Input shaping techniques reduce the residual vibration in flexible structures by convolving the command input with a sequence of impulses. The exact cancellation of the residual structural vibration via input shaping is dependent on the amplitudes and instances of impulse application. A majority of the current input shaping schemes are inherently open-loop where impulse application at inaccurate instances can lead to system performance degradation. In this paper, we develop a closed-loop control design framework for input shaped systems. This framework is based on the realization that the dynamics of input shaped systems give rise to time delays in the input. Thus, we exploit the feedback control theory of time delay systems for the closed-loop control of input shaped flexible structures. A Riccati equation-based and a linear matrix inequality-based frameworks are developed for the stabilization of systems with uncertain, multiple input delays. Next, the aforementioned framework is applied to two input shaped flexible structure systems. This framework guarantees closed-loop system stability and performance when the impulse train is applied at inaccurate instances. Two illustrative numerical examples demonstrate the efficacy of the proposed closed-loop input shaping controller. [S0022-0434(00)00103-9]
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e-mail: vkapila@duke.poly.edu
e-mail: atzes@poly.edu
e-mail: qyan01@utopia.poly.edu
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September 2000
Technical Papers
Closed-Loop Input Shaping for Flexible Structures Using Time-Delay Control1
Vikram Kapila,
e-mail: vkapila@duke.poly.edu
Vikram Kapila
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
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Anthony Tzes,
e-mail: atzes@poly.edu
Anthony Tzes
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
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Qiguo Yan
e-mail: qyan01@utopia.poly.edu
Qiguo Yan
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
Search for other works by this author on:
Vikram Kapila
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
e-mail: vkapila@duke.poly.edu
Anthony Tzes
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
e-mail: atzes@poly.edu
Qiguo Yan
Department of Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201
e-mail: qyan01@utopia.poly.edu
Contributed by the Dynamic Systems and Control Division for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received by the Dynamic Systems and Control Division April 5, 1999; revised manuscript received December, 1999. Associate Technical Editor: Y. Hurmuzla.
J. Dyn. Sys., Meas., Control. Sep 2000, 122(3): 454-460 (7 pages)
Published Online: December 1, 1999
Article history
Received:
April 5, 1999
Revised:
December 1, 1999
Citation
Kapila, V., Tzes, A., and Yan, Q. (December 1, 1999). "Closed-Loop Input Shaping for Flexible Structures Using Time-Delay Control." ASME. J. Dyn. Sys., Meas., Control. September 2000; 122(3): 454–460. https://doi.org/10.1115/1.1286269
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