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Second‐order sliding mode control of underactuated mechanical systems II: Orbital stabilization of an inverted pendulum with application to swing up/balancing control
Author(s) -
Santiesteban Raul,
Floquet Thierry,
Orlov Yury,
Riachy Samer,
Richard JeanPierre
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1203
Subject(s) - inverted pendulum , control theory (sociology) , underactuation , swing , position (finance) , pendulum , controller (irrigation) , double inverted pendulum , computer science , sliding mode control , double pendulum , orbit (dynamics) , bounded function , mathematics , physics , control (management) , engineering , mathematical analysis , nonlinear system , finance , quantum mechanics , artificial intelligence , acoustics , agronomy , economics , biology , aerospace engineering
Orbital stabilization of an underactuated cart–pendulum system is under study. The quasihomogeneous control synthesis is utilized to design a second‐order sliding mode controller that drives the actuated cart to a periodic reference orbit in finite time, while the non‐actuated pendulum produces bounded oscillations. A modified Van der Pol oscillator is introduced into the synthesis as an asymptotic generator of the periodic motion. The resulting closed‐loop system is capable of moving from one orbit to another by simply changing the parameters of the Van der Pol modification. Performance issues of the proposed synthesis are illustrated in numerical and experimental studies of the swing up/balancing control problem of moving a pendulum, located on an actuated cart, from its stable downward position to the unstable inverted position and stabilizing it about the vertical. Copyright © 2007 John Wiley & Sons, Ltd.