Apparatus for controlling a fully-premixed burner combustion system is arranged to control the fuel supply 21 at one of a number of predetermined rates of flow and a fan 18 so that it operates at one of a number of predetermined speeds, each fan speed corresponding to a particular predetermined value of the fuel flow rate. The speed of the fan is increased from zero and is adjusted to a reference fan speed, but the fan is switched off if the maximum fan speed is reached without the required air flow being achieved.
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