A Class of Bounded and Partially Bounded Nonlinear Controllers for First and Second Order Dynamical Systems
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Authors
Clemente, Eddie
Rodríguez-Liñán, M. C.
Meza-Sánchez, Marlen
Monay-Arredondo, Luis
Herrera, Leonardo
Subjects
Partially bounded nonlinear control
bounded nonlinear control
sector nonlinearities
bounded nonlinear control
sector nonlinearities
Advisors
Date of Issue
2021-06-30
Date
June 30, 2021
Publisher
IEEE
Language
Abstract
This letter proposes structurally simple, bounded and partially bounded nonlinear controllers that offer satisfactory performance, demonstrated by their application to first and second-order dynamical systems. This is done by taking advantage of the properties of a particular class of bounded sector nonlinear functions that can be parameterized in bound value and slope. In contrast to the classical methods of saturated control, the proposed controllers' design can be defined as an explicit summation of sector nonlinear functions, whose Lyapunov global stability proof can be straightforwardly demonstrated for the single and double integrator dynamics. Thus, the proposed approach derives nonlinear controllers where each term is bounded (or partially bounded) by design. Although the stability proof is provided for single and double integrator dynamics, one of the controllers is tested in a first-order nonlinear system and another in a nonlinear second-order system, both to achieve tracking. The numerical results evidence good performance even for large initial errors, and without the further introduction of auxiliary dynamics, such as compensation terms or feedback linearization. This is done by only tuning the gains of each term, while maintaining boundedness (or partial boundedness) properties on the control input.
Type
Article
Description
17 USC 105 interim-entered record; under review.
The article of record as published may be found at http://dx.doi.org/10.1109/LCSYS.2021.3088760
The article of record as published may be found at http://dx.doi.org/10.1109/LCSYS.2021.3088760
Series/Report No
Department
Mechanical and Aerospace Engineering (MAE)
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
TecNM
CONACYT and TecNM/I.T.
CONACYT and TecNM/I.T.
Funder
11391.21-P
406498
406498
Format
6 p.
Citation
Clemente, Eddie, et al. "A Class of Bounded and Partially Bounded Nonlinear Controllers for First and Second Order Dynamical Systems." IEEE Control Systems Letters (2021).
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.