Swing-up time analysis of pendulum

• Autorzy: Furuta K. , Iwase M.
• Języki publikacji: EN

Abstrakty

EN

Swing-up control of a single pendulum from the pendant to the upright position is firstly surveyed. The control laws are comparatively studied based on swing-up time from a given initial state to the upright position. The State Dependent Riccati Equation is found effective for designing the swing-up control law under saturating control input. The control law is extended to a linear combination of sine function of the angle and the angular velocity, and a variable structure control with a sliding mode given by the linear combination. Making the swing-up time correspond to a colour, which is similar to the Fractal analysis, colour maps of the swing-up time for given control parameters and initial conditions yield interesting Fractal-like figures.

Słowa kluczowe

EN

pendulum control; state dependent Riccati equation; nonlinear control; artificial gravity; fractal

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 153--163
• Opis fizyczny: Bibliogr. 22 poz., 20 rys.

Twórcy

autor

Furuta K.

• Department of Computers and Systems Engineering, Tokyo Denki University Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan

autor

Iwase M.

• Department of Computers and Systems Engineering, Tokyo Denki University Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan

• Department of Computers and Systems Engineering, Tokyo Denki University Hatoyama-cho, Hiki-gun, Saitama 350-0394, Japan,

Bibliografia

• [1] A. Stephenson, “On a new type of dynamical stability”, Manchester Memoirs 8, 1–10 (1908).
• [2] D.J. Acheson, “A pendulum theorem”, Proc. R.Soc. Lond. A (443), 239–245 (1993).
• [3] D.J. Acheson, “Upside-down pendulums”, Nature 336, 215– 216 (1993).
• [4] J. Baillieul and B. Lehman, “Open-loop control using oscillatory input”, in CRC Control Handbook, edited by W.S.Levine, 967–980 (1996).
• [5] A.E. Bryson (Jr.) and D.G. Luenberger, “The synthesis of regulator logic using state-variable concepts”, Proceedings of IEEE, 58, 1803–1811 (1970).
• [6] B. Friedland, Control System Design, McGraw-Hill Publishing Company, 1986.
• [7] Z. Minglian, H. Jiankang, and H. Weidong, “Humanimitating intelligent control and triple inverted pendulum”, Chinese J. of Aeronautics 2, 135–146 (1996).
• [8] K.G. Eltohamy and C.Y. Kuo, “Real time stabilization of a triple link inverted pendulum using single control input”, IEE Proc-Control Theory Appl. 5, 498–504 (1997).
• [9] K.G. Eltohamy and C.Y. Kuo, “Nonlinear optimal control of a triple link inverted pendulum with single control input”, Int. J. Control 2, 239–256 (1998).
• [10] T. Hoshino, H. Kawai, and K. Furuta, “Stabilization of the triple spherical inverted pendulum – a simultaneous design approach”, Autommatisierungstechnik 48, 577–587 (2000).
• [11] Napoleon, T. Hoshino, and K. Furuta, “Hand over control of unstable object using maniulators”, The 20th IEEE CDC, Sydney, 2000.
• [12] W. Maletinsky, M.F. Sennning, and F. Wiederkehr, “Observer based control of a double pendulum”, IFAC Congress Kyoto, XIII(63), 61–65 (1981).
• [13] M.W. Spong and L. Praly, “Control of underactuated mechanical systems using switching and saturation”, in Control Using Logic-based Switching, edited by A.S. Morse, London, Springer, 135–150 (1997).
• [14] K. Furuta, T. Ochiai, and N.Ono, “Attitude control of a triple inverted pendulum”, Internat. J. Control 39, 1351–1365 (1984).
• [15] S. Mori, H. Nishihara, and K. Furuta, “Control of unstable mechanical systems: Control of pendulum”, Internat. J. Control 23, 673–692 (1976).
• [16] K. Furuta, M. Yamakita, and S. Kobayashi, “Swing-up control of inverted pendulum using pseudo-state feedback”, Proc. Instn. Mech. Engrs., 206, 263–269 (1993).
• [17] K.J. ˚Astr¨om and K. Furuta, “Swinging-up a pendulum by energy control”, Proc IFAC Congress, E, 37–95 (1996).
• [18] M. Yamakita and K. Furuta, “Toward robust state transfer control of titech double pendulum”, The °Astr¨om Symposium on Control, ed. by Wittenmark and Rantzer, 73–269 (1999).
• [19] J.A. Acosta, F. Gordillo and J. Aracil, “A new sg law for swinging the Furuta pendulum up”, 5th IFAC Symposium Nonlinear Control Systems, 3, 818–823 (2001).
• [20] I. Fantoni and R. Lozano, “Stabilization of the Furuta pendulum around its homoclinic orbit”, 5th IFAC Symposium Nonlinear Control Systems, 3, 830–835 (2001).
• [21] J. Zhao and M.W. Spong, “Hybrid control for global stabilization of the cart-pendulum system”, Automatica 37, 1941–1951 (2001).
• [22] K. Furuta, “Plenary talk”, 15-th IFAC World Congress Barcelona, Plenary Papers, Survey Papers and Milestones, 35–44 (2002). Beyond, New York, Springer, 2004.
• [24] R.L. Devancy, An Introduction to Chaotic Dynamical Systems, 2nd eddition, Addison-Wesley Publishing Company, 1989.
• [25] W. Blajer, “A projection method approach to constrained dynamic analysis”, J. Appl. Mech. 59, 643–649 (1992).
• [26] C.P. Mracek and J.R. Cloutier, “A preliminary control design for the nonlinear benchmark problem”, IEEE Conference on Control Applications, 265–272 (1996).