Input shaping reduces residual vibration in computer controlled machines by convolving a sequence of impulses with a desired system command. The resulting shaped input is then used to drive the system. The impulse sequence has traditionally contained only positively valued impulses. However, when the impulses are allowed to have negative amplitudes, the rise time can be improved. Unfortunately, excitation of unmodeled high modes and overcurrenting of the actuators may accompany the improved rise time. Solutions to the problem of high-mode excitation and overcurrenting are presented. Furthermore, a simple look-up method is presented that facilitates the design of negative input shapers. The performance of negative shapers is evaluated experimentally on two systems; one driven by a piezo actuator and the other equipped with DC motors.

1.
Banerjee, A. K., and Singhose, W. E., 1995, “Minimum Time Fuel Efficient Maneuver of Flexible Spacecraft with Vibration Amplitude Constraint,” AAS Astrodynamics Specialist Conference, Halifax, Nova Scotia, Canada, Vol. AAS 95–318.
2.
Brooke, A., Kendrick, D., and Meeraus, A., 1988, GAMS: A User’s Guide, The Scientific Press, Redwood City, CA.
3.
Drapeau, V., and Wang, D., 1993, “Verification of a Closed-loop Shaped-input Controller for a Five-bar-linkage Manipulator,” Proc. of the IEEE International Conference on Robotics and Automation, Atlanta, GA, Vol. 3, pp. 216–221.
4.
Hillsley
K. L.
, and
Yurkovich
S.
,
1993
, “
Vibration Control of a Two-Link Flexible Robot Arm
,”
Journal Of Dynamics And Control
, Vol.
3
, pp.
261
280
.
5.
Hyde, J. M., and Seering, W. P., 1991, “Using Input Command Pre-Shaping to Suppress Multiple Mode Vibration,” Proc. of the IEEE International Conference on Robotics and Automation, Sacramento, CA, Vol. 3, pp. 2604–2609.
6.
Jansen, J. F., 1992, Control and Analysis of a Single-Link Flexible Beam with Experimental Verification, ORNL/TM-12198, Oak Ridge National Laboratory.
7.
Jones, S. D., and Ulsoy, A. G., 1994, “Control Input Shaping for Coordinate Measuring Machines,” Proc. of the American Control Conference, Baltimore, MD, Vol. 3, pp. 2899–2903.
8.
Liu
Q.
, and
Wie
B.
,
1992
, “
Robust Time-Optimal Control of Uncertain Flexible Spacecraft
,”
J. of Guidance, Control, and Dynamics
, Vol.
15
(
3
), pp.
597
604
.
9.
Magee, D. P., and Book, W. J., 1994, “Filtering Schilling Manipulator Commands to Prevent Flexible Structure Vibration,” American Control Conference, Baltimore, MD, pp. 2538–42.
10.
Magee, D. P., and Book, W. J., 1995, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion,” American Control Conference, Seattle, WA.
11.
Murphy
B. R.
, and
Watanabe
I.
,
1992
, “
Digital Shaping Filters for Reducing Machine Vibration
,”
IEEE Transactions on Robotics and Automation
, Vol.
8
, Apr., pp.
285
289
.
12.
Pao, L., and Singhose, W., 1996, “Unity Magnitude Input Shapers and Their Relation to Time-Optimal Control,” IFAC World Congress, San Francisco, CA.
13.
Pao, L. Y., and Singhose, W. E., 1995, “On the Equivalence of Minimum Time Input Shaping with Traditional Time-Optimal Control,” IEEE Conference on Control Applications, Albany, NY, pp. 1120–5.
14.
Rappole, B. W., Singer, N. C., and Seering, W. P., 1993, “Input Shaping With Negative Sequences for Reducing Vibrations in Flexible Structures,” Proc. of the American Control Conference, San Francisco, CA, Vol. 3, pp. 2695–2699.
15.
Seth, N., Rattan, K. S., and Brandstetter, R. W., 1993, “Vibration Control of a Coordinate Measuring Machine,” IEEE Conference on Control Applications, Dayton, OH, pp. 368–73.
16.
Singer, N. C., 1989, Residual Vibration Reduction in Computer Controlled Machines, Technical Report MIT Artificial Intelligence Laboratory Technical Report Number AITR-1030, MIT Artificial Intelligence Lab.
17.
Singer
N. C.
, and
Seering
W. P.
,
1990
, “
Preshaping Command Inputs to Reduce System Vibration
,”
ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL
, Vol.
112
, Mar., pp.
76
82
.
18.
Singer, N. C., and Seering, W. P., 1992, “An Extension of Command Shaping Methods for Controlling Residual Vibration Using Frequency Sampling,” IEEE International Conference on Robotics and Automation, Nice, France, Vol. 1, pp. 800–805.
19.
Singh
T.
, and
Vadali
S. R.
,
1994
, “
Robust Time-Optimal Control; A Frequency Domain Approach
,”
J. of Guidance, Control and Dynamics
,
17
(
2
), pp.
346
353
.
20.
Singhose
W.
,
Derezinski
S.
, and
Singer
N.
,
1996
, “
Extra-Insensitive Input Shapers for Controlling Flexible Spacecraft
,”
J. of Guidance, Control, and Dynamics
, Vol.
19
(
2
), pp.
385
91
.
21.
Singhose
W.
,
Seering
W.
, and
Singer
N.
,
1994
, “
Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs
,”
ASME Journal of Mechanical Design
Vol.
116
, June pp.
654
659
.
22.
Singhose
W.
, and
Singer
N.
,
1996
, “
Initial Research on the Effects of Input Shaping on Trajectory Following
,”
IEEE Transactions on Robotics and Automation
, Vol.
12
, No.
6
, pp.
881
887
.
23.
Singhose, W. E., Porter, L. J., Tuttle, T. D., and Singer, N. C., in press, “Vibration Reduction Using Multi-Hump Input Shapers,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL.
24.
Singhose, W. E., Seering, W. P., and Singer, N. C., 1996, “Input Shaping for Vibration Reduction with Specified Insensitivity to Modeling Errors,” Japan-USA Symposium on Flexible Automation, Boston, MA.
25.
Smith
O. J. M.
,
1957
, “
Posicast Control of Damped Oscillatory Systems
,”
Proceedings of the IRE
, Vol.
45
, Sept., pp.
1249
1255
.
26.
Smith, O. J. M., 1958, Feedback Control Systems, McGraw-Hill, New York, pp. 331–345.
27.
Tallman, G. H., and Smith, O. J. M., 1958, “Analog Study of Dead-Beat Posicast Control,” IRE Transactions on Automatic Control, Mar., pp. 14–21.
28.
The MathWorks, 1., 1991, MATLAB User’s Guide, Natick, MA.
29.
Tuttle, T. D., and Seering, W. P., 1994, “A Zero-placement Technique for Designing Shaped Inputs to Suppress Multiple-mode Vibration,” Proc. of the American Control Conference, Baltimore, MD, Vol. 3, pp. 2533–2537.
30.
Tzes
A.
, and
Yurkovich
S.
,
1993
, “
An Adaptive Input Shaping Control scheme for Vibration Suppression in Slewing Flexible Structures
,”
IEEE Transactions on Control Systems Technology
, Vol.
1
, June, pp.
114
121
.
31.
Wie
B.
,
Sinha
R.
, and
Liu
Q.
,
1993
, “
Robust Time-Optimal Control of Uncertain Structural Dynamic Systems
,”
J. of Guidance, Control, and Dynamics
, Vol.
15
(
5
), pp.
980
983
.
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