State estimation in mechanical systems of fractional-order based on a family of proportional ρ-integral observers
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 prov...
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| Veröffentlicht in: | Nonlinear dynamics 2023-11, Vol.111 (21), p.19879-19899 |
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| container_issue | 21 |
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| container_title | Nonlinear dynamics |
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| creator | Martínez-Fuentes, Oscar Muñoz-Vázquez, Aldo Jonathan Fernández-Anaya, Guillermo Tlelo-Cuautle, Esteban |
| description | 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
ρ
-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. |
| doi_str_mv | 10.1007/s11071-023-08919-4 |
| format | Article |
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ρ
-integral observers employed to estimate unmeasured state variables of nonlinear fractional systems of commensurate order. 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ρ
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| subjects | Algorithms Automotive Engineering Canonical forms Classical Mechanics Control Control theory Derivatives Design Dynamic stability Dynamical Systems Engineering High gain Integrals Mechanical Engineering Mechanical systems Nonlinear systems Observers Original Paper Robustness (mathematics) State estimation System effectiveness Variables Vibration |
| title | State estimation in mechanical systems of fractional-order based on a family of proportional ρ-integral observers |
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