This paper presents an approximate analytical solution for the weakly nonlinear closed-loop dynamics of the sliding phase of a sliding mode controlled rotary inverted pendulum based on the multiple scale method. A locally stable nonlinear sliding mode control law with starting configurations above the horizontal line is presented for the rotary inverted pendulum. The analytical expressions derived from the nonlinear solution of the reduced-order closed-loop dynamics provide both qualitative and quantitative insight into the closed-loop response leading to proper selection of parameters that guarantee stabilization and improve controller performance. The approximate analytical solution is verified through comparison with the exact numerical solution. The control performance predicted by the analytical solution is experimentally demo.
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March 2012
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Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design
Hashem Ashrafiuon,
Hashem Ashrafiuon
Director, Center for Nonlinear Dynamics and Control Professor e-mail:
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Alan M. Whitman
Alan M. Whitman
Professor Emeritus
Department of Mechanical Engineering, Villanova University, Villanova
, PA 19085
Search for other works by this author on:
Hashem Ashrafiuon
Director, Center for Nonlinear Dynamics and Control Professor e-mail:
Alan M. Whitman
Professor Emeritus
Department of Mechanical Engineering, Villanova University, Villanova
, PA 19085J. Dyn. Sys., Meas., Control. Mar 2012, 134(2): 024503 (9 pages)
Published Online: December 30, 2011
Article history
Received:
February 2, 2011
Revised:
September 26, 2011
Online:
December 30, 2011
Published:
December 30, 2011
Citation
Ashrafiuon, H., and Whitman, A. M. (December 30, 2011). "Closed-Loop Dynamic Analysis of a Rotary Inverted Pendulum for Control Design." ASME. J. Dyn. Sys., Meas., Control. March 2012; 134(2): 024503. https://doi.org/10.1115/1.4005358
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