling and control of a horizontally slewing inextensible Timoshenko beam, taking into account the centrifugal stiffening effect and a tip payload, are considered. Partial differential equations of motion and orthogonality conditions for the constrained modes are derived. A finite dimensional dynamic model simplified by using the orthogonality conditions is obtained. To achieve the joint angle trajectory tracking with simultaneous suppression of elastic vibrations, a nonlinear controller is designed using input-output linearization and elastic-mode stabilization. A sufficient condition for asymptotic stability of the closed-loop system is established. Numerical examples with the role of slenderness ratio of the slewing beam highlighted are presented to demonstrate the effectiveness of the proposed control strategy.

1.
Akhrif, O., Blankenship, G. L., and Bennett, W. H., 1989, “Robust Control for Rapid Reorientation of Flexible Structures,” Proc. 1989 American Control Conference, Pittsburgh, PA, June, pp. 1142–1147.
2.
Arai, F., Fukuda, T., Hosogai, H., and Yajima, N., 1989, “Control of Bending-Torsion Coupled Vibrations of Flexible Structures,” Distributed Parameter Systems: Modeling and Simulation, T. Futagami, S. G. Tzafestas and Y. Sunahara, eds., Elsevier Science Publishers, North-Holland, pp. 411–416.
3.
Barbieri
E.
, and
O¨zgu¨ner
U.
,
1988
, “
Unconstrained and Constrained Mode Expansions for a Flexible Slewing Link
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT AND CONTROL
, Vol.
110
, No.
4
, pp.
416
421
.
4.
Baruh
H.
, and
Tadikonda
S. S. K.
,
1989
, “
Issues in the Dynamics and Control of Flexible Robot Manipulators
,”
J. of Guidance, Control, and Dynamics
, Vol.
12
, No.
5
, pp.
659
671
.
5.
Bayo
E.
,
1989
, “
Timoshenko Versus Bernoulli-Euler Beam Theories for the Inverse Dynamics of Flexible Robots
,”
Int. J. of Robotics and Automations
, Vol.
4
, No.
1
, pp.
53
56
.
6.
Bennett, W. H., Akhrif, O., and Dwyer, T. A. W., 1990, “Robust Nonlinear Control of Flexible Space Structures,” Proc. 1990 American Control Conference, San Diego, CA, May, pp. 2430–2436.
7.
Book, W. J., 1990, “Modeling, Design, and Control of Flexible Manipulator Arms: A Tutorial Review,” Proc. 29th Conf. on Decision and Control, Honolulu, Hawaii, Dec. pp. 500–506.
8.
Boutaghou
Z. E.
, and
Erdman
A. G.
,
1991
, “
A Unified Approach for the Dynamics of Beams Undergoing Arbitrary Spatial Motion
,”
ASME Journal of Vibration and Acoustics
, Vol.
113
, pp.
494
502
.
9.
Bruch
J. C.
, and
Mitchell
T. P.
,
1987
, “
Vibrations of a Mass-Loaded Clamped-Free Timoshenko Beam
,”
J. of Sound and Vibration
, Vol.
114
, pp.
341
345
.
10.
Choura
S.
,
Jayasuriya
S.
, and
Medick
M. A.
,
1991
, “
On the Modeling and Open-Loop Control of a Rotating Thin Flexible Beam
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, No.
1
, pp.
26
33
.
11.
Das
A.
, and
Singh
S. N.
,
1990
, “
Dual Mode Control of an Elastic Robotic Arm: Nonlinear Inversion and Stabilization by Pole Assignment
,”
Int J. Systems Sci.
, Vol.
21
, No.
7
, pp.
1185
1204
.
12.
De Luca
A.
,
Lucibello
P.
, and
Ulivi
G.
,
1989
, “
Inversion Techniques for Trajectory Control of Flexible Robot Arms
,”
J. of Robotic Systems
, Vol.
6
, No.
4
, pp.
325
344
.
13.
De Luca
A.
, and
Siciliano
B.
,
1989
, “
Trajectory Control of a Nonlinear One-Link Flexible Arm
,”
Int. J. Control
, Vol.
50
, No.
5
, pp.
1699
1715
.
14.
