Need help on speed control of single phase ac induction motor
If it's an induction motor and the speed controller supplies the AC at the frequency required for a given speed there won't be overshoot. Obviously slip will need to be corrected for but that can be detected and corrected for but it can be a little tricky.

Without more details on your controller i.e. whether it can produce variable frequency drive power I can't really say any more. It does sound like the type of circuit you mentioned may not be suitable for variable speed control.