A word or two about fuel metering on turbine engines. They are generally controlled by a governor, so as inlet pressure or temperature varies, the governor will trim fuel up or down to keep RPM where it belongs.
Multi-spool engines (turbofan e.g.) may have two governors, one on each shaft,
and either one may "take charge" to keep things within limits.
And some engines - often military models - may have temperature controls that act as a governor.