Analysis of a Double Pendulum System with Joint Actuation by a Non-Linear Control

Abstract:

This article presents the study of a double pendulum system with distributed mass carrying an actuator at the joint between the two rods. This actuator can move the outer rod in order to inject or remove energy from the system, which is modeled as a body with variable position of the center of mass. The objective of this work is to develop a control technique that can make the pendulum swing up and rotate itself, similar to many other double pendulum investigations, but in the present case without any actuation on the fixed joint. The system is modeled with Simulink® software, using the parameters of a real model.

• Periodical: Applied Mechanics and Materials (Volume 849)
• Pages: 13-26
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.849.13
• Online since: August 2016
• Authors: Marcelo Pereira*, H.I. Weber
• Keywords: Non-Linear Control, Rotating Double Pendulum, Variable Center of Mass, Variable Inertia

References

[1] M.C. Pereira, H.I. Weber, In: plane position of a rotary arm using a reaction wheel. Proceedings of DINCON'11, Águas de Lindóia, Brazil, pp.136-139, (2011).

[2] M. Spong, P. Corke and R. Lozano, In: Nonlinear control of the Reaction Wheel Pendulum, Automatica #37 pp.1845-1851, (2001).

DOI: 10.1016/s0005-1098(01)00145-5

[3] K.J. Åström, K. Furuta, M. Iwashiro, and T. Hoshino, In: Energy based strategies for swinging up a double pendulum, IFAC World Congress. Beijing, China, (1995).

DOI: 10.1016/s1474-6670(17)57101-3

[4] J. Awrejcewicz and G. Kudra, In: Dynamics of a real triple pendulum – modeling and experimental observation, ENOC 2008, St. Petersburg, Russia, (2008).

[5] M.C. Pereira, H.I. Weber, In: Analysis of the oscillation of a self-excited pendulum due to varying length, Proceedings of PANACM'2015, Buenos Aires, Argentina, pp.272-280, (2015).

[6] K.J. Åström and K. Furuta, In: Swinging up a pendulum by energy control, Automatica 36, 287-295, (2000).

DOI: 10.1016/s0005-1098(99)00140-5

[7] M. Bugeja, In: Non-linear swing-up and stabilizing control of an inverted pendulum system, Proceedings of the IEEE Int. Conf. on Computer as a Tool, EUROCON'03, Ljubljana, Slovenia (2003).

DOI: 10.1109/eurcon.2003.1248235

[8] G. Zhai, In: Swinging up and Stabilizing an Inverted Pendulum by Switching Control, International Conference on Mechatronics and Automation, ICMA 2007, pp.521-526, (2007).

DOI: 10.1109/icma.2007.4303597

[9] C.C. Chung and J. Hauser, In: Nonlinear control of a swinging pendulum, Automatica, 31: 6, p.851–862, (1995).

DOI: 10.1016/0005-1098(94)00148-c

[10] A.M. Tusset, V. Piccirillio, A.M. Bueno ; J.M. Balthazar, D. Sado, J.L.F. Palacios and R.M.L.R.F. Brasil, In: Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker. Journal of Vibration and Control, pp.1-17, (2015).

DOI: 10.1177/1077546314564782

[11] R.H. Avanço, H.A. Navarro, J.M. Balthazar, A.M. Bueno and A.M. Tusset, In: Statements on nonlinear dynamics behavior of a pendulum, excited by a crank-shaft-slider mechanism, Meccanica (Milano. Print), pp.1-20, (2015).

DOI: 10.1007/s11012-015-0310-1

[12] K. Magnus, In: Vibrations, Blackie & Son Limited, Glasgow, (1965).

[13] S.H. Strogatz, In: Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering, Perseus, (1994).