Abstract
This paper deals with the stability problem of two types of inverted pendulum controlled by a fractional order PD controller. Rotational inverted pendulum and cart inverted pendulum are under-actuated mechanical systems with two degrees of freedom and one control input. Detailed mathematical models of both pendulums are derived using the Rodriguez method. Fractional order PD controller is introduced for inverted pendulum stabilization. Stability regions in control parameters space are calculated using the D-decomposition approach, based on which tuning of the fractional order controller can be carried out. Numerical simulations and experimental realization are given to demonstrate the effectiveness of the proposed method.
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Kwon, T., Hodgins J.: Control systems for human running using an inverted pendulum model and a reference motion capture sequence, In: 2010 ACM SIGGRAPH Eurographics Symposium on Computer Animation, July 2010
Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
Neimark, Y.I.: D-decomposition of the space of the quasi-polynomials. Appl. Math. Mech. 13, 349–380 (1949). (in Russian)
Mandić, P.D., Lazarević, M.P., Šekara: T.B.: D-decomposition method for stabilization of inverted pendulum using fractional order PD controller. In: Proceedings of First International Conference on Electrical, Electronic and Computing Engineering (2014)
Mandić, P.D., Lazarević, M.P., Šekara, T.B.: Fractional order PD control of Furuta pendulum: D-decomposition approach. In: Proceedings of IEEE International Conference on Fractional Differentiation and its Applications (2014)
Mandić, P.D., Lazarević, M.P., Šekara, T.B.: D-decomposition technique for stabilization of Furuta pendulum : fractional approach. Bull. Poly. Acad. Tech. 64, 189–196 (2016)
Čović, V., Lazarević, M.P.: Robot Mechanics, Faculty of Mechanical Engineering, Belgrade (2009). (in Serbian)
Khalil, H.: Nonlinear Systems. Prentice Hall, Upper Saddle River (2002)
Mandić, P.D., Lazarević, M.P., Šekara, T.B., Jovanović, R.Ž.: Stabilization of the cart pendulum system by fractional order control with experimental realization. In: Paper Submitted for ICFDA 2016 Conference, Novi Sad, 18–20 July 2016
Šekara, T.B., Rapaić, M.R., Lazarević, M.P.: An efficient method for approximation of non-rational transfer functions. Electronics 17(1), 40–44 (2013)
Acknowledgment
Authors gratefully acknowledge the support of Ministry of Education, Science and Technological Development of the Republic of Serbia under the project TR 33047 (P.D.M.) as well as the support of projects TR 35006 (M.P.L.) and TR 33020 (T.B.Š).
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Mandić, P.D., Lazarević, M.P., Šekara, T.B. (2017). Stabilization of Inverted Pendulum by Fractional Order PD Controller with Experimental Validation: D-decomposition Approach. In: Rodić, A., Borangiu, T. (eds) Advances in Robot Design and Intelligent Control. RAAD 2016. Advances in Intelligent Systems and Computing, vol 540. Springer, Cham. https://doi.org/10.1007/978-3-319-49058-8_4
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DOI: https://doi.org/10.1007/978-3-319-49058-8_4
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