fault diagnosis in fractional order singular systems

What is it about?

This study proposes the design of an unknown input fractional order proportional–integral observer for fault diagnosis of linear fractional order singular (FOS) systems. The considered system is rectangular in general form. The necessary and sufficient conditions for the existence of the proposed observer are derived, and a systematic design approach is presented. The proposed observer is non-singular and uses only the original coefficient matrices to estimate the norm-bounded actuator faults. Also, the unknown input appearing in measurement is considered and the effects of unknown inputs are decoupled from observer dynamics. By introducing a continuous frequency distributed model and using indirect Lyapunov approach, the convergence conditions of the proposed observer are derived in terms of linear matrix inequalities. Furthermore, for a class of non-linear FOS systems with both output disturbances and input uncertainties, a non-linear observer is developed based on the proposed design approach. The existence and convergence of this observer are proved. Finally, the effectiveness of the proposed method is illustrated via two examples.

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Why is it important?

Singular system model (known as descriptor, generalized, semistate or differential algebraic system) arises from a convenient and natural modeling process. This model considers the physical constraints or static relations and more generally impulsive behaviors caused by an improper transfer matrix. Singular systems have received considerable attention since they arise in many fields of system design and control; these systems have a profound background in electrical systems, large-scale interconnected systems, power systems, mechanical systems with constraints and chemical processes. Safety and reliability are critical requirements of modern systems. Therefore, the research on fault diagnosis for dynamic systems is of great significance. In this regard, many approaches and methods have been proposed in three main categories: model-based, signal based and knowledge-based methods. In model-based fault diagnosis methods, the mathematical model of the monitored process is used to achieve analytical redundancy. It is worth mentioning that the effectiveness and sensitivity of a model-based method strictly depend on the accuracy of the plant's model. Fractional order differential equations describe many physical phenomena more effectively due to their long memory and hereditary properties. Fractional order models can provide a more accurate description of different systems such as electrical circuits, electrochemical process, flexible structures, and thermal systems. The fractional order singular (FOS) models describe singular systems in which there are fractional order components. These systems include electrochemical processes, fractional order largescale systems, and electrical circuits with fractional order components. FOS systems have complexities due to the simultaneous presence of fractional order dynamics and the singular nature of the system.