Fuel control unit is the generic term given to any of several types of control system

Control system

A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...

s for gas turbine engines.
Gas turbine engines are primarily controlled by the amount of fuel

Jet fuel

Jet fuel is a type of aviation fuel designed for use in aircraft powered by gas-turbine engines. It is clear to straw-colored in appearance. The most commonly used fuels for commercial aviation are Jet A and Jet A-1 which are produced to a standardized international specification...

 supplied to the combustion chamber

Combustion chamber

A combustion chamber is the part of an engine in which fuel is burned.-Internal combustion engine:The hot gases produced by the combustion occupy a far greater volume than the original fuel, thus creating an increase in pressure within the limited volume of the chamber...

s. With this in mind, the very simplest fuel control for a turbine engine is a fuel valve operated by the pilot. Many pre-production models of early turbojet engines featured just that, but it was soon found that this kind of control was difficult and dangerous in actual use.