Second Order Step by Step Sliding mode Observer for Fault Estimation in a Class of Nonlinear Fractional Order Systems

This paper considers fault estimation in nonlinear fractional order systems in observer form. For this aim, a step by step second order sliding mode observer is used. By means of a fractional inequality, the stability of the observer estimation errors is analyzed and some conditions are introduced to guarantee finite time convergence of estimation errors. Finally, in a numerical example, effectiveness of this observer is demonstrated.

[1]  Chee Pin Tan,et al.  Sliding mode observers for fault detection and isolation , 2002 .

[2]  M. Bettayeb,et al.  Observation and sliding mode observer for nonlinear fractional-order system with unknown input. , 2016, ISA transactions.

[3]  Maamar Bettayeb,et al.  Super-Twisting Algorithm-Based Sliding-Mode Observer for Synchronization of Nonlinear Incommensurate Fractional-Order Chaotic Systems Subject to Unknown Inputs , 2017 .

[4]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[5]  Hui Li,et al.  State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems , 2016, Signal Process..

[6]  M. I. Castellanos,et al.  Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs , 2007, Int. J. Syst. Sci..

[7]  Michel Kinnaert,et al.  Distributed Fault Diagnosis and Fault-Tolerant Control , 2016 .

[8]  Mohamed Naceur Abdelkrim,et al.  Fault detection based on fractional order models: Application to diagnosis of thermal systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[9]  Mohamed Darouach,et al.  Design of unknown input fractional-order observers for fractional-order systems , 2013, Int. J. Appl. Math. Comput. Sci..

[10]  Lei Zhang,et al.  Fault Estimation for Nonlinear Dynamic System Based on the Second-Order Sliding Mode Observer , 2016, Circuits Syst. Signal Process..

[11]  Sarah K. Spurgeon,et al.  Sliding mode observers for fault detection and isolation , 2000, Autom..

[12]  Shabnam Pashaei,et al.  A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances. , 2016, ISA transactions.

[13]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .