Use of Microcontroller for this Application

Although I agree this appears to be over your head, I'll give you the benefit of the doubt in that maybe this is a language barrier issue.

First, the term "autotransformer" refers to the way a transformer is connected, in that the the primary and secondary are the same set of wires, not separated as they are in an "isolation transformer". It's not that it is "automated". You seem to be equating that term with "dimmer", they are not even close.

What you MIGHT have been thinking of is what is called a "Variac" or "Variable Transformer" , which is often built as an autotransformer in terms of the wiring connections. It operates similar to old wire-wound dimmers in that a rotating element moves across coil connections to change the voltage but in this case does so by changing the transformer ratio, not the resistance as a dimmer did. Still, at its core, nothing is inherently "automatic" about a Variac, in its simplest form the rotating element just has a big knob.

You CAN buy a motorized Variac wherein the rotating portion is attached to a small gear motor that can be controlled by remote signals: ie turn clockwise, turn counterclockwise. In theory if one already had a non-automated version of a motorized Variac, one could automate it with a micro controller I suppose. In practice when you go to purchase a motorized Variac, it likely already comes with a very simple control interface for the motor, often with a voltage feedback and PID loop to have it maintain a stead output voltage with a varying input. It's not rocket science... Sure, that can be done in a separate micro controller, but why?

if what you meant was that you currently have a manual Variac and you want to automate it with a micro controller, sure, you can do that. But what you are leaving out of this is the issue of fitting a motor operator onto the Variac after the fact. Possible? Yes, with a decent machine shop at your disposal and a lot of time and effort in designing a mechanical coupling method, proper torque requirements, gear reduction and controllable stepper or servo motor. But in that scenario, the micro controller is the simple part of it.