This paper presents a new, robust, time-optimal control strategy for flexible manipulators controlled by acceleration-limited actuators. The strategy is designed by combining the well-known, open-loop, time-optimal solution with wave-based feedback control. The time-optimal solution is used to design a new launch wave input to the wave-based controller, allowing it to recreate the time-optimal solution when the system model is exactly known. If modeling errors are present or a real actuator is used, the residual vibrations, which would otherwise arise when using the time-optimal solution alone, are quickly suppressed due to the additional robustness provided by the wave-based controller. A proximal time-optimal response is still achieved. A robustness analysis shows that significant improvements can be achieved using wave-based control in conjunction with the time-optimal solution. The implications and limits are also discussed.
Issue Section:
Research Papers
1.
Dwivedy
, S. K.
, and Eberhard
, P.
, 2006, “Dynamic Analysis of Flexible Manipulators, A Literature Review
,” Mech. Mach. Theory
0094-114X, 41
(7
), pp. 749
–777
.2.
Benosman
, M.
, and Vey
, G. L.
, 2004, “Control of Flexible Manipulators: A Survey
,” Robotica
0263-5747, 22
(5
), pp. 533
–545
.3.
Robinett
, R. D.
, III, Dohrmann
, C. R.
, Eisler
, G. R.
, Feddema
, J.
, Parker
, G. G.
, Wilson
, D. G.
, and Stokes
, D.
, 2002, Flexible Robot Dynamics and Controls
, Kluwer Academic
, Dordrecht
/Plenum
, New York
.4.
Sage
, H. G.
, De Mathelin
, M. F.
, and Ostertag
, E.
, 1999, “Robust Control of Robot Manipulators: A Survey
,” Int. J. Control
0020-7179, 72
(16
), pp. 1498
–1522
.5.
Tokhi
, M. O.
, and Azad
, A. K. M.
, 2008, Flexible Robot Manipulators: Modeling, Simulation and Control
, IET
, London
.6.
Pao
, L. Y.
, 1996, “Minimum-Time Control Characteristics of Flexible Structures
,” J. Guid. Control Dyn.
0731-5090, 19
, pp. 123
–129
.7.
Pao
, L. Y.
, and La-orpacharapan
, C.
, 2004, “Shaped Time-Optimal Feedback Controllers for Flexible Structures
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 126
, pp. 173
–186
.8.
Pao
, L.
, and Franklin
, G.
, 1994, “The Robustness of a Proximate Time-Optional Controller
,” IEEE Trans. Autom. Control
0018-9286, 39
, pp. 1963
–1966
.9.
Romano
, M.
, Agrawal
, B.
, and Bernelli-Zazzera
, F.
, 2002, “Experiments on Command Shaping Control of a Manipulator With Flexible Links
,” J. Guid. Control Dyn.
0731-5090, 25
(2
), pp. 232
–239
.10.
Singer
, N. C.
, and Seering
, W. P.
, 1990, “Preshaping Command Inputs to Reduce System Vibrations
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 112
, pp. 76
–82
.11.
Banerjee
, A. K.
, and Singhose
, W. E.
, 1998, “Command Shaping in Tracking Control of a Two-Link Flexible Robot
,” J. Guid. Control Dyn.
0731-5090, 21
, pp. 1012
–1015
.12.
Singh
, T.
, and Vadali
, S. R.
, 1993, “Robust Time-Delay Control
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 115
(2A
), pp. 303
–306
.13.
Singh
, T.
, and Vadali
, S. R.
, 1995, “Robust Time-Delay Control of Multimode Systems
,” Int. J. Control
0020-7179, 62
(6
), pp. 1319
–1339
.14.
Singh
, T.
, 2002, “Minimax Design of Robust Controllers for Flexible Systems
,” J. Guid. Control Dyn.
0731-5090, 25
(5
), pp. 868
–875
.15.
Singhose
, W.
, Derezinski
, S.
, and Singer
, N.
, 1996, “Extra-Insensitive Input Shapers for Controlling Flexible Spacecraft
,” J. Guid. Control Dyn.
0731-5090, 19
, pp. 385
–91
.16.
Muenchhof
, M.
, and Singh
, T.
, 2003, “Jerk Limited Time Optimal Control of Flexible Structures
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 125
(1
), pp. 139
–143
.17.
Hillsley
, K. L.
, and Yurkovich
, S.
, 1993, “Vibration Control of a Two-Link Flexible Robot Arm
,” Journal of Dynamics and Control
, 3
, pp. 261
–280
.18.
Huey
, J. R.
, “The Intelligent Combination of Input Shaping and PID Feedback Control
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.19.
Halevi
, Y.
, 2005, “Control of Flexible Structures Governed by the Wave Equation Using Infinite Dimensional Transfer Functions
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 127
, pp. 579
–588
.20.
O’Connor
, W. J.
, and Lang
, D.
, 1998, “Position Control of Flexible Robot Arms Using Mechanical Waves
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 120
(3
), pp. 334
–339
.21.
O’Connor
, W. J.
, 2003, “A Gantry Crane Problem Solved
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 125
(4
), pp. 569
–576
.22.
O’Connor
, W. J.
, 2006, “Wave-Echo Control of Lumped Flexible Systems
,” J. Sound Vib.
0022-460X, 298
, pp. 1001
–1018
.23.
O’Connor
, W. J.
, 2007, “Wave-Based Analysis and Control of Lump-Modeled Flexible Robots
,” IEEE Trans. Rob. Autom.
1042-296X, 23
, pp. 342
–352
.24.
O’Connor
, W. J.
, Ramos
, F.
, McKeown
, D. J.
, and Feliu
, V.
, 2009, “Wave-Based Control of Non-Linear Flexible Mechanical Systems
,” Nonlinear Dyn.
0924-090X,” 57
(1-2
), pp. 113
–123
.25.
O’Connor
W. J.
, and Fumagalli
, A.
, 2009, “Refined Wave-Based Control Applied to Nonlinear, Bending, and Slewing Flexible Systems
,” ASME J. Appl. Mech.
0021-8936, 76
(4
), p. 041005
.26.
Kenison
, M.
, and Singhose
, W.
, 2002, “Concurrent Design of Input Shaping and Proportional Plus Derivative Feedback Control
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 124
, pp. 398
–405
.Copyright © 2011
by American Society of Mechanical Engineers
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