Now that you blew the speed control (or maybe the motor) from overvoltage, exactly what is wrong with it is unpredictable. Replacing the burnt capacitor is part of a trial and error process to getting it fixed. It is uncommon to use a more systematic approach to repairing devices such as speed controls because of the time needed to test individual components (like transistors).
If this is a DC motor, then the "speed control" has other functions in it too. Like converting AC to DC (rectifying). Fundamentally a DC motor speed control raises nd lowers the voltage. For a motor with two wires going into it you can substitute another brand of speed control that delivers the desired voltage with the needed number of amperes. Note that a motor draws more amperes as it starts up compared with running at normal speed.
I suggest that you immediately disconnect (at the panel or in the outlet box) that 120 volt receptacle that has 220 volts going to it.
If this is a DC motor, then the "speed control" has other functions in it too. Like converting AC to DC (rectifying). Fundamentally a DC motor speed control raises nd lowers the voltage. For a motor with two wires going into it you can substitute another brand of speed control that delivers the desired voltage with the needed number of amperes. Note that a motor draws more amperes as it starts up compared with running at normal speed.
I suggest that you immediately disconnect (at the panel or in the outlet box) that 120 volt receptacle that has 220 volts going to it.