The first-order transfer function is therefore preferred due to low complexity and the accuracy of the predictions is almost the same with the second-order system. Hence, the pilot gas fuel valve model is expressed in Equation \ref{eq:7} and the main gas fuel valve model is shown in Equation \ref{eq:8}.
\[G_{1}(s)=\frac{1}{0.172s+1}\label{eq:7}\]
\[G_{1}\left(s\right)=\frac{1}{0.222s+1}\label{eq:8}\]
The proposed models from system identification are further validated using validation dataset in parameter testing to determine the best b . The first evaluation is the comparison of the proposed  system identification model with Rowen’s model as in Table \ref{277442}. The proposed system identification parameter, b for both pilot and main gas fuel valves exhibit a very high accuracy with improved MAE and RMSE compared to Rowen’s parameter assumption.