Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 48, Issue 1 / 2013 | Next article >>
Yu.G. Martynenko and A.M. Formal'skii, "Controlled Pendulum on a Movable Base," Mech. Solids. 48 (1), 6-18 (2013)
Year 2013 Volume 48 Number 1 Pages 6-18
DOI 10.3103/S0025654413010020
Title Controlled Pendulum on a Movable Base
Author(s) Yu.G. Martynenko (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia)
A.M. Formal'skii (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192, Russia, formal@imec.msu.ru)
Abstract A plane motion of a multilink pendulum hinged to a movable base (a wheel or a carriage) is considered. The control torque applied between the base and the first link of the pendulum is independent of the base position and velocity and is bounded in absolute value. The coordinate determining the base position is cyclic. The mathematical model of the system permits one to single out the equations describing the pendulum motion alone, which differ from the well-known equations of motion of a pendulum with a fixed suspension point both in the structure and in the parameters occurring in these equations. The phase portrait of motions of a control-free one-link pendulum suspended on a wheel or a carriage is obtained. A feedback control ensuring global stabilization of the unstable upper equilibrium of the pendulum is constructed. Time-optimal control synthesis is outlined.
Keywords pendulum, unstable equilibrium, controllability domain, time optimality, communication, vibration frequency
References
1.  Yu. G. Martynenko and A. M. Formal'skii, "The Theory of the Control of a Monocycle," Prikl. Mat. Mekh. 69 (4), 569-583 (2005) [J. Appl. Math. Mech. (Engl. Transl.) 69 (4), 516-528 (2005)].
2.  Yu. G. Martynenko and A. M. Formal'skii, "Problems of Control of Unstable Systems," Uspekhi Mekh. 3 (2), 71-135 (2005).
3.  Yu. G. Martynenko and A. M. Formal'skii, "A Control of the Longitudinal Motion of a Single-Wheel Robot on an Uneven Surface," Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 4, 165-173 (2005) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 44 (4), 662-670 (2005)].
4.  F. L. Chernousko, L. D. Akulenko, and B. N. Sokolov, Control of Oscillations (Nauka, Moscow, 1980) [in Russian].
5.  Y. Aoustin and A. M. Formal'sky, "Simple Anti-Swing Feedback Control for a Gantry Crane," Robotica 21, 655-666 (2003).
6.  N. N. Bolotnik, I. M. Zeidis, K. Zimmermann, and S. F. Yatsun, "Dynamics of Controlled Motion of Vibration-Driven Systems," Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 5, 157-167 (2006) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 45 (5), 831-840 (2006)].
7.  A. M. Formal'skii, Displacement of Anthropomorphic Mechanisms (Nauka, Moscow, 1982) [in Russian].
8.  Khaled Gamal Eltohamy and Chen-Yuan Kuo, "Nonlinear Generalized Equations of Motion for Multi-Link Inverted Pendulum Systems," Int. J. Syst. Sci. 30 (5), 505-513 (1999).
9.  S. Lam and E. J. Davison, "The Real Stabilizability Radius of the Multi-Link Inverted Pendulum," in Proc. 2006 American Control Conf. Minneapolis, Minnesota, USA (2006), pp. 1814-1819.
10.  T. G. Strizhak, Methods for Studying `Pendulum'-Type Dynamical Systems (Nauka, Alma-Ata, 1981) [in Russian].
11.  A. M. Formal'skii, " Stabilization of an Inverted Pendulum with a Fixed or Movable Suspension Point," Dokl. Ross. Akad. Nauk 406 (2), 175-179 (2006) [Dokl. Math. (Engl. Transl.) 73 (1), 152-156 (2006)].
12.  A. M. Formal'skii, " An Inverted Pendulum on a Fixed and a Moving Base," Prikl. Mat. Mekh. 70 (1), 62-71 (2006) [J. Appl. Math. Mech. (Engl. Transl.) 70 (1), 56-64 (2006)].
13.  A. M. Formal'skii, "Stabilization of Unstable Mechanical Systems," J. Optimiz. Theory Appl. 144 (2), 227-253 (2010).
14.  N. G. Chetaev, Stability of Motion (Izdat. AN SSSR, Moscow, 1962) [in Russian].
15.  B. A. Smol'nikov, Problems of Mechanics and Robots Optimization (Nauka, Moscow, 1991) [in Russian].
16.  A. M. Formal'skii, Controllability and Stability of Systems with Restricted Resources (Nauka, Moscow, 1974) [in Russian].
17.  E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Wiley, New York, 1967; Nauka, Moscow, 1972).
18.  L. S. Pontryagin, V. G. Boltyanskii, R. V.Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Nauka, Moscow, 1983; Gordon & Breach Sci. Publ., New York, 1986).
19.  S. A. Reshmin and F. L. Chernous'ko, "Time-Optimal Control of an Inverted Pendulum in the Feedback Form," Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 3, 51-62 (2006) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 45 (3), 383-394 (2006)].
20.  S. A. Reshmin and F. L. Chernous'ko, "A Time-Optimal Control Synthesis for a Nonlinear Pendulum," Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 1, 13-22 (2007) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 46 (1), 9-18 (2007)].
21.  S. A. Reshmin and F. L. Chernousko, "Optimal in the Speed of Response Synthesis of Control in Problems of Swaying and Damping of Nonlinear Pendulum Oscillations," in Proc. 9th Chetaev Conf. "Analytical Mechanics, Stability, and Control of Motion", Vol. 3 (Irkutsk, 2007), pp. 179-196 [in Russian].
22.  R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 1 Gostekhizdat, Moscow-Leningrad, 1951 [in Russian].
23.  F. R. Gantmakher, Theory of Matrices (Nauka, Moscow, 1967) [in Russian].
24.  Ya. G. Panovko and I. I. Gubanova, Stability and Oscillations of Elastic Systems (Consultant Bureau, New York 1965; Nauka, Moscow, 1987).
Received 08 June 2011
Link to Fulltext
<< Previous article | Volume 48, Issue 1 / 2013 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100