TY - JOUR
T1 - Experimental evaluation of regulated non-linear under-actuated mechanical systems via saturation-functions-based bounded control
T2 - The cart-pendulum system case
AU - Soria-López, Alberto
AU - Martínez-García, Juan Carlos
AU - Aguilar-Ibañez, Carlos F.
PY - 2013
Y1 - 2013
N2 - The authors are concerned in this study by bounded control of single input non-linear under-actuated mechanical systems. The authors focus the exposition on a feedback-based stabilisation-bounded control action shaped by saturation functions, and the proposed approach was illustrated via the design and the experimental evaluation of a simple stabilising controller for the cart-pendulum system, a well-known control benchmark. The proposed simple control strategy is built around a lumped linear continuous time-invariant description of the concerned under-actuated non-linear system. Namely, a model consisted of a cascade non-linear dynamical system constituted by a chain of four integrators affected by a high-order smooth non-linear perturbation. Assuming initialisation of the under-actuated system to the upper-half plane, the proposed feedbackbased regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasi-linear. Control boundedness is provided in both involved control actions by specifically designed saturation functions. The first bounded control action brings the non-actuated coordinate near to the upright position and keep it inside of a well characterised small vicinity, whereas the second bounded control action asymptotically brings the whole state of the dynamical system to the origin. The necessary closed-loop stability analysis uses standard linear stability arguments as well as the traditional well-known Lyapunov method and the LaSalle's invariance principle. The proposed control law ensures global stability of the closed-loop system in the upper-half plane.
AB - The authors are concerned in this study by bounded control of single input non-linear under-actuated mechanical systems. The authors focus the exposition on a feedback-based stabilisation-bounded control action shaped by saturation functions, and the proposed approach was illustrated via the design and the experimental evaluation of a simple stabilising controller for the cart-pendulum system, a well-known control benchmark. The proposed simple control strategy is built around a lumped linear continuous time-invariant description of the concerned under-actuated non-linear system. Namely, a model consisted of a cascade non-linear dynamical system constituted by a chain of four integrators affected by a high-order smooth non-linear perturbation. Assuming initialisation of the under-actuated system to the upper-half plane, the proposed feedbackbased regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasi-linear. Control boundedness is provided in both involved control actions by specifically designed saturation functions. The first bounded control action brings the non-actuated coordinate near to the upright position and keep it inside of a well characterised small vicinity, whereas the second bounded control action asymptotically brings the whole state of the dynamical system to the origin. The necessary closed-loop stability analysis uses standard linear stability arguments as well as the traditional well-known Lyapunov method and the LaSalle's invariance principle. The proposed control law ensures global stability of the closed-loop system in the upper-half plane.
UR - http://www.scopus.com/inward/record.url?scp=84883865329&partnerID=8YFLogxK
U2 - 10.1049/iet-cta.2012.0958
DO - 10.1049/iet-cta.2012.0958
M3 - Artículo
SN - 1751-8644
VL - 7
SP - 1642
EP - 1650
JO - IET Control Theory and Applications
JF - IET Control Theory and Applications
IS - 12
ER -