Abstract: It is known that power is normally extracted within a gas turbine engine from a shaft in order to drive auxiliary devices such as electrical power generators. With high extraction rates from such shafts there is mismatching in rotational speeds between the shafts which must be adjusted through leakage taken from valves 8, 9. By measuring parameters and in particular pressure at a number of positions or parts within an engine arrangement 1 and comparing those parameters either through ratios or directly with reference values a controller can be configured in order to choose the correct sequence and scheduling of the valves 8, 9 opening to balance shaft speed. In such circumstances more efficient operation of the engine arrangement can be achieved over a wider range of engine speeds including idling.