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Swing-up control of inverted pendulum systems

Published online by Cambridge University Press:  09 March 2009

Alan Bradshaw  and
Jindi Shao
Alan Bradshaw
Affiliation:
Engineering DepartmentLancaster UniversityLancasterLAI 4YR (UK)
Jindi Shao
Affiliation:
Engineering DepartmentLancaster UniversityLancasterLAI 4YR (UK)
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Summary

In Part I a technique for the swing-up control of single inverted pendulum system is presented. The requirement is to swing-up a carriage mounted pendulum system from its natural pendent position to its inverted position. It works for all carriage balancing single inverted pendulum systems as the swing-up control algorithm does not require knowledge of the system parameters. Comparison with previous swing-up controls shows that the proposed swing-up control is simpler, eaiser. more efficient, and more robust.

In Part II the technique is extended to the case of the swing-up control of double inverted pendulum systems. Use is made of a novel selective partial-state feedback control law. The nonlinear, open-loop unstable, nonminimum-phase. and interactive MIMO pendulum system is actively linearised and decoupled about a neutrally stable equilibrium by the partial-state feedback control. This technique for swing-up control is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.

Keywords

Inverted pendulumNonlinear unstable systemsSwing-up controlPartial-state feedback
Type
Article
Information
Robotica , Volume 14 , Issue 4 , July 1996 , pp. 397 - 405
Copyright
Copyright © Cambridge University Press 1996

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References

1.Shao, J., “Dynamics & Nonlinear Control of Unstable Inverted Pendulum Systems” PhD Thesis (Engineering Department of Lancaster University, Britain, 1995).Google Scholar
2.Todd, D.J., Walking Machines-an Introduction to Legged Robots (Kogan Page Ltd, London, 1985).Google Scholar
3.Raibert, M.H., Legged Robots that Balance (The MIT Press. London, 1986).Google Scholar
4.Mori, S., Nishihara, H. and Furuta, K., “Control of Unstable Mechanical System, Control of Pendulum” Int. J. Control 23, No. 5, 673–692 (1976).CrossRefGoogle Scholar
5.Furuta, K., Yamakita, M. and Kobayashi, S., “Swing Up Control of Inverted Pendulum” IECON”91 (1991) pp. 2193–2198.Google Scholar
6.Furuta, K., Yamakita, M., Kobayashi, S. and Nishimura, M. “A New Inverted Pendulum Apparatus for Education” IFAC Advances in Control Education, Massachusetts, USA (1991) pp. 133–138.Google Scholar
7.Bradshaw, A., Seward, D.W. and Nagy, F.N.“Robo Sapiens: a Personal Assistant Robot”Proc. of Joint Hungarian British Mechatronks Conf.,Budapest, (Sept. 1994) pp. 159–164.Google Scholar
8.Brogan, W.L.Modern Control Theory (Prentice-Hall, New Jersey, 1991).Google Scholar
9.Higdon, D.T. and Cannon, R.H. “On the Control of Unstable Multiple-Output Mechanical Systems” ASME Winter Annual Meeting, Philadelphia (November, 1963) paper No. 63-WA-148.Google Scholar
10.Furuta, K., Kajiwara, H. and Kosuge, K. “Digital Control of a Double Inverted Pendulum on an Inclined Rail” Int. J. Control 32, No. 5. 907–924 (1980).CrossRefGoogle Scholar
11.Furuta, K., Ochiai, T. and Ono, N. “Attitude Control of a Triple Inverted Pendulum” Int. J. Control 39, No. 6, 1351–1365 (1984).CrossRefGoogle Scholar
12.Farwig, H.M.Z. and Unbenauen, H. “Discrete Computer Control of a Triple Inverted Pendulum” Optimal Control Applications and Methods 11, 157–171 (1990).CrossRefGoogle Scholar