TY - JOUR
T1 - Stabilization of the cart pole system
T2 - by sliding mode control
AU - Aguilar-Ibáñez, Carlos
AU - Mendoza-Mendoza, Julio
AU - Dávila, Jorge
N1 - Publisher Copyright:
© 2014, The Author(s).
PY - 2014/12/1
Y1 - 2014/12/1
N2 - This paper presents a control strategy designed as a combination of a PD controller and a twisting-like algorithm to stabilize the damped cart pole system, provided that the pendulum is initially placed within the upper-half plane. To develop the strategy, the original system is transformed into a four-order chain of integrator form, where the damping force is included through an additional nonlinear perturbation. The strategy consists of simultaneously bringing the position and velocity of the pendulum to within a compact region by applying the PD controller. Meanwhile, the system state variables are brought to the origin by the twisting-like algorithm. The corresponding convergence analysis is done using several Lyapunov functions. The control strategy is illustrated with numerical simulations.
AB - This paper presents a control strategy designed as a combination of a PD controller and a twisting-like algorithm to stabilize the damped cart pole system, provided that the pendulum is initially placed within the upper-half plane. To develop the strategy, the original system is transformed into a four-order chain of integrator form, where the damping force is included through an additional nonlinear perturbation. The strategy consists of simultaneously bringing the position and velocity of the pendulum to within a compact region by applying the PD controller. Meanwhile, the system state variables are brought to the origin by the twisting-like algorithm. The corresponding convergence analysis is done using several Lyapunov functions. The control strategy is illustrated with numerical simulations.
KW - Inverted cart pendulum
KW - Lyapunov method
KW - Sliding control mode
UR - http://www.scopus.com/inward/record.url?scp=85027955302&partnerID=8YFLogxK
U2 - 10.1007/s11071-014-1624-6
DO - 10.1007/s11071-014-1624-6
M3 - Artículo
SN - 0924-090X
VL - 78
SP - 2769
EP - 2777
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 4
ER -