well depends what you mean by single phase. all 230v ac motors are single phase but some eg vacuum cleaner / electric drill are able run on dc as well if they have a comutator (brushes). on the other hand many ac motors are of an entierly different design which typically uses a capacitor to create a phase shift for staring. these motors have no brushes and wont run on dc. the type with brushes will have a very high no-load speed and this will reduce when the motor is loaded. the other common type will try and maintain the same speed irrespctive of load. traditionally, the brushed type was the easiest to control but with modern electronics many things are possible. its more common however to use a low voltage stepper motor as control is easier.
Single phase for those who dont know is just normal mains supply
Most of what you suggest runs at a fixed speed or 2 or 3 fixed speeds as they have diffferent switched windings.
No good for for PID control !
Drill controller will NOT be isolated from the mains
so thats a safety issue if you link it to anything else.
Besides, those controllers are tailoreded to a custom motor in the drill so adapting it may be another issue !
As for stepper motors providing airflow needed for this application - No chance .... LOL
