This paper analyzes the signals captured during the movement of a mechanical manipulator carrying a liquid container. In order to study the signals, an experimental setup is implemented. The system acquires data from the sensors, in real time, and, in a second phase, processes them through an analysis package. The analysis package runs offline and handles the recorded data. The results show that the Fourier spectrum of several signals presents a fractional behavior. The experimental study provides useful information that can assist in the design of a control system to be used in reducing or eliminating the effect of vibrations.
Issue Section:
Modeling
1.
Singer
, N. C.
, and Seering
, W. P.
, 1988, “Using Acausal Shaping Techniques to Reduce Robot Vibration
,” Proceedings of IEEE International Conference on Robotics and Automation
, Philadelphia, PA
, pp. 1434
–1439
.2.
Magee
, D. P.
, and Wayne
, J. B.
, 1995, “Filtering Micro-Manipulator Wrist Commands to Prevent Flexible Base Motion
,” Proceedings of the American Control Conference
, Seatle, WA
, pp. 924
–928
.3.
Cannon
, D. W.
, Magee
, D. P.
, Book
, W. J.
, and Lew
, J. Y.
, 1996, “Experimental Study on Micro∕Macro Manipulator Vibration Control
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Minneapolis, MN
, pp. 2549
–2554
.4.
Lew
, J. Y.
, Trudnowski
, D. J.
, Evans
, M. S.
, and Bennett
, D. W.
, 1995, “Micro Manipulator Motion Control to Suppress Macro Manipulator Structural Vibrations
,” Proceedings of the IEEE International Conference on Robotics and Automation
, Vol. 3
, pp. 3116
–3120
.5.
Yoshikawa
, T.
, Hosoda
, K.
, Doi
, T.
, and Murakami
, H.
, 1993 “Quasi-Static Trajectory Tracking Control of Flexible Manipulator by Macro-Micro Manipulator System
,” Proceedings of the IEEE International Conference on Robotics and Automation
, pp. 210
–215
.6.
Grundelius
, M.
, 2001, “Methods for Control of Liquid Slosh
,” Ph.D. thesis, Lund Institute of Technology, Sweden.7.
Feddema
, J. T.
, Dohrmann
, C. R.
, Parker
, G. G.
, Robinett
, R. D.
, Romero
, V. J.
, and Schmitt
, D. J.
, 1997, “Control for Slosh Free Motion of an Open Container
,” IEEE Control Syst. Mag.
0272-1708, 17
(1
), pp. 29
–36
.8.
Machado
, J. A. T.
, 1997, “Analysis and Design of Fractional-Order Digital Control Systems
,” Syst. Anal. Model. Simul.
0232-9298, 27
, pp. 107
–122
.9.
Machado
, J. A. T.
, 2003, “A Probabilistic Interpretation of the Fractional-Order Differentiation
,” Fractional Calculus Appl. Anal.
1311-0454, 6
(1
), pp. 73
–80
.10.
Tarasov
, V. E.
, and Zaslavsky
, G. M.
, 2006, “Fractional Dynamics of Systems With Long-Range Interaction
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 11
(8
), pp. 885
–898
.11.
Korabel
, N.
, Zaslavsky
, G. M.
, and Tarasov
, V. E.
, 2007, “Coupled Oscillators With Power-Law Interaction and Their Fractional Dynamics Analogues
,” Commun. Nonlinear Sci. Numer. Simul.
1007-5704, 12
(8
), pp. 1405
–1417
.12.
Tarasov
, V. E.
, and Zaslavsky
, G. M.
, “Conservation Laws and Hamilton’s Equations for Systems With Long-Range Interaction and Memory
,” Commun. Nonlinear Sci. Numer. Simul.
, in press.13.
Marcos
, M. G.
, Duarte
, F. B. M.
, and Machado
, J. A. T.
, “Fractional Dynamics in the Trajectory Control of Redundant Manipulators
,” Commun. Nonlinear Sci. Numer. Simul.
, in press.14.
Podlubny
, I.
, 2002, “Geometrical and Physical Interpretation of Fractional Integration and Fractional Differentiation
,” Fractional Calculus Appl. Anal.
1311-0454, 5
(4
), pp. 357
–366
.15.
Bohannan
, G. W.
, 2002, “Analog Realization of a Fractional Control Element—Revisited
,” mechatronics.ece.usu.edu/foc/cdc02tw/cdrom/aditional/FOC_Proposal_Bohannan.pdfmechatronics.ece.usu.edu/foc/cdc02tw/cdrom/aditional/FOC_Proposal_Bohannan.pdf16.
Barbosa
, R. S.
, Machado
, J. A. T.
, and Ferreira
, I. M.
, 2004, “Tuning of PID Controllers Based on Bode’s Ideal Transfer Function
,” Nonlinear Dyn.
0924-090X, 38
, pp. 305
–321
.17.
Oustaloup
, A.
, Moreau
, X.
, and Nouillant
, M.
, 1997, “From Fractal Robustness to Non-Integer Approach in Vibration Insulation: The CRONE Suspension
,” Proceedings of the 36th Conference on Decision and Control
, San Diego, CA
, Vol. 5
, pp. 4979
–4984
.18.
Lima
, M. F. M.
, Machado
, J. A.
, and Crisóstomo
, M.
, 2005, “Experimental Set-Up for Vibration and Impact Analysis in Robotics
,” WSEAS Trans. on Systems
, 4
(5
), pp. 569
–576
.19.
Lima
, M. F. M.
, Machado
, J. A.
, and Crisóstomo
, M.
, 2006, “Windowed Fourier Transform of Experimental Robotic Signals With Fractional Behavior
,” Proceedings of the IEEE International Conference on Computational Cybernetics
, Tallin, Estonia
, pp. 21
–26
.20.
Gabor
, D.
, 1946, “Theory of Communication
,” J. IEE
, 93
(26
), pp. 429
–457
.21.
Ronald
, L. A.
, and Duncan
, W. M.
, 2004, Signal Analysis
, IEEE
, New York
.22.
Oppenheim
, A. V.
, Schafer
, R. W.
, and Buck
, J. R.
, 1989, Discrete-Time Signal Processing
, 2nd ed., Prentice-Hall
, Englewood Cliffs, NJ
.23.
Harris
, F. J.
, 1978, “On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform
,” Proc. IEEE
0018-9219, 66
(1
), pp. 51
–83
.24.
Lima
, M. F. M.
, Machado
, J. A.
, and Crisóstomo
, M.
, 2006, “Fractional Order Fourier Spectra in Robotic Manipulators With Vibrations
,” Second IFAC Workshop on Fractional Differentiation and its Applications
, Porto, Portugal
, pp. 386
–391
.25.
Lima
, M. F. M.
, Machado
, J. A.
, and Crisóstomo
, M.
, 2007, “Fractional Dynamics in Mechanical Manipulation
,” Proceedings of the ASME 2007 International Design Engineering Technical Conference and Computers and Information in Engineering Conference
, IDETC/CIE, 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (MSNDC), September 4–7, Las Vegas, NV
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.