Input shaping has been shown to yield good performance in the control of flexible structures while being insensitive to modeling errors. However, previous studies do not take into account the distributions of the parameter variations. We develop a new input shaping method that allows the ranges of system parameter values to be weighted according to the expected modeling errors. Comparisons with previously proposed input shaper designs are presented to illustrate the qualities of the new input shaper design method. These new shapers will be shown to have better robustness under uncertainty in structural parameters and shorter shaper lengths for lightly damped systems. [S0022-0434(00)02201-2]

1.
Book
,
W. J.
,
1993
, “
Controlled Motion in an Elastic World
,”
ASME J. Dyn. Syst., Meas., Control
,
115
, No.
2
,June, pp.
252
261
.
2.
Junkins, J. L., and Kim, Y. 1993, Introduction to Dynamics and Control of Flexible Structures.
3.
Singer
,
N.
, and
Seering
,
W.
,
1990
, “
Preshaping Command Inputs to Reduce System Vibration
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, No.
1
, Mar., pp.
76
82
.
4.
Singh
,
T.
, and
Vadali
,
S. R.
,
1994
, “
Robust Time-Optimal Control: A Frequency Domain Approach
,”
AIAA J. Guid., Contr., Dyn.
,
17
, No.
2
, Mar.–Apr., pp.
346
353
.
5.
Singhose
,
W.
,
Seering
,
W.
, and
Singer
,
N.
,
1994
, “
Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs
,”
ASME J. Mech. Des.
,
116
, No.
2
, June, pp.
654
659
.
6.
Wie
,
B.
,
Sinha
,
R.
, and
Liu
,
Q.
,
1993
, “
Robust Time-Optimal Control of Uncertain Structural Dynamic Systems
,”
AIAA J. Guid., Contr., Dyn.
,
16
, No.
5
, Sept.–Oct., pp.
980
983
.
7.
Smith, O. J. M., 1957, “Posicast Control of Damped Oscillatory Systems,” Proc. of the IRE, Sept., pp. 1249–1255.
8.
Singhose, W., Seering, W., and Singer, N., 1996, “Input Shaping for Vibration Reduction With Specified Insensitivity to Modeling Errors,” Proc. Japan-USA Symposium on Flexible Automation, Boston, MA.
9.
Magee, D. P., 1996, “Optimal Arbitrary Time-Delay Filtering to Minimize Vibration in Elastic Manipulator Systems,” PhD thesis, Georgia Institute of Technology.
10.
de Roover, D., and Sperling, F. B., 1997, “Point-to-Point Control of a High Accuracy Positioning Mechanism,” Proc. American Control Conf., Albuquerque, NM, June, pp. 1350–1354.
11.
Rappole, B. W., Singer, N. C., and Seering, W. P., 1994, “Multiple-Mode Impulse Shaping Sequences for Reducing Residual Vibrations,” 23rd ASME Biennial Mechanisms Conf., Minneapolis, MN, DE-71, pp. 11–16.
12.
Singhose, W., Seering, W., and Singer, N., 1995, “The Effect of Input Shaping on Coordinate Measuring Machine Repeatability,” Proc. IFToMM World Congress on the Theory of Machines and Mechanisms, Milan, Italy, 4, pp. 2930–2934.
13.
Tuttle
,
T. D.
, and
Seering
,
W. P.
,
1997
, “
Experimental Verification of Vibration Reduction
,”
AIAA J. Guid., Contr., Dyn.
,
20
, No.
4
, July–Aug., pp.
658
664
.
14.
Singer, N. C., Singhose, W. E., and Kriikku, E., 1997, “An Input Shaping Controller Enabling Cranes to Move Without Sway,” Proc. ANS Topical Meeting on Robotics and Remote Systems, Augusta, GA.
15.
Jansen, J. F., 1992, “Control and Analysis of a Single-Link Flexible Beam with Experimental Verification,” ORNL/TM-12198, Oak Ridge National Laboratory.
16.
Magee, D. P., and Book, W., 1995, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion,” Proc. American Control Conf., Seattle, WA, June, pp. 924–928.
17.
Feddema
,
J.
,
Dohrmann
,
C.
,
Parker
,
G.
,
Robinett
,
R.
,
Romero
,
V.
, and
Schmitt
,
D.
,
1997
, “
Control for Slosh-Free Motion of an Open Container
,”
IEEE Control Systems Magazine
,
17
, No.
1
, Feb., pp.
29
36
.
18.
Pao
,
L. Y.
,
1997
, “
An Analysis of the Frequency, Damping, and Total Insensitivities of Input Shaping Designs
,”
AIAA J. Guid., Contr., Dyn.
,
20
, No.
5
, Sept.–Oct., pp.
909
915
.
19.
Kirkpatrick, S., Gellet, C., and Vecchi, M., 1983, “Optimization by Simulated Annealing,” Science, pp. 671–680.
20.
van Laarhoven, P. J. M., and Aarts, E. H. L., 1987, Simulated Annealing: Theory and Applications, Reidel Publishing Company.
21.
Pao
,
L. Y.
, and
Lau
,
M. A.
,
1999
, “
Expected Residual Vibration of Traditional and Hybrid Input Shaping Designs
,”
AIAA J. Guid., Contr., Dyn.
,
22
, No.
1
, Jan.–Feb., pp.
162
165
.
22.
Bhat
,
S. P.
, and
Miu
,
D. K.
,
1991
, “
Solutions to Point-to-Point Control Problems Using Laplace Transform Technique
,”
ASME J. Dyn. Syst., Meas., Control
,
113
, No.
3
, Sept., pp.
425
431
.
23.
Pao, L. Y., and Singhose, W. E., 1995, “On the Equivalence of Minimum Time Input Shaping with Traditional Time-Optimal Control,” Proc. IEEE Conf. Control Applications, Albany, NY, Sept., pp. 1120–1125.
24.
Tuttle, T. D., and Seering, W. P., 1994, “A Zero-placement Technique for Designing Shaped Inputs to Suppress Multiple-mode Vibration,” Proc. American Control Conf., Baltimore, MD, June, pp. 2533–2537.
25.
Pao, L. Y., Chang, T. N., and Hou, E., 1997, “Input Shaper Designs for Minimizing the Expected Level of Residual Vibration in Flexible Structures,” Proc. American Control Conf., Albuquerque, NM, June, pp. 3542–3546.
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