The optimal placement of sensors and actuators in active vibration control of flexible linkage mechanisms is studied. First, the vibration control model of the flexible mechanism is introduced. Second, based on the concept of the controllability and the observability of the controlled subsystem and the residual subsystem, the optimal model is developed aiming at the maximization of the controllability and the observability of the controlled modes and minimization of those of the residual modes. Finally, a numerical example is presented, which shows that the proposed method is feasible. Simulation analysis shows that to achieve the same control effect, the control system is easier to realize if the sensors and actuators are located in the optimal positions.
1.
Zhang
, X. M.
, Shao
, C. J.
, and Erdman
, A. G.
, 2002, “Active Vibration Controller Design and Comparison Study of Flexible Linkage Mechanism Systems
,” Mech. Mach. Theory
0094-114X, 37
(9
), pp. 985
–997
.2.
Seung
, B. C.
, and Chae
, C. C.
, 1994, “Vibration Control of Flexible Linkage Mechanisms Using Piezoelectric Films
,” Mech. Mach. Theory
0094-114X, 29
(4
), pp. 535
–546
.3.
Zhang
, X. M.
, Liu
, H. Z.
, and Cao
, W. Q.
, 1996, “Vibration Control of Flexible Mechanisms
,” Chin. J. Mech. Eng.
0577-6686, 32
(1
), pp. 9
–16
.4.
Zhang
, X. M.
, 1999, “Active Residual Vibration Control for Flexible Linkage Mechanisms
,” J. Vib. Eng.
, 12
(3
), pp. 397
–402
.5.
Shao
, C. J.
, Zhang
, X. M.
, and Shen
, Y. W.
, 2000, “Complex Mode Vibration Control of High Speed Flexible Linkage Mechanisms
,” J. Sound Vib.
0022-460X, 234
(3
), pp. 491
–506
.6.
Sannah
, M.
, and Smaili
, A.
, 1998, “Active Control of Elastodynamic Vibrations of a Four-Bar Mechanism System With a Smart Coupler Link Using Optimal Multivariable Control: Experimental Implementation
,” ASME J. Mech. Des.
1050-0472, 120
, pp. 316
–326
.7.
Liao
, C. Y.
, and Sung
, C. K.
, 1993, “An Elastodynamic Analysis and Control of Flexible Linkages Using Piezoceramic Sensors and Actuators
,” ASME J. Mech. Des.
1050-0472, 115
, pp. 658
–665
.8.
Zhang
, X. M.
, Shao
, C. J.
, and Li
, S. P.
, 2001, “Robust H∞ Vibration Control for Flexible Linkage Mechanism Systems with Piezoelectric Sensors and Actuators
,” J. Sound Vib.
0022-460X, 243
(1
), pp. 45
–155
.9.
Bruant
, I.
, Coffignal
, G.
, and Lene
, F.
, 2001, “A Methodology for Determination of Piezoelectric Actuator and Sensor Location on Beam Structures
,” J. Sound Vib.
0022-460X, 243
(5
), pp. 861
–882
.10.
Devasia
, S.
, Meressi
, T.
, Paden
, B.
, and Bayo
, E.
, 1993, “Piezoelectric Actuator Design for Vibration Suppression: Placement and Sizing
,” J. Guid. Control Dyn.
0731-5090, 16
, pp. 859
–864
.11.
Dhingra
, A. K.
, and Lee
, B. H.
, 1995, “Multiobjective Design of Actively Controlled Structures Using a Hybrid Optimization Method
,” Int. J. Numer. Methods Eng.
0029-5981, 38
, pp. 3383
–3401
.12.
Kondoh
, S.
, Yatomi
, C.
, and Inoue
, K.
, 1992, “The Positioning of Sensors and Actuators in the Vibration Control of Flexible Systems
,” JSME Int. J., Ser. III
0914-8825, 33
, pp. 145
–152
.13.
Burke
, S. E.
, and Sullivan
, J. M.
, 1995, “Distribution Transducer Shading via Spatial Gradient Electrodes
,” Proceedings of SPIE (Society of Photo-Optical Instrumentation Engineers), Smart Structures and Materials: Smart Structures and Integrated Systems
, 2443
, pp. 716
–726
.14.
Gabbert
, U.
, and Schulz
, I.
, 1996, “On Optimal Placement of Piezoelectric Actuators in Vibration Control of Adaptive Structures
,” Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition, Symposium on Active Control of Vibration and Noise
, Atlanta, Georgia
, DE-Vol. 93
, pp. 271
–277
.15.
Zhang
, X. M.
, Shao
, C. J.
, Shen
, Y. W.
, and Erdman
, A. G.
, 2002, “Complex Mode Dynamic Analysis for Flexible Mechanism Systems With Piezoelectric Sensors and Actuators
,” J. Multibody Syst. Dyna.
, 8
(1
), pp. 51
–70
.16.
Fletcher
, F.
, 1987, Practical Method of Optimization
, 2nd ed., Wiley
.17.
Zhang
, X. M.
, 2004, “Integrated Optimal Design of Flexible Mechanism and Vibration Control
,” Int. J. Mech. Sci.
0020-7403, 46
, pp. 1607
–1620
.Copyright © 2006
by American Society of Mechanical Engineers
You do not currently have access to this content.
