TY - GEN
T1 - Bounded control based on saturation functions of nonlinear under-actuated mechanical systems
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
AU - Aguilar-Ibanez, Carlos
AU - Martinez-Garcia, Juan C.
AU - Soria-Lopez, Alberto
PY - 2011
Y1 - 2011
N2 - We are concerned in this paper by bounded control of nonlinear underactuated dynamical systems. We focus our exposition on a feedback-based stabilization bounded control action shaped by saturation functions. A simple stabilizing controller for the well-known cart-pendulum system is then designed in this paper. Our control strategy describes in lumped linear time-invariant terms the concerned underactuated nonlinear system as a cascade nonlinear dynamical system consisted of a simple chain of four integrators with a high-order smooth nonlinear perturbation, and assumes initialization of the resulting underactuated system in the upperhalf plane. Our proposed feedback-based regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasilinear. Control boundedness is provided in both involved control actions by specific saturation functions. The first bounded control action brings the non-actuated coordinate near to the upright position and keep it inside of a well-characterized 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 theorem. Our proposed control law ensures global stability of the closed-loop system in the upper half plane, while avoiding the necessity of solving either partial differential equations, nonlinear differential equations or fixed-point controllers. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
AB - We are concerned in this paper by bounded control of nonlinear underactuated dynamical systems. We focus our exposition on a feedback-based stabilization bounded control action shaped by saturation functions. A simple stabilizing controller for the well-known cart-pendulum system is then designed in this paper. Our control strategy describes in lumped linear time-invariant terms the concerned underactuated nonlinear system as a cascade nonlinear dynamical system consisted of a simple chain of four integrators with a high-order smooth nonlinear perturbation, and assumes initialization of the resulting underactuated system in the upperhalf plane. Our proposed feedback-based regulation design procedure involves the simultaneous combination of two control actions: one bounded linear and one bounded quasilinear. Control boundedness is provided in both involved control actions by specific saturation functions. The first bounded control action brings the non-actuated coordinate near to the upright position and keep it inside of a well-characterized 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 theorem. Our proposed control law ensures global stability of the closed-loop system in the upper half plane, while avoiding the necessity of solving either partial differential equations, nonlinear differential equations or fixed-point controllers. We illustrate the effectiveness of the proposed control strategy via numerical simulations.
KW - Cart-Pendulum System
KW - Cascade Interconnected Systems
KW - Global Stabilization
KW - Nonlinear Feedback-Based Bounded Control
KW - Saturation Functions
KW - Underactuated Nonlinear Mechanical Systems
UR - http://www.scopus.com/inward/record.url?scp=84860675028&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160190
DO - 10.1109/CDC.2011.6160190
M3 - Contribución a la conferencia
AN - SCOPUS:84860675028
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1759
EP - 1764
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 12 December 2011 through 15 December 2011
ER -