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The Furuta pendulum, or rotational inverted pendulum, consists of a driven arm which rotates in the horizontal plane and a pendulum attached to that arm which is free to rotate in the vertical plane. It was invented in 1992 at (Tokyo Institute of Technology ) by Katsuhisa Furuta 〔Furuta, K., Yamakita, M. and Kobayashi, S. (1992) “Swing-up control of inverted pendulum using pseudo-state feedback”, Journal of Systems and Control Engineering, 206(6), 263-269.〕〔Xu, Y., Iwase, M. and Furuta, K. (2001) “Time optimal swing-up control of single pendulum”, Journal of Dynamic Systems, Measurement, and Control, 123(3), 518-527.〕〔Furuta, K., Iwase, M. (2004) “Swing-up time analysis of pendulum”, Bulletin of the Polish Academy of Sciences: Technical Sciences, 52(3), 153-163.〕〔Iwase, M., Åström, K.J., Furuta, K. and Åkesson, J. (2006) “Analysis of safe manual control by using Furuta pendulum”, Proceedings of the IEEE International Conference on Control Applications, 568-572.〕 and his colleagues. It is an example of a complex nonlinear oscillator of interest in control system theory. The pendulum is underactuated and extremely non-linear due to the gravitational forces and the coupling arising from the Coriolis and centripetal forces. Since then, dozens, possibly hundreds of papers and theses have used the system to demonstrate linear and non-linear control laws.〔J.Á. Acosta, “Furuta's Pendulum: A Conservative Nonlinear Model for Theory and Practise,” Mathematical Problems in Engineering, vol. 2010, Article ID 742894, 29 pages. http://www.hindawi.com/journals/mpe/2010/742894.html〕〔Åkesson, J. and Åström, K.J. (2001) “Safe Manual Control of the Furuta Pendulum”, In Proceedings 2001 IEEE International Conference on Control Applications (CCA'01), pp. 890-895.〕〔Olfati-Saber, R. (2001) “Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles”, PhD Thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA. http://www.cds.caltech.edu/~olfati/thesis/〕 The system has also been the subject of two texts.〔Fantoni, I. and Lozano, R. (2002) “Non-linear control of underactuated mechanical systems”, Springer-Verlag, London.〕〔Egeland, O. and Gravdahl, T. (2002) “Modeling and Simulation for Automatic Control”, Marine Cybernetics, Trondheim, Norway, 639 pp., ISBN 82-92356-00-2.〕 ==Equations of motion== Despite the great deal of attention the system has received, very few publications successfully derive (or use) the full dynamics. Many authors 〔〔 have only considered the rotational inertia of the pendulum for a single principal axis (or neglected it altogether 〔). In other words, the inertia tensor only has a single non-zero element (or none), and the remaining two diagonal terms are zero. It is possible to find a pendulum system where the moment of inertia in one of the three principal axes is approximately zero, but not two. A few authors 〔〔〔〔Hirata, H., Haga, K., Anabuki, M., Ouchi, S. and Ratiroch-Anant, P. (2006) “Self-Tuning Control for Rotation Type Inverted Pendulum Using Two Kinds of Adaptive Controllers”, Proceedings of the 2006 IEEE Conference on Robotics, Automation and Mechatronics, 1-6. http://lab8.ec.u-tokai.ac.jp/RAM062.pdf〕〔Ratiroch-Anant, P., Anabuki, M. and Hirata, H. (2004) “Self-tuning control for rotational inverted pendulum by eigenvalue approach”, Proceedings of TENCON 2004, IEEE Region 10 Conference, Volume D, 542-545. http://lab8.ec.u-tokai.ac.jp/TENCON2004_D-542.pdf〕〔Baba, Y., Izutsu, M., Pan, Y. And Furuta, K. (2006) “Design of control method to rotate pendulum”, Proceedings of SICE-ICASE International Joint Conference, Korea.〕 have considered slender symmetric pendulums where the moments of inertia for two of the principal axes are equal and the remaining moment of inertia is zero. Of the dozens of publications surveyed for this wiki only a single conference paper 〔Craig, K. and Awtar, S. (2005) “Inverted pendulum systems: rotary and arm-driven a mechatronic system design case study”, Proceedings of the 7th Mechatronics Forum International Conference, Atlanta. http://www-personal.umich.edu/~awtar/craig_awtar_1.pdf〕 and journal paper 〔Awtar, S., King, N., Allen, T., Bang, I., Hagan, M., Skidmore, D. and Craig, K. (2002) “Inverted pendulum systems: Rotary and arm-driven – A mechatronic system design case study”, Mechatronics, 12, 357-370. http://www-personal.umich.edu/~awtar/invertedpendulum_mechatronics.pdf〕 were found to include all three principal inertial terms of the pendulum. Both papers used a Lagrangian formulation but each contained minor errors (presumably typographical). The equations of motion presented here are an extract from a (paper )〔Cazzolato, B.S and Prime, Z (2011) "On the Dynamics of the Furuta Pendulum", Journal of Control Science and Engineering, Volume 2011 (2011), Article ID 528341, 8 pages. http://downloads.hindawi.com/journals/jcse/2011/528341.pdf〕 on the Furuta pendulum dynamics derived at the University of Adelaide. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Furuta pendulum」の詳細全文を読む スポンサード リンク
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