De Schutter, J., Van Brussel, H., Adams, N., Froment, A., and Faillot, J. L., 1988, “Control of Flexible Robots Using Generalized Nonlinear Decoupling,” 2nd IFAC Symp. on robot Control (Syroco ’88), Karlsruhe, FRG, Dec. pp. 113–118.
15.
Franklin, G. F., Powell, J. D., and Emami-Naeini, A., 1991, Feedback Control of Dynamic Systems, 2nd edition, Addison Wesley, Reading, Mass., pp. 388–390.
16.
Ghaemmaghami
P.
, and
Juang
J. N.
,
1989
, “
A Controller Design for Multibody Large Angle Maneuvers
,”
Mech. Struct. & Mach.
, Vol.
17
, pp.
33
52
.
17.
Hanagud
S.
, and
Sarkar
S.
,
1989
, “
Problem of the Dynamics of a Cantilever Beam Attached to a Moving Base
,”
J. of Guidance, Control, and Dynamics
, Vol.
10
, No.
3
, pp.
438
441
.
18.
Kane
T. R.
,
Ryan
R. R.
, and
Bannerjee
A. K.
,
1987
, “
Dynamics of a Cantilever Beam Attached to a Moving Base
,”
J. of Guidance, Control, and Dynamics
, Vol.
10
, pp.
139
151
.
19.
Kwatny, H. G., and Bennett, W. H., 1988, “Nonlinear Dynamics and Control Issues for Flexible Space Platforms,” Proc. 27th IEEE Conf. on Decision and Control, Austin, Texas, Dec., pp. 1702–1706.
20.
Magrab, E. B., 1979, Vibrations of Elastic Structural Members, Sijthoff and Noordhoff, the Netherlands, pp. 210–213.
21.
Meirovitch, L., 1967, Analytical Methods in Vibrations, MacMillan, Toronto, Canada, pp. 443–445.
22.
Naganathan
G.
, and
Soni
A. H.
,
1987
, “
Coupling Effects of Kinematics and Flexibility in Manipulators
,”
The Int. J. of Robotics Research
, Vol.
6
, No.
1
, pp.
75
85
.
23.
Padilla
C. E.
, and
von Flotow
A. H.
,
1992
, “
Nonlinear Strain-Displacement Relations and Flexible Multibody Dynamics
,”
J. of Guidance, Control, and Dynamics
, Vol.
15
, No.
1
, pp.
128
136
.
24.
Patel
R. V.
,
Toda
M.
, and
Sridhar
B.
,
1977
, “
Robustness of Linear Quadratic State Feedback Designs in the Presence of System Uncertainty
,”
IEEE Trans. Automat. Contr.
, Vol.
AC–21
, pp.
945
949
.
25.
Seraji, H., 1989, “Robust High Performance Control for Robotic Manipulators,” IEEE Int. Conf. Robotics and Automation, Scottsdale, AZ, Apr., pp. 1663–1669.
26.
Simo
J. C.
, and
Vu-Quoc
L.
,
1986
a, “
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
849
854
.
27.
Simo
J. C.
, and
Vu-Quoc
L.
,
1986
b, “
On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II
,”
ASME Journal of Applied Mechanics
, Vol.
53
, pp.
855
863
.
28.
Simo
J. C.
, and
Vu-Quoc
L.
,
1987
, “
The Role of Nonlinear Theories in Transient Dynamics Analysis of Flexible Structure
,”
J. of Sound and Vibration
, Vol.
119
, pp.
487
508
.
29.
Wang
D.
, and
Vidyasagar
M.
,
1991
, “
Control of a Class of Manipulators with a Single Flexible Link—Part II: Observer-Controller Stabilization
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, pp.
662
668
.
30.
Yigit
A.
,
Scott
R. A.
, and
Ulsoy
A. G.
,
1988
, “
Flexural Motion of a Rotating Beam Attached to a Rigid Body
,”
J. of Sound and Vibration
, Vol.
121
, No.
2
, pp.
201
210
.
31.
Yuan, K., and Lin, L. C., 1990, “Motor Based Control of Manipulators with Flexible Joints and Links,” IEEE Int. Conf. on Robotics and Automation, Cincinnati, OH, May, pp. 1809–1814.
This content is only available via PDF.
You do not currently have access to this content.