Method of Virtual Sensor Design for Faulty Physical Sensor Replacement

The paper considers the problem of virtual sensor design for nonlinear dynamic systems with non-smooth nonlinearities described by continuous-time models for faulty physical sensor replacement. The main purpose of virtual sensors is generating the estimates of the unmeasured components of the considered system to provide additional information for effective control and fault diagnosis. Besides, virtual sensors can be used for faulty physical sensor replacement. The methods of virtual sensor design for solving this problem differ from standard procedure since information from faulty physical sensor does not use to design the virtual sensor replacing this sensor. It is assumed that to solve the problem, the system is equipped by diagnostic system allowing detecting faulty sensor. For every such a sensor, the virtual sensor generating estimate replacing the faulty sensor is designed. To solve the problem, so-called logic-dynamic approach is used which does not guarantee optimal solution but uses only methods of linear algebra to solve the problem for systems with non-smooth nonlinearities. This approach contains three steps. Initially, the nonlinear term is removed from system and linear model is designed. Then, a possibility to estimate the faulty sensor and to insert in the model the transformed nonlinear term is checked. Finally, stability of sensor is provided. The virtual sensor can be designed in identification canonical form or Jordan canonical form. The advantage of the first form is a standard procedure of the virtual sensor design while Jordan form allows obtaining simpler solution. The relations allowing designing the virtual sensor as in identification canonical as Jordan canonical form are derived.

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