Input shaping is an effective method for reducing oscillatory motion in linear systems. Many physical systems, however, exhibit discontinuous dynamics, such as saturation, rate limiting, backlash, and dead-zone. These hard nonlinearities can degrade the vibration reducing properties of shaped signals. This paper investigates the detrimental effects of dead-zone on a class of input-shaped commands. A mitigation strategy is proposed for reducing these detrimental effects when the value of the dead-zone can be estimated. The robustness of this mitigation approach to uncertainties in the dead-zone width is also determined. Theoretical developments are experimentally verified using an industrial 10 ton bridge crane.
Issue Section:
Research Papers
1.
Singer
, N.
, Singhose
, W.
, and Kriikku
, E.
, 1997, “An Input Shaping Controller Enabling Cranes to Move Without Sway
,” ANS Seventh Topical Meeting on Robotics and Remote Systems
, Augusta, GA.2.
Sorensen
, K.
, Singhose
, W.
, and Dickerson
, S.
, 2005, “A Controller Enabling Precise Positioning and Sway Reduction in Cranes With On-Off Actuation
,” IFAC World Congress
, Prague, Vol. 16
.3.
Blackburn
, D. F.
, Singhose
, W.
, Kitchen
, J. P.
, Petrangenaru
, V. P.
, Lawrence
, J.
, Kamoi
, T.
, and Taura
, A.
, 2006, “Advanced Input Shaping Algorithm for Nonlinear Tower Crane Dynamics
,” Eighth International Conference on Motion and Vibration Control
, Daejeon, Korea.4.
Sorensen
, K. L.
, Singhose
, W. E.
, and Dickerson
, S.
, 2007, “A Controller Enabling Precise Positioning and Sway Reduction in Bridge and Gantry Cranes
,” Control Eng. Pract.
0967-0661, 15
(7
), pp. 825
–837
.5.
Seth
, N.
, Rattan
, K.
, and Brandstetter
, R.
, 1993, “Vibration Control of a Coordinate Measuring Machine
,” IEEE Conference on Control Applications
, Dayton, OH, pp. 368
–373
.6.
Singhose
, W.
, Singer
, N.
, and Seering
, W.
, 1996, “Improving Repeatability of Coordinate Measuring Machines With Shaped Command Signals
,” Precis. Eng.
0141-6359, 18
(2–3
), pp. 138
–146
.7.
Jones
, S.
, and Ulsoy
, A. G.
, 1999, “An Approach to Control Input Shaping With Application to Coordinate Measuring Machines
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 121
(2
), pp. 242
–247
.8.
Singhose
, W. E.
, Porter
, L. J.
, Tuttle
, T. D.
, and Singer
, N. C.
, 1997, “Vibration Reduction Using Multi-Hump Input Shapers
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 119
(2
), pp. 320
–326
.9.
Tuttle
, T. D.
, and Seering
, W. P.
, 1996, “Vibration Reduction in Flexible Space Structures Using Input Shaping on Mace: Mission Results
,” IFAC World Congress
, San Francisco, CA.10.
Fortgang
, J.
, Singhose
, W.
, Marquez
, J. J.
, and Perez
, J.
, 2005, “Command Shaping for Micro-Mills and CNC Controllers
,” American Control Conference
, Portland, OR, pp. 4531
–4536
.11.
Love
, L. J.
, Magee
, D. P.
, and Book
, W. J.
, 1994, “A Comparison of Joint Control Algorithms for Teleoperated Pick and Place Tasks Using a Flexible Manipulator
,” IEEE International Conference on Systems, Man, and Cybernetics
, Vol. 2
, pp. 1257
–1262
.12.
Magee
, D. P.
, and Book
, W. J.
, 1995, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion
,” American Control Conference
, Seattle, WA, pp. 924
–928
.13.
Smith
, O. J. M.
, 1957, “Posicast Control of Damped Oscillatory Systems
,” Proc. IRE
0096-8390, 45
(9
), pp. 1249
–1255
.14.
Singer
, N. C.
, and Seering
, W. P.
, 1990, “Preshaping Command Inputs to Reduce System Vibration
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 112
(1
), pp. 76
–82
.15.
Singhose
, W.
, Seering
, W.
, and Singer
, N.
, 1994, “Residual Vibration Reduction Using Vector Diagrams to Generate Shaped Inputs
,” ASME J. Mech. Des.
0161-8458, 116
(2
), pp. 654
–659
.16.
Tuttle
, T. D.
, and Seering
, W. P.
, 1994, “A Zero-Placement Technique for Designing Shaped Inputs to Suppress Multiple-Mode Vibration
,” American Control Conference
, Baltimore, MD, pp. 2533
–2537
.17.
Singhose
, W.
, Singer
, N.
, and Seering
, W.
, 1995, “Comparison of Command Shaping Methods for Reducing Residual Vibration
,” European Control Conference
, Rome, Italy, Vol. 2
, pp. 1126
–1131
.18.
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, Vol. 1
, pp. 307
–313
.19.
Huey
, J. R.
, and Singhose
, W.
, 2005, “Stability Analysis of Closed-Loop Input Shaping Control
,” IFAC World Congress
, Prague.20.
Lawrence
, J.
, Falkenberg
, M.
, and Singhose
, W.
, 2004, “Input Shaping for a Flexible, Nonlinear, One-Link Robotic Arm With Backlash
,” Japan-USA Symposium on Flexible Automation
, Denver, CO.21.
Lawrence
, J.
, Singhose
, W.
, and Hekman
, K.
, 2005, “Friction-Compensating Command Shaping for Vibration Reduction
,” ASME J. Vibr. Acoust.
0739-3717, 127
, pp. 307
–314
.22.
Sorensen
, K.
, and Singhose
, W.
, 2007, “Oscillatory Effects of Common Hard Nonlinearities on Systems Using Two-Impulse ZV Input Shaping
,” American Control Conference
, New York, pp. 5539
–5544
.23.
Sorensen
, K. L.
, and Singhose
, W. E.
, 2008, “Command-Induced Vibration Analysis Using Input Shaping Principles
,” Automatica
0005-1098, 44
, pp. 2392
–2397
.24.
Bhat
, S. P.
, and Miu
, D. K.
, 1990, “Precise Point-to-Point Positioning Control of Flexible Structures
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 112
, pp. 667
–674
.25.
Park
, U. H.
, Lee
, J. W.
, Lim
, B. D.
, and Sung
, Y. G.
, 2001, “Design and Sensitivity Analysis of an Input Shaping Filter in the Z-Plane
,” J. Sound Vib.
0022-460X, 243
(1
), pp. 157
–171
.26.
Tao
, G.
, and Kokotovic
, P. V.
, 1995, “Continuous-Time Adaptive Control of Systems With Unknown Backlash
,” IEEE Trans. Autom. Control
0018-9286, 40
(6
) pp. 1083
–1087
.Copyright © 2011
by American Society of Mechanical Engineers
You do not currently have access to this content.