Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case

Carlos Aguilar-Ibanez, Juan C. Martinez-Garcia, Alberto Soria-Lopez

Resultado de la investigación: Capítulo del libro/informe/acta de congresoContribución a la conferencia

6 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Título de la publicación alojada2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Páginas1759-1764
Número de páginas6
DOI
EstadoPublicada - 1 dic 2011
Evento2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, Estados Unidos
Duración: 12 dic 201115 dic 2011

Serie de la publicación

NombreProceedings of the IEEE Conference on Decision and Control
ISSN (versión impresa)0191-2216

Otros

Otros2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
PaísEstados Unidos
CiudadOrlando, FL
Período12/12/1115/12/11

Huella dactilar

Underactuated Mechanical Systems
Bounded Control
Pendulum
Pendulums
Saturation
Underactuated System
Control Strategy
Dynamical system
Controller
Nonlinear dynamical systems
Nonlinear Perturbations
Lyapunov Methods
Nonlinear Dynamical Systems
Linear Stability
Global Stability
Half-plane
Initialization
Closed-loop
Nonlinear Differential Equations
Closed-loop System

Citar esto

Aguilar-Ibanez, C., Martinez-Garcia, J. C., & Soria-Lopez, A. (2011). Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case. En 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 1759-1764). [6160190] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6160190
Aguilar-Ibanez, Carlos ; Martinez-Garcia, Juan C. ; Soria-Lopez, Alberto. / Bounded control based on saturation functions of nonlinear under-actuated mechanical systems : The cart-pendulum system case. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. pp. 1759-1764 (Proceedings of the IEEE Conference on Decision and Control).
@inproceedings{5ba7e82eea544b95b94a48273cac23d2,
title = "Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case",
abstract = "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.",
keywords = "Cart-Pendulum System, Cascade Interconnected Systems, Global Stabilization, Nonlinear Feedback-Based Bounded Control, Saturation Functions, Underactuated Nonlinear Mechanical Systems",
author = "Carlos Aguilar-Ibanez and Martinez-Garcia, {Juan C.} and Alberto Soria-Lopez",
year = "2011",
month = "12",
day = "1",
doi = "10.1109/CDC.2011.6160190",
language = "Ingl{\'e}s",
isbn = "9781612848006",
series = "Proceedings of the IEEE Conference on Decision and Control",
pages = "1759--1764",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

}

Aguilar-Ibanez, C, Martinez-Garcia, JC & Soria-Lopez, A 2011, Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case. En 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011., 6160190, Proceedings of the IEEE Conference on Decision and Control, pp. 1759-1764, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, Estados Unidos, 12/12/11. https://doi.org/10.1109/CDC.2011.6160190

Bounded control based on saturation functions of nonlinear under-actuated mechanical systems : The cart-pendulum system case. / Aguilar-Ibanez, Carlos; Martinez-Garcia, Juan C.; Soria-Lopez, Alberto.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 1759-1764 6160190 (Proceedings of the IEEE Conference on Decision and Control).

Resultado de la investigación: Capítulo del libro/informe/acta de congresoContribución a la conferencia

TY - GEN

T1 - Bounded control based on saturation functions of nonlinear under-actuated mechanical systems

T2 - The cart-pendulum system case

AU - Aguilar-Ibanez, Carlos

AU - Martinez-Garcia, Juan C.

AU - Soria-Lopez, Alberto

PY - 2011/12/1

Y1 - 2011/12/1

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

ER -

Aguilar-Ibanez C, Martinez-Garcia JC, Soria-Lopez A. Bounded control based on saturation functions of nonlinear under-actuated mechanical systems: The cart-pendulum system case. En 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 1759-1764. 6160190. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6160190