the control is not specifically for ac fan, it can be any ac motor...
Well, no. There are different kinds of AC motors.
Induction motors (typically used in mains-powered fans) run at a speed determined by the mains frequency and the load on the motor, but their speed cannot vary by more than a few percent or they will stall. On/off control of an induction motor with a triac may be OK but don't expect to control speed very much.
Universal motors are found in things like power tools (drills, saws), kitchen appliances (blenders), etc. They can actually run on AC or DC. They are very noisy as compared to induction motors (so not usually used in fans) and have a relatively shorter life. Their speed can be controlled with a triac circuit.
There are other kinds of AC motors as well but those are the most common. Good luck. Be careful, keep your sneakers on and one hand in a pocket.