From your statements it transpires that you do not have the data pertaining to the fuel flow Vs power and rpm of the turbine. Maybe you HAVE to generate the data ? WATCH OUT.

I have worked on a turbine ( where all performance details were known ) where the fuel pump was also driven by the same turbine it was supplying the fuel ! Initially the turbine was cranked by a battery operated prime mover and at a particular rpm, that drive declutched and the trubine fired - the fuel flow was directly regulated with a pump-mounted-servo valve. Till we stabilized the control loop, the only thing that used to happen was a over-speed trip cutting in at about a few seconds after the turbine was fired. ( The DAS and control computer was in an adjacent room and that provided such a comfortable feeling...)

In your case, can you not try and control the trubine speed in open loop starting with the bare minimum fuel to sustain rotation with a FIXED load ? If you can calibrate the turbine fuel Vs rpm for this fixed load, then you can see if closed loop can be brought in. Once this is stabilized then the load variations can be brought in.

Turbines are fast but calibrating them is a slow process ( and not a very safe one at that ).

Raghu