State estimation in mechanical systems of fractional-order based on a family of Proportional $\rho$-Integral observers

被引:0
作者
Martinez-Fuentes, Oscar [1 ]
Munoz-Vazquez, Aldo Jonathan [2 ]
Fernandez-Anaya, Guillermo [3 ]
Tlelo-Cuautle, Esteban [1 ]
机构
[1] INAOE, Dept Elect, Luis Enrique Erro 1, Cholula 72840, Puebla, Mexico
[2] Texas A&M Univ, Higher Educ Ctr McAllen, Dept Multidisciplinary Engn, 6200 Tres Lagos Blvd, Mcallen, TX 78504 USA
[3] Univ Iberoamer Ciudad de Mexico, Dept Fis & Matemat, Prol Paseo Reforma 880, Mexico City 01219, Alvaro Obregon, Mexico
关键词
Mittag-Leffler observers; Integral observers; Mittag-Leffler stability; Nonlinear fractional-order systems; Caputo derivative; SLIDING-MODE-OBSERVER; DISTURBANCE OBSERVER; PHYSICAL INTERPRETATION; DYNAMICAL-SYSTEMS; TIME; DESIGN; SYNCHRONIZATION; CONTROLLER; OPTIMIZATION; CALCULUS;
D O I
10.1007/s11071-023-08919-4
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
In control theory, there are many proposals to solve the problem of observer design. This paper studies the Mittag-Leffler stability of a class of dynamic observers for nonlinear fractional-order systems, given in the observable canonical form and defined by the Caputo fractional derivative. We prove that the Riemann-Liouville integral could be employed to provide robustness against noisy measurements during the estimation problem. Based on this advantage, the main result of this paper consists of the design of a family of high gain proportional rho-integral observers employed to estimate unmeasured state variables of nonlinear fractional systems of commensurate order. Three illustrative numerical examples of mechanical systems are provided, which corroborate the effectiveness of the proposed algorithms.
引用
收藏
页码:19879 / 19899
页数:21
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