Fractional fault-tolerant dynamical controller for a class of commensurate-order fractional systems

ABSTRACT

A fault-tolerant control scheme is proposed for a class of commensurate-order fractional nonlinear systems that consists of two fractional-order observers (hybrid scheme). The diagnosis of the faults is performed by means of a model-free fractional proportional integral reduced-order observer that uses the fractional algebraic observability property. A fractional dynamical controller obtained in a natural way from the dynamics of a fractional high-gain observer is designed, which is constructed from a fractional generalised observability canonical form; the controller performs output tracking, thus eliminating the effects of the faults. A stability analysis on the overall system demonstrates that the origin is Mittag–Leffler stable. The proposed methodology is assessed by means of simulations on the fractional models of the Van der Pol oscillator and a DC motor.

KEYWORDS:

• Fractional fault-tolerant dynamical controller
• fractional commensurate-order systems
• fractional proportional integral reduced-order observer
• fractional high-gain observer
• fractional generalised observability canonical form

Acknowledgments

The authors thank the anonymous reviewers for their comments, that served to improve this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

F. Meléndez-Vázquez

Fidel Meléndez-Vázquez received his B.Sc. degree in Mechatronics from Tecnológico de Estudios Superiores de Coacalco, México in 2010, and the M.Sc. degree in Manufacturing Engineering from Instituto Politécnico Nacional, Ciudad de México in 2013. Currently, he is studying the Ph.D. degree in Automatic Control in the CINVESTAV-IPN, Ciudad de México. His research interests are fault diagnosis and fractional-order systems.

O. Martínez-Fuentes

Oscar Martínez-Fuentes received the B.Sc. degree in mechanical and electrical engineering from the University of Veracruz, Xalapa Campus, Mexico, in 2013 and the M.Sc. degree in Automatic Control from the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV), Zacatenco Campus, Mexico, in 2015, where He is currently Ph.D. student of the automatic control department. His research interests include nonlinear observers design, control and stability of fractional nonlinear systems and analysis of fractional differential equations.

R. Martínez-Guerra

Rafael Martínez-Guerra was born in Mexico City in 1959, he earns his Ph. D. Degree from Universidad Autonoma Metropolitana in 1996. Currently, he is a researcher at the Automatic Control Department of the CINVESTAV-IPN (Center of Research and Advanced Studies of IPN) and member of the National System Researchers since 1992 (level II, currently). He is author and co-author of more 68 papers in International Journals and more than 117 contributions in International Conference in Proceedings. He is co-author of 5 books (3 Springer) His main research interests are in the areas of Nonlinear Systems, Differential Geometric and Differential Algebraic Methods, Fractional Nonlinear Observers, Fractional Fault Detection and Diagnosis Problem, Secure Communications, Fractional Synchronization and Chaos.