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PEM fuel cell fractional order modeling and identification

This workshop series focuses on the equivalent electrical circuit model and fractional order modeling of fuel cells, as well as the identification of fractional order model parameters through experimentation and results.

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PEM fuel cell fractional order modeling and identification

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  1. PEM fuel cell fractional order modeling and identification Tiebiao Zhao MESA (Mechatronics, Embedded Systems and Automation)Lab School of Engineering, University of California, Merced E: tzhao3@ucmerced.eduPhone:2092015212 Lab: CAS Eng 820 (T: 228-4398) Sep. 8, 2014. Monday 4:00-6:00 PM Applied Fractional Calculus Workshop Series @ MESA Lab @ UCMerced

  2. Outline • Equivalent electrical circuit model • Fractional order model of fuel cell • Identification of fractional order model’s parameters • Experimentation and results AFC Workshop Series @ MESALAB @ UCMerced

  3. Equivalent electrical circuit model AFC Workshop Series @ MESALAB @ UCMerced

  4. The linearized model The phase shift at high frequencies is multiple of 90, the fuel cell impedance at high frequencies is characterized by a phase shift of 45° AFC Workshop Series @ MESALAB @ UCMerced

  5. Fractional model • Gas diffusion phenomena • Warburg impedance AFC Workshop Series @ MESALAB @ UCMerced

  6. The Warburg impedance is then given by: • Taylor series approximation • Fractional transfer function AFC Workshop Series @ MESALAB @ UCMerced

  7. Identification of fractional order model’s parameters • The first one involves having a prior knowledge of derivation orders and therefore estimating only the coefficients of the derivative operators by Least Square method for example • The second approach consists in estimating the coefficients and orders of the derivative operators, when unknown, by non-linear algorithms. • The third method estimates the derivative operators coefficients and only one derivation order named “commensurate fractional order”, as all other orders are integer multiples of the commensurate order. AFC Workshop Series @ MESALAB @ UCMerced

  8. Least square method adapted to fractional order model • Discretization of the continuous time fractional model • Linear formulation of the model by a change of variables • Estimation of the new parameters using the least square method • Return to the initial parameters by reversing the variable change AFC Workshop Series @ MESALAB @ UCMerced

  9. Model discretization AFC Workshop Series @ MESALAB @ UCMerced

  10. Linear form of the model AFC Workshop Series @ MESALAB @ UCMerced

  11. Parametric estimation AFC Workshop Series @ MESALAB @ UCMerced

  12. Inversion of the variable change AFC Workshop Series @ MESALAB @ UCMerced

  13. Experiments AFC Workshop Series @ MESALAB @ UCMerced

  14. Future work • Modeling on Lipo battery • Try different order • Time-varying fractional order model of battery AFC Workshop Series @ MESALAB @ UCMerced

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