Some ceiling fans control their speed with a pull chain switch. Others control the speed with a different switch. For a small fee plus expenses I could demonstrate this for you.
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"Don't disturb my circles." translation of Archimedes last words
So I assume that you already know how the table fans and pedestrial fans are controlled. Ok . you have a regulator placed on the wall for controlling the fan. when you turn the knob, a rope from the regulator tighen the rotor of the fan motor and reduce speed, same like some bicycle brake....very simple
Vary the "average" supply voltage with, say, a mark-space ratio control unit. That would do it...
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