Observation and sliding mode observer for nonlinear fractional-order system with unknown input
Nadia Djeghali1, Said Djennoune1, Maamar Bettayeb2
1Laboratoire de Conception et Conduite des Systèmes de Production, University Mouloud Mammeri, Tizi-Ouzou, Algeria.
This study introduces observability and left invertibility for nonlinear fractional-order systems, linking them to integer-order systems. It also proposes a sliding mode observer for fault detection and estimation in these systems, proving finite-time convergence.
Area of Science:
- Control Theory
- Nonlinear Systems
- Fractional Calculus
Background:
- Fractional-order systems are increasingly used in modeling complex phenomena.
- Observability and invertibility are crucial for system analysis and control.
- Fault detection and estimation are vital for system reliability.
Purpose of the Study:
- Introduce observability and left invertibility for nonlinear fractional-order systems.
- Develop a sliding mode observer for fault detection and estimation.
- Analyze the properties and performance of the proposed observer.
Main Methods:
- Transformation to an equivalent nonlinear integer-order system.
- Step-by-step design of a first-order sliding mode observer.
- Lyapunov stability theory for finite-time convergence analysis.
Main Results:
- Established observability and left invertibility for nonlinear fractional-order systems.
- Demonstrated the deduction of these properties from equivalent integer-order systems.
- Designed a sliding mode observer with proven finite-time convergence for fault detection.
Conclusions:
- The proposed methods provide a framework for analyzing and controlling nonlinear fractional-order systems.
- The sliding mode observer is effective for fault detection and estimation.
- Numerical examples validate the theoretical findings and practical applicability.
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