DLE gas turbines are designed for low emission operation which is achieved by LPM combustion to produce a uniform temperature in the chamber \citep{ayed2017cfd,Funke_2018}. Fig. \ref{eq:4} illustrates the comparison between DLE gas turbine and the conventional type, highlighting the differences in the fuel system design. DLE gas turbine’s primary feature is the introduction of a pilot gas fuel valve to the main gas fuel valve used in the conventional model \citep{hermann2019experimental}. A larger volume of the DLE combustion chamber is also observed due to the space utilization for the pilot gas fuel valve integration. In DLE gas turbine operation, the air intake is drawn into the compressor and compressed before it reaches the pre-mixing chamber. In the premixing chamber, 60% of the air is diffused into the fuel and an additional 40% is sent to the combustion chamber. The diffusion is controlled by varying the opening of the pilot fuel valve to maintain a consistent turbine temperature during the entire operation \citep{hackney2016predictive,Huitenga_2014}. Due to the different setup from the conventional, modelling of fuel valves and system for DLE gas turbine representation is therefore required.
The first step for technical modelling of the fuel valves and the system is the collection of available knowledge. From Figure \ref{490782}, the valve positioner model is a first-order transfer function as in Equation \ref{eq:4} b in the equation denotes the time constant for the valve to reach steady state.