It's a DC motor since it has permanent magnet fields, applying AC to this would just make it hum loudly and start smoking after some time.
The motor is labelled "VOLTS 240AC" and, although I'm for sure not certain, the PCB doesn't really look like it is converting AC to DC. Still, the brushes are confusing since normally you'd expect then it's a DC motor. I guess maybe it's one of these https://en.wikipedia.org/wiki/Universal_motor
Does it have field coils or permanent magnets? Going by the picture it appears to have permanent magnets, so is a DC motor.
From the looks of it seems something on the PCB went up in smoke and the motor itself might be fine.
I forgot to add the pic but although there could be something wrong on the PCB too, the motor definitely has a problem. This came out of the motor:
That's insulation from the windings.
My advice is scrap it, if you can get a cheaper one, than the price of a motor and parts for the controller, otherwise it still might be worth repairing.
I suspect the controller is also faulty. The fact it doesn't appear to be burned doesn't mean it works.
It's possible the controller caused the motor to blow up, although I would suspect it's the other way round.
Going by the photograph, the controller appears to be a phase controller. There will be four didoes (either discrete components or a bridge rectifier module), which converts the AC to DC for the motor, a thyristor (the three legged component), a DIAC (the blue cylinder) and a few resistors and capacitors. The TRIAC is the most likely component to fail, followed by the rectifier diodes.