The error signal represent the different between two speeds the first is the refrence speed Nr and the actual speed N which drives the speed governor.

The speed governor is characterized by either droop or isochronous governor control.

The transfer function for the speed governor is given by the following equation:

The Gas-turbine Fuel System

Based on the demand signal Wd the gas-turbine fuel system generate produce the fuel signal Wf.

Mainly the gas-turbine system consist of two components :

First: valve positioner, represented by the following equation:

Second: fuel system actuator, represented by the equation:

The Torque

The torque characteristics depends on many different elements like: fuel supply (Wf) and turbine speed (N).

Also The lower limit of fuel flow (Wfl) and the rated speed of the turbine (Nrated) are also responsible for the torque, F2.

The torque equation as follow:

The Acceleration limiter

The acutual speed of the turbine change due to the consept of acceleration.

The acceleration controller control the speed of the gas turbine by adjusting the fuel flow in the startup stage.

The transfer function model of the acceleration control loop is shown:

The Temperature Controller

The exhaust temperature(Tx) is mainly depended on two parameters,the fuel suuply signal and the actual speed of gas the turbine.this realtion could be represented by the following equation:

The temperature controller only will be active when Tx value exceeds the set point value given by the refrence temoerature.the TF for the temperature controller as follow

The Temperature limiter

Combinig all the mentioned above from the thermocouple,radination shield to the temp controller,we can represent the transfer function model of temperature limiter loop as follow:

The LTFM of HDGT model has been obtained by superposition of the transfer function between the input signals and output signal from. Reference speed, Fuel flow rate under no load condition, Load torque and fuel flow lower limit and rated speed signal from turbine torque function are considered as the input signals for linearization. The LTFM is obtained from the algebraic sum of these transfer function and expressed in Equation .