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

Content Provider	IEEE Xplore Digital Library
Author	Aguilar-Ibanez, C. Martinez-Garcia, J.C. Soria-Lopez, A.
Copyright Year	2011
Description	Author affiliation: Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, 07000 México, D.F., México (Martinez-Garcia, J.C.; Soria-Lopez, A.) \|\| CIC-IPN, Av. Juan de Dios Bátiz s/n casi esq. Miguel Othón de Mendizábal, Unidad Profesional Adolfo López Mateos, Col. Nueva Industrial Vallejo, Delegación Gustavo A. Madero, C.P 07738, México D.F., México (Aguilar-Ibanez, C.)
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.
Starting Page	1759
Ending Page	1764
File Size	521542
Page Count	6
File Format	PDF
ISBN	9781612848006
ISSN	07431546
e-ISBN	9781612848013
e-ISBN	9781612847993
DOI	10.1109/CDC.2011.6160190
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-12-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Stability analysis Asymptotic stability Nonlinear dynamical systems Lyapunov methods Equations Closed loop systems Mathematical model Cart-Pendulum System Underactuated Nonlinear Mechanical Systems Cascade Interconnected Systems Nonlinear Feedback-Based Bounded Control Global Stabilization Saturation Functions
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Modeling and Simulation Control and Optimization

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