Nonlinear Optimal Internal Forces Control and Application to Swing-Up and Stabilization of Pendulum

[+] Author and Article Information
Satoshi Suzuki

The 21st Century COE Project Office, Tokyo Denki University (TDU), 2-2 Kanda Nishiki-cho, Chiyodaku, 101-84-57 Japan

Katsuhisa Furuta, Akihiko Sugiki, Shoshiro Hatakeyama

School of Science and Engineering, TDU, Ishizaka, Hatoyama, Saitama 350-0394 Japan

J. Dyn. Sys., Meas., Control 126(3), 568-573 (Dec 03, 2004) (6 pages) doi:10.1115/1.1789972 History: Received April 26, 2002; Online December 03, 2004
Copyright © 2004 by ASME
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Iwasaki, T., Hara, S., and Yamauchi, H., 2000, “Structure/Control Design Integration With Finite Frequency Positive Real Property,” Proc. of the American Control Conference, Chicago, IL., pp. 549–553.
Blajer,  W., 1992, “A Projection Method Approach to Constrained Dynamic Analysis,” J. Appl. Mech., 59, pp. 643–649.
Cloutier, J. R., and Cockburn, J. C., 2001, “The State-Dependent Nonlinear Regulator With State Constraints,” Proc. of the American Control Conference, Arlington, VA., pp. 390–395.
Cloutier, J. R., and Zipfel, P. H., 1999, “Hypersonic Guidance via the State-Dependent Ricatti Equation Control Method,” Proc. of the 1999 IEEE Int. Conf. on Control Applications, Kohala Coast-Island of Hawai’i, pp. 219–224.
Palumbo, N. F., and Jackson, T. D., 1999, “Integrated Missile Guidance and Control: A State Dependent Riccati Differential Equation Approach,” Proc. of the 1999 IEEE Int. Conf. on Control Applications, Kohala Coast-Island of Hawai’i, pp. 243–248.
Xin, M., Balakrishnan, S. N., and Huang, Z., 2001, “Robust State Dependent Riccati Equation Based Robot Manipulator Control,” Proc. of the 2001 IEEE Int. Conf. on Control Applications, Mexico City, Mexico, pp. 369–374.
Furuta, K., 2002, “Super-Mechano Systems,” 15th World Congress of IFAC, Barcelona, Spain, in Plenary lecture.
Lukes,  W. M., 1969, “Optimal Regulation of Nonlinear Dynamical Systems,” SIAM J. Control Optim., 7(1), pp. 75–100.
Lu,  W. M., and Doyle,  J. C., 1995, “H Control of Nonlinear Systems: a Convex Characterization,” IEEE Trans. Autom. Control, 40(9), pp. 1668–1675.
Beard,  R. W., Sardis,  G. N., and Wen,  J. T., 1997, “Galerkin Approximations of the Generalized Hamilton-Jacobi-Bellman Equation,” Automatica, 33(12), pp. 2159–2177.
Cloutier, J. R., D’Souza, C. N., and Mracek, C. P., 1996, “Nonlinear Regulation and Nonlinear H Control via the State-Dependent Ricatti Equation Technique: Part 1, Theory,” Proc. of the Int. Conf. on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, FL.
Huang, Y., and Jadbabaie, A., 1999, “Nonlinear H Control: An Enhanced Quasi-LPV Approach,” 14th World Congress of IFAC, Beijing, P.R., China, pp. 85–90.
Huang, Y., and Lu, W., 1996, “Nonlinear Optimal Control: Alternatives to Hamilton–Jacobi Equation,” Proc. of the 35th Conf. on Decision and Control, Kobe, Japan, pp. 3942–3947.
Anderson, B. D. O., and Moore, J. B., 1990, Optimal Control—Linear Quadratic Methods, Prentice Hall, Englewood Cliffs, NJ.
Sznaier, M., Cloutier, J., Hull, R., Jacques, D., and Mracek, C., 1998, “A Receding Horizon State Dependent Riccati Equation Approach to Suboptimal Regulation of Nonlinear Systems,” Proc. of the 37th IEEE Conf. on Decision and Control, Tampa, FL, pp. 1792–1797.
Chung,  C. C., and Hauser,  J., 1995, “Nonlinear Control of a Swinging Pendulum,” Automatica, 31(6), pp. 851–862.
Lin,  Z., Saberi,  A., Gutmann,  M., and Shamash,  Y. A., 1996, “Linear Controller for an Inverted Pendulum Having Restricted Rravel: a High-and-Low Approach,” Automatica, 32(6), pp. 933–937.
Åström,  K. J., and Furuta,  K., 2000, “Swinging Up a Pendulum by Energy Control,” Automatica, 36(2), pp. 287–296.
Xu,  Y., Iwase,  M., and Furuta,  K., 2001, “Time Optimal Swing-Up Control of Single Pendulum,” ASME J. Dyn. Syst., Meas., Control, 123, pp. 518–527.
Furuta,  K., Yamakita,  M., and Kobayashi,  K., 1992, “Swing-Up Control of Inverted Pendulum Using Pseudo-State Feedback,” J. Syst. Control Engineering,206, pp. 263–269.
Koga,  M., Toriumi,  H., and Sampei,  M., 1998, “An Integrated Software Environment for Design and Real-Time Implementation of Control Systems,” Control Eng. Pract., 6(10), pp. 1287–1293.


Grahic Jump Location
Model of one link Furuta pendulum
Grahic Jump Location
One-link Furuta pendulum
Grahic Jump Location
Shape of weighting functions
Grahic Jump Location
Experimental result (IFC: internal forces control, NSDC: nonlinear state-dependent control)
Grahic Jump Location
Transition of weighting functions (IFC: internal forces control, NSDC: nonlinear state-dependent control)




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