A control of an eccentric flywheel that ensures the global asymptotically stability of the equilibrium position of the translational oscillator with rotating actuator is designed. It is shown that this control is robust. A method to estimate the robustness region in the space of system parameters of the mechanical system is proposed. The obtained results are illustrated against a specific model.
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References
E. A. Barbashin, Introduction to the Theory of Stability, Wolters-Noordhoff, Groningen (1970).
R. T. Bupp, D. S. Bernstein, and V. T. Coppola, “Vibration suppression of multi-modal translational motion using a rotational actuator,” in: Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, USA (1994), pp. 4030–4034.
C. D. Hall, “Resonance capture in axial gyrostats,” J. Astronaut. Sci., 43, 127–138 (1995).
R. J. Kinsey, D. L. Mingori, and R. H. Rand, “Nonlinear controller to reduce resonance effects during despin of a dual-spin spacecraft through precession phase lock,” in: Proc. Conf. on Decision and Control, Tucson, AZ (1992), pp. 3025–3030.
R. J. Kinsey, D. L. Mingori, and R. H. Rand, “Spinup through resonance of rotating unbalanced systems with limited torque,” in: Proc. AIAA/AAS Astrodynamics Conf., Washington, DC (1990), pp. 805–813.
A. S. Khoroshun, “Stability of the horizontal flight of an airplane,” Int. Appl. Mech., 52, No. 1, 432–436 (2016).
A. S. Khoroshun, “Stability and speed control of a series-wound DC motor,” Int. Appl. Mech., 52, No. 4, 122–129 (2016).
A. S. Khoroshun, “Stabilitzation of the upper equilibrium position of a pendulum by spinning an inertial flywheel,” Int. Appl. Mech., 52, No. 5, 547–556 (2016).
Y. Liu and H. Yu, “A survey of underactuated mechanical systems,” IET Control Theory Appl., 7, No. 7, 921–935 (2013).
Reza Olfati-Saber, Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles, Ph.D. Thesis, Department of Electrical Engineering and Computer Sciense, MIT, USA (2001).
N. Qaiser, A. Hussain, N. Iqbal, and N. Qaiser, “Dynamic surface control for stabilization of the oscillating eccentric rotor,” in: Proc. Institution of Mechanical Engineers, Part I: J. Syst. Contr. Eng., 221(3), 311–319 (2007).
B. Song and J. K. Hedrick, Dynamic Surface Control of Uncertain Nonlinear Systems. An LMI Approach, Springer–Verlag, London (2011).
D. Swaroop, J. K. Hedrick, P. P. Yip, and J. C. Gerdes, “Dynamic surface control for a class of nonlinear systems,” IEEE Trans. of Automatic Control, 45, No. 11, 1893–1899 (2000).
C.-J. Wan, D. S. Bernstein, and V. T. Coppola, “Global stabilization of the oscillating eccentric rotor,” in: Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, USA (1994), pp. 4024–4029.
R. K. Yee, Spinup Dynamics of a Rotating System with Limiting Torque, Master’s Thesis, UCLA (1981).
Y. Zhang, L. Li, B. Cheng, and X. Zhang, “An active mass damper using rotating actuator for structural vibration control,” Adv. Mech. Eng., 8(7), 1–9 (2016).
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Translated from Prikladnaya Mekhanika, Vol. 54, No. 5, pp. 123–135, September–October, 2018.
* This study was granted by the President of Ukraine in line with competitive project F70/141-2017 of the State Fund for Fundamental Research.
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Khoroshun, A.S. Stabilization of Translation by an Eccentric Flywheel*. Int Appl Mech 54, 600–610 (2018). https://doi.org/10.1007/s10778-018-0914-y
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DOI: https://doi.org/10.1007/s10778-018-0914-y