Abstract
Recently, an impulse vector was introduced as an effective mathematical tool to design and analyze input shapers. In this paper, we generalize the ZV (zero vibration) and ZVD (zero vibration and derivative) shapers by using impulse vectors. The proposed generalized ZVD shaper is defined by letting the ratio m of the third impulse vector magnitude to the first impulse vector magnitude in the impulse vector diagram to be variable. Then two extreme cases of the generalized ZVD shaper are the ZV and ZVD shaper when m = 0 and m = 1, respectively. The generalized ZVD shaper has the performance between ZV and ZVD shaper performance in view of robustness to modeling errors. The validity of the proposed generalized ZVD shaper is demonstrated by simulation and experimental works using an up-and-down flexible beam device.
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S. Xu, G. Sun, and Z. Li, “Finite frequency vibration suppression for space flexible structures in tip position control,” International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1021–1029, 2018.
Y. Wu, and M. Deng, “Operator-based robust nonlinear optimal vibration control for an L-shaped arm driven by linear pulse motor,” International Journal of Control, Automation and Systems, vol. 15, no. 5, pp. 2026–2033, 2017.
C.-W. Ha, D. Lee, K.-H. Rew, and K.-S. Kim, “An impulse-time perturbation approach for a systematic extra-insensitive input shaper,” International Journal of Control, Automation and Systems, vol. 16, no. 3, pp. 1239–1246, 2018.
Convolve, Inc., Input Shaping®, Input ShaperTM, 2018. Available online at http://convolve.com (last accessed March 2019).
M. J. Maghsoudi, Z. Mohamed, M. O. Tokhi, and M. S. Z. Abidin, “Control of a gantry crane using input shaping schemes with distributed delay,” Transactions of the Institute of Measurement and Control, vol. 39, no. 3, pp. 361–370, 2017.
N. Singer, M. Tanquary, and K. Pasch, “System for removing selected unwanted frequencies in accordance with altered settings in a user interface of a data storage device,” US Patent 6,314,473, 1999.
T. Singh, and S. R. Vadali, “Input-shaped control of three-dimensional maneuvers of flexible spacecraft,” J. of Guidance, Control, and Dynamics, vol. 16, no. 6, pp. 1061–1068, 1993.
S. Jones, and A. Ulsoy, “An approach to control input shaping with application to coordinate measuring machine,” J. of Dynamic Systems, Measurement, and Control, vol. 121, pp. 242–247, 1999.
J. Cheng, C. K. Ahn, H. R. Karimi, J. Cao, and W. Qi, “An event-based asynchronous approach to Markov jump systems with hidden mode detections and missing measurements,” IEEE Trans. Systems, Man, and Cybernetics: Systems, vol. 49, no. 9, pp. 1749–1757, 2019.
C.-G. Kang, “Origin of stability analysis: ‘On Governors’ by J. C. Maxwell,” IEEE Control Systems Magazine, vol. 36, no. 5, pp. 77–88, 2016.
O. J. M. Smith, “Posicast control of damped oscillatory systems,” Proceedings of the IRE, vol. 45, pp. 1249–1255, 1957.
N. Singer, Residual Vibration Reduction in Computer-controlled Machines, Ph.D. Thesis, Massachusetts Institute of Technology, 1989.
N. Singer, and W. Seering, “Preshaping command inputs to reduce system vibration,” J. of Dynamic Systems, Measurement and Control, vol. 112, pp. 76–82, 1990.
W. Singhose, Command Generation for Flexible Systems, Ph.D. Thesis, Massachusetts Institute of Technology, 1987.
W. Singhose, “Command shaping for flexible systems: A review of the first 50 years,” Int. J. of Precision Engineering and Manufacturing, vol. 10, no. 4, pp. 153–168, 2009.
T. Singh, and S. R. Vadali, “Robust time-delay control of multimode systems,” International Journal of Control, vol. 62, no. 6, pp. 1319–1339, 1995.
S. S. Gurleyuk, and S. Cinal, “Robust three-impulse sequence input shaper design,” Journal of Vibration and Control, vol. 13, no. 12, pp. 1807–1818, 2007.
M. D. Baumgart, and L. Y. Pao, “Discrete time-optimal command shaping,” Automatica, vol. 43, pp. 1403–1409, 2007.
J. Vaughan, A. Yano, and W. Singhose, “Robust negative input shapers for vibration suppression,” J. of Dynamic Systems, Measurement and Control, vol. 131, p. 031014, 2009.
