Speed Control Ceiling Fans

Here's one site that has an explanation, including how to DYI a fan controller.

http://wiki.diyfaq.org.uk/index.php/Fan_Speed_Controller

The nominal fan motor is a shaded pole induction motor. Most classes on motors only explain this style of motor does not require starting circuitry. An implication of this style of shading a motor pole is the motor rarely operates synchronously with the AC frequency. By adding a series component the current flowing through the motor is reduced. This reduces the maximum amount of torque available to oppose the load of moving air. By using a series capacitor, very little power is dissipated at the current limiting component.

Actually all the ceiling fans I have installed or repaired on this side of the briney have two windings a start and run winding with a capacitor in series with the start winding to give a 90 degrees phase shift between the run and start windings. Secondly the speed control is done by a tapped reactor adding inductive reactance to the motor supply to lower the torque available.

I have replaced many a capacitor in the motors but not to date a tapped reactor for all capacitors have a limited life span and die quicker when exposed to heat. The capacitors used are paper type which are naturally nonpolarised.

Electronic controls instead of inductive must be symmetrical in output else a DC component is created which creates more heating in the windings. Triacs can be used if selected correctly or even an SCR connected across the positive and negative while the AC is connected to the motor in series configuration through the AC of the bridge.