The vibration control of a slewing flexible structure by collocated and noncollocated feedback is presented in this paper. A stability criterion derived from the root locus method in frequency domain is applied to predict the closed-loop system stability of the distributed parameter model whose analytical transfer functions are formulated. It is shown that the control law design requires neither distributed state sensing/estimation nor functional feedback gain; moreover, the spillover problem associated with discrete parameter model can be prevented. Implementation of the noncollocated feedback in a slewing beam experiment validates that the control law is effective in pointing accuracy while suppressing the tip vibration.

Issue Section:
Technical Papers
Topics:
Control equipment, Design, Flexible structures, Feedback, Stability, Closed loop systems, Distributed parameter models, Transfer functions, Vibration, Vibration control
1.
Balas
M. J.
,
1982
, “
Trends in Space Structure Control Theory: Fondest Hopes, Wildest Dream
,”
IEEE Transaction on AC
, Vol.
AC-27
, No.
3
, pp.
522
–
535
, June.
2.
Banks
S. P.
and
Abbasi-Ghelmansarai
,
1983
, “
Realization Theory and the Infinite Dimensional Root Locus
,”
Int. J. of Control
, Vol.
38
, No.
3
, pp.
589
–
606
.
3.
Chait
Y.
,
Radcliffe
C.
and
MacCluer
C.
,
1988
, “
Frequency Domain Stability Criterion for Vibration Control of the Bernoulli-Euler Beam
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
110
, no.
3
, pp.
303
–
307
, Sept.
4.
Desoer
C. A.
and
Wang
Y. T.
,
1980
, “
On the Generalized Nyquist Stability Criterion
,”
IEEE Transaction on AC
, Vol.
AC-25
, No.
2
, pp.
187
–
196
.
5.
Fujii
H.
and
Ishijima
S.
,
1989
, “
Mission Function Control for Slew Maneuver of a Flexible Space Structure
,”
J. of Guidance
, Vol.
12
, No.
6
, pp.
858
–
865
, Nov.–Dec.
6.
Fujii
H.
,
Ohtsuka
T.
and
Udou
S.
,
1991
, “
Mission Function Control for a Slew Maneuver Experiment
,”
J. of Guidance
, Vol.
14
, No.
5
, pp.
986
–
992
, Sept–Oct.
7.
Ito
K.
and
Kunimatsu
N.
,
1991
, “
Semigroup Model and Stability of the Structurally Damped Timoshenko Beam with Boundary Control
,”
Int. J. of Control
, Vol.
54
, No.
2
, pp.
367
–
391
.
8.
Juang
J. N.
,
Horta
L. G.
, and
Robertshaw
H. H.
,
1986
, “
A Slewing Control Experiment for Flexible Structures
,”
J. of Guidance
, Vol.
9
, No.
5
, pp.
599
–
607
, Sept.–Oct.
9.
Junkins
J. L.
,
Rahman
Z. H.
and
Bang
H.
,
1991
, “
Near-minimum-Time Control of Distributed Parameter System: Analytical and Experimental Results
,”
J. of Guidance
, Vol.
14
, No.
2
, pp.
406
–
415
, Mar.–Apr.
10.
Kim
J. U.
and
Renardy
Y.
,
1987
, “
Boundary Control of the Timoshenko Beam
,”
SIAM, J. Control and Optimization
, Vol.
25
, No.
6
, pp.
1417
–
1429
, Nov.
11.
Liu
Y. C.
and
Yang
S. M.
,
1995
, “
Vibration Control Experiment of a Slewing Flexible Beam
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
117
, No.
3
, pp.
432
–
435
, Sept.
12.
Liu
Y. C.
and
Yang
S. M.
,
1993
, “
Three Simple and Efficient Methods for Vibration Control of Slewing Flexible Structures
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
115
, No.
4
, pp.
725
–
730
, Dec.
13.
Morgul
O.
,
1990
, “
Boundary Control of a Flexible Beam Attached to a Rigid Body: Planar Motion
,”
Int. J. of Control
, vol.
51
, no.
1
, pp.
11
–
31
.
14.
Morgul
O.
,
1991
, “
Boundary Control of a Timoshenko Beam Attached to a Rigid Body: Planar Motion
,”
Int. J. of Control
, Vol.
54
, No.
4
, pp.
763
–
791
.
15.
Singh
G.
,
Kabamba
P. T.
, and
McClamroch
N. H.
,
1989
, “
Planar, Time-Optimal, Rest-to-Rest Slewing Maneuvers of Flexible Spacecraft
,”
J. of Guidance
, Vol.
12
, No.
1
, pp.
71
–
81
, Jan.–Feb.
16.
Taylor, L. W. and Naidu, D. S., “Experience in the Distributed Parameter Modeling of the Spacecraft Control Laboratory Experiment (SCORE) Structure,” AIAA paper 877–0895.
17.
Yang
B.
and
Mote
CD.
,
1991
a, “
Frequency-Domain Vibration Control of Distributed Gyroscopic Systems
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
113
, No.
1
, pp.
18
–
25
, Mar.
18.
Yang
B.
and
Mote
C. D.
,
1991
b, “
Active Vibration Control of the Axially Moving String in the S Domain
,”
ASME Journal of Applied Mechanics
, Vol.
58
, pp.
189
–
196
.
19.
Yang
B.
,
1992
, “
Noncolocated Control of a Damped String Using Time Delay
,”
ASME Journal op Dynamic Systems, Measurement, and Control
, Vol.
114
, No.
4
, pp.
736
–
740
, Dec.
20.
Yang
S. M.
,
1993
, “
Stability Criteria of Structural Control Systems with Noncolocated Velocity Feedback
,”
AIAA J.
, Vol.
31
, No.
7
, pp.
1351
–
1353
.
21.
Yang
S. M.
and
Liu
Y. C.
,
1994
, “
Optimal Output Feedback Control of Slewing Flexible Structures with Spillover Stabilization
,”
J. of the Astronautical Science
, Vol.
42
, No.
4
, pp.
473
–
484
.
22.
Yang
S. M.
and
Liu
Y. C.
,
1995
, “
Frequency Domain Control of Flexible Beams with Piezoelectric Actuators
,”
JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
117
, No.
4
, pp.
541
–
546
.
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