Consider a solid$-$oxide fuel cell system which has three inputs $($molar flow rate of fuel

$H_{2}O),$ air $)$ and current $($I$)),$ four states $($pressures of $H_2,H_{2}O,N_2$ and $O_2)$ and one

output $($voltage$,V).$

The measurement model is given by the voltage equation for the stack,

ubrace$(V_s$ubrace${)}_{y_t}=N_0\{\begin{array}{c}{E}_0+\frac{s}{2F}(T_s-T_o))+\frac{R{T}_s}{2F}log(\frac{P_{H_2}{P}_{O_2}^{0\mathrm{.}5}}{P_{H_{2}O}{P}_{\text{a}\text{t}\text{m}}^{0\mathrm{.}5}}\end{array}$

$\{$:$-0\mathrm{.}2$exp$(-2870(\frac{1}{1196\mathrm{.}15}-\frac{1}{T_s}))-\frac{2R{T}_s}{2F}(\frac{j}{2j_o})-(-\frac{R{T}_s}{4F}ln(1-\frac{j}{j_L}))\}$

where, I is current, $K_r=\frac{N_o}{4F},j=\frac{\text{I}}{A_c}.$ The simulation of SOFC model is carried out using

the parameters given in Table $1($Model simulink file is given to you$).$

Table $1$: SOFC stack model parameters

Simulate the system $($using simulink file$)$ for variation in at$-$least four different step

inputs in current value