Advances in P.E.M. Fuel Cell Stack Observer Design Using a Takagi–Sugeno Approach with Unmeasurable Premise Variables

Abstract

This article presents the development of a nonlinear state observer based on a Takagi–Sugeno approach that is applied to a PEMFCS (Proton Exchange Membrane Fuel Cell Stack) model. The Fuel Cell model which takes into consideration the auxiliary elements associated to the stack, has been validated through the use of the professional software AMESim by a co-simulation with Matlab-Simulink. The paper’s objective is to construct a TS fuzzy observer such that it can estimate the states of the considered nonlinear systems despite the unmeasurable premise variables. The observer construction method implies the use of Input to State Stability which eliminates the necessity of the Lipschitz constant, aiming at a bounded estimation error convergence. The conditions for obtaining the observer gains are expressed in the end as Linear Matrix Inequalities.

Appendix

Other notations employed in this paper are the following:

$$ cst1 = \frac{{R_{v} \cdot T_{st} }}{{V_{ca} }}\;cst2 = \frac{{R_{{O_{2} }} \cdot T_{st} }}{{V_{ca} }}\;cst3 = \frac{{R_{a} \cdot T_{st} }}{{V_{rm} }}\;cst4 = \frac{{M_{v} }}{{M_{{O_{2} }} }}\;cst5 = \frac{{KK_{1} R_{{H_{2} }} T_{st} }}{{V_{an} }}\;cst6 = \frac{{A_{an} C_{d,an} \sqrt \gamma \left( {\frac{2}{\gamma + 1}} \right)^{{\frac{\gamma + 1}{{2 \cdot \left( {\gamma - 1} \right)}}}} }}{{\sqrt {\bar{R} \cdot T_{atm} } }} $$