L. Y. Pao, and M. A. Lau, “Robust input shaper control design for parameter variations in flexible structures,” J. of Dynamic Systems, Measurement, and Control, vol. 122, pp. 63–70, 2000.
K.-H. Rew, C.-W. Ha, and K.-S. Kim, “An impulse-time perturbation approach for enhancing the robustness of extra-insensitive input shapers,” Automatica, vol. 49, pp. 3425–3431, 2013.
C.-G. Kang, “On the derivative constraints of input shaping control,” J. of Mechanical Science and Technology, vol. 25, no. 2, pp. 549–554, 2011.
C.-G. Kang, “Performance measure of residual vibration control,” J. of Dynamic Systems, Measurement and Control, vol. 133, no. 4, pp. 044501 (6 pages), 2011.
C.-G. Kang, and J.-H. Kwak, “On a simplified residual vibration ratio function for input shaping control,” Asian Journal of Control, vol. 16, no. 1, pp. 277–283, 2014.
W. Singhose, “A vector diagram approach to shaping inputs for vibration reduction,” MIT Artificial Intelligence Lab Memo No. 1223, 1990.
W. Singhose, W. Seering, and N. Singer, “Residual vibration reduction using vector diagrams to generate shaped inputs,” J. of Mechanical Design, vol. 116, pp. 654–659, 1994.
C.-G. Kang, “Impulse vectors for input shaping control: A mathematical tool to design and analyze input shapers,” IEEE Control Systems Magazine, vol. 39, no. 4, pp. 40–55, 2019.
Canonical Group Ltd., Ubuntu, 2019. Available online at https://www.ubuntu.com (last accessed Mar., 2019).
RTAI Team, The RealTime Application Interface for Linux (RTAI), 2019. Available online at https://www.rtai.org (last accessed Mar., 2019).
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Recommended by Editor Kyoung Kwan Ahn. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2017R1D1A1B04029966).
Rubayet Hassan received his B.S. and M.S. degrees in mechanical engineering from Khulna University of Engineering and Technology, and Bangladesh University of Engineering and Technology, respectively, both in Dhaka, Bangladesh. Currently, he is a graduate student in mechanical engineering at Konkuk University, Korea. His research interests include braking of a railway vehicle, dynamics, and control.
Kyung-Youn Kim is a professor in the School of Electrical and Electronic Engineering, and the Director of the Inverse Problems in Engineering Lab at Jeju National University, Korea. He received his B.S., M.S., and Ph.D. degrees in electronic engineering from Kyungbuk National University, in 1983, 1986, and 1990, respectively. He was a visiting professor at University of Maryland at Baltimore County in U.S.A in 1994, and at Rensselaer Polytechnic Institute in U.S.A in 2005. He served as the Director of Information Telecommunication Center during 2010-2012, and the Dean of the College of Engineering during 2017-2019 at Jeju National University. His research interests include inverse problems, electrical impedance tomography, electrical capacitance tomography, process tomography, and global positioning systems.
Chul-Goo Kang is a professor in the School of Mechanical Engineering at Konkuk University, Korea. He received his B.S. and M.S. degrees in mechanical design and production engineering from Seoul National University, in 1981 and 1985, respectively. He received a Ph.D. degree in mechanical engineering from University of California, Berkeley, in 1989. In 1990, he joined the faculty of mechanical engineering, Konkuk University, and he is currently the Director of Intelligent Control and Robotics Lab, and Railway Vehicle Lab. He served as Organizing Chair of the International Conf. on Control, Automation and Systems in 2012. In 2015, he was the President of Korea Robotics Society, and Editor-In-Chief of the Journal of the Korean Society for Urban Railway. He is currently a member of the National Academy of Engineering of Korea. His research interests include motion control, input shaping control, force sensor, robot manipulation, and railway vehicles.
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Kang, CG., Hassan, R. & Kim, KY. Analysis of a Generalized ZVD Shaper Using Impulse Vectors. Int. J. Control Autom. Syst. 18, 2088–2094 (2020). https://doi.org/10.1007/s12555-019-0214-2
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DOI: https://doi.org/10.1007/s12555-019-0214-2