0
TECHNICAL PAPERS

Time Optimal Swing-Up Control of Single Pendulum

[+] Author and Article Information
Yongcai Xu

ESS Tech. Inc., Feemont Ca

Masami Iwase, Katsuhisa Furuta

School of Science and Engineering, Department of Computers and Systems Engineering, Tokyo Denki University, Saitama, Japan

J. Dyn. Sys., Meas., Control 123(3), 518-527 (Feb 11, 2000) (10 pages) doi:10.1115/1.1383027 History: Received February 11, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.

References

Mori,  S., Nishihara,  H., and Furuta,  K., 1976, “Control Of Unstable Mechanical Control Of Pendulum,” Int. J. Control, 23, No. 5, pp. 673–692.
Furuta, K., Yamakita, M., and Kobayashi, S., 1992, “Swing-up Control of Inverted Pendulum Using Pseudo-state Feedback,” Proc. of Institute of Mechanical Engineers, Vol. 206, pp. 263–269.
Shiriaev, A. S., Ludvigsen, H., Egeland, O., and Fradkov, A. L., 1999, “Swinging up of Simplified Furuta Pendulum,” Proc. of ECC ’99.
Åström, K. J., and Furuta, K., 1996, “Swing Up a Pendulum by Energy Control,” IFAC 13th Triennial World Congress, San Francisco.
Yamakita, M., Iwashiro, M., Sugahara, Y., and Furuta, K., 1996, “Robust Swing Up Control of Double Pendulum,” Proceedings of the American Control Conference, Seattle, Washington.
Yurkovich,  S., and Widjaja,  M., 1996, “Fuzzy Controller Synthesis for an Inverted Pendulum System,” Control Engineering Practice, 4, No. 4, pp. 455–469.
Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., and Mischenko, E. F., 1962, The Mathematical Theory of Optimal Processes, Interscience Publishers.
Kirk, D. E., 1970, Optimal Control Theory, Prentice-Hall, Englewood, NJ.
Polak, E., 1971, Computational Methods in Optimization: A Unified Approach, Academic Press, New York.
Canon, M. D., Cullum, C. D., and Polak, E., 1970, Theory of Optimal Control and Mathematical Programming, McGraw-Hill, New York.
Lee,  Y. D., Kim,  B. H., and Gyoo,  H., 1999, “Evolutionary Approach for Time Optimal Trajectory Planning of a Robotic Manipulator,” Information Sciences, 113, No. 3–4, pp. 245–260.
Melikyan,  A. A., 1994, “Necessary Optimality Conditions for a Singular Surface in the Form of Synthesis,” J. Optim. Theory Appl., 82, No. 2, pp. 203–217.
Meier,  E. B., and Bryson,  A. E., 1990, “Efficient Algorithm for Time-Optimal Control of a Two-Link Manipulator,” Journal of Guidance, 13, No. 5.
Van Willigenburg,  L. G., and Loop,  R. P. H., 1991, “Computation of Time-optimal Controls Applied to Rigid Manipulators With Friction,” Int. J. Control, 54, No. 5, pp. 1097–1117.
Gäfert, M., Svensson, J., and Åström, K. A., Friction and Friction Compensation in the Furuta Pendulum, Proc. of ECC ’99.
Arczewski,  K., and Blajer,  W., 1996, “A Unified Approach to the Modelling of Holonomic and Nonholonomic Mechanical Systems,” Mathematical Modelling of Systems, 2, No. 3, pp. 157–174.
Furuta, K., and Xu, Y., 1999, “Project of Super-Mechano Systems—Study on Single Pendulum,” Proc. of SMC ’99, Tokyo Japan, Vol. 3, pp. 123–128.
Gabasov, R., and Kirillova, F. M., 1999, “Numerical Methods of Open-loop and Closed-loop Optimization of Linear Control Systems,” Report.
Lewis, F. L., 1986, Optimal Control, Wiley, New York.
Wu,  C. J., 1995, “Minimum-time Control for an Inverted Pendulum Under Force Constraints,” Journal of Intelligent & Robotic Systems, 12, No. 2, pp. 127–143.
Czogala,  E. M., and Pawlak,  Z. A., 1995, “Idea of a Rough Fuzzy Controller and its Application to the Stabilization of a Pendulum-car System,” Fuzzy Sets Syst., 72, No. 1, pp. 61–73.
Gregory, J., and Lin, C., 1992, Constrained Optimization in the Calculus of Variations and Optimal Control Theory, Van Nostrand Reinhold.
Eltohamy,  K. G., and Kuo,  C. Y., 1998, “Nonlinear Optimal Control of a Triple Link Inverted Pendulum With Single Control Input,” Int. J. Control, 69, No. 2, pp. 239–256.
Huang,  S. J., and Huang,  C. L., 1996, “Control of a Sliding Inverted Pendulum Using a Neural Network,” International Journal of Computer Application, 9, No. 2–3, pp. 67–75.
Liu, Y., and Kojima, H., 1994, “Optimal Design Method of Nonlinear Stabilizing Control System of Inverted Pendulum by Genetic Algorithm,” Nippon Kikai Gakkai Ronbunshu, C Hen, Vol. 60, No. 577, pp. 3124–3129.
Lin,  Z., Saberi,  A., Gutmann,  M., and Shamash,  Y., 1996, “Linear Controller of an Inverted Pendulum having Restricted Travel: a High-and-low Gain Approach,” Automatica, 32, No. 6, pp. 933–937.

Figures

Grahic Jump Location
Relation between input amplitude vin and torque τ of the motor. vd is the threshold of the dead zone
Grahic Jump Location
Comparison of time optimal control using nonlinear optimization (NO) and linear programming (LP): The upper shows the optimal input, and the lower shows the angle of the pendulum, where the solid line is of NO case and the dotted line is of LP case
Grahic Jump Location
Verification of necessary condition using simplified pendulum model: the upper is the angle as a result of optimal swing-up control, and the lower shows the optimal input (dotted line) and the corresponding switching function (solid line)
Grahic Jump Location
Verification of necessary condition using real pendulum model (8): the upper shows the angles of the pendulum (θ1: solid line) and the arm (θ0: dotted line) in Fig. 1. The lower shows the optimal input (dotted line) and the switching function (dashed line).
Grahic Jump Location
Illustration of Furuta Pendulum: a pendulum is hinged to a rotating arm connected to a direct-drive motor
Grahic Jump Location
Design of time optimal swing-up control of Furuta Pendulum: the upper is the designed input for swing-up, and the lower shows angles of the pendulum (θ1: solid line) and the arm (θ0: dashed line) in swing-up motion
Grahic Jump Location
Result of experiment: the dotted line shows the computed trajectory of the pendulum angle θ1. The dashed line is of the experimental result.
Grahic Jump Location
Result of experiment: the dotted line shows the computed trajectory of the arm rotation angle θ0. The dashed line is of the experimental result.
Grahic Jump Location
Optimal input used in experiment: the dotted line shows the designed input. The dashed line shows the input used in experiment.
Grahic Jump Location
Photos of swing-up control of Furuta Pendulum
Grahic Jump Location
Simulation result of swing-up control based on energy-based approach: the upper shows the angle of pendulum, and the lower shows the input
Grahic Jump Location
Result of swing-up control of the perturbed pendulum: the lower is the same control input as Fig. 6. The upper shows the angle of the pendulum (θ1: solid line) and the arm (θ0: dotted line)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In