TY - JOUR
T1 - On the stabilization of the inverted-cart pendulum using the saturation function approach
AU - Aguilar-Ibañez, Carlos
AU - Martínez-García, Juan C.
AU - Soria-López, Alberto
AU - Rubio, José De Jesús
PY - 2011
Y1 - 2011
N2 - A simple stabilizing controller for the cart-pendulum system is designed in this paper. Our control strategy describes the underactuated system as a chain of integrators with a high-order smooth nonlinear perturbation and assumes initialization of the system in the upper half plane. The design procedure involves two sequentially associated control actions: one linear and one bounded quasilinear. The first control action brings the nonactuated coordinate near to the upright position and keeps it inside of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
AB - A simple stabilizing controller for the cart-pendulum system is designed in this paper. Our control strategy describes the underactuated system as a chain of integrators with a high-order smooth nonlinear perturbation and assumes initialization of the system in the upper half plane. The design procedure involves two sequentially associated control actions: one linear and one bounded quasilinear. The first control action brings the nonactuated coordinate near to the upright position and keeps it inside of a well-characterized small vicinity, whereas the second control action asymptotically brings the whole state of the system to the origin. The corresponding closed-loop stability analysis uses standard linear stability arguments as well as the traditional Lyapunov method and the LaSalle's theorem. Our proposed control law ensures global stability of the system in the upper half plane. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
UR - http://www.scopus.com/inward/record.url?scp=84855227208&partnerID=8YFLogxK
U2 - 10.1155/2011/856015
DO - 10.1155/2011/856015
M3 - Artículo
SN - 1024-123X
VL - 2011
JO - Mathematical Problems in Engineering
JF - Mathematical Problems in Engineering
M1 - 856015
ER -