Constructing a servo using arduino and DC motor

Edit:.................Solved.
I have since understood that this is not a viable project. I have removed the processor board from a standard servo and used that to provide the function that I require.
So, I can mark this thread as Solved.

I should state up front, I don't want to control an existing servo. Most threads I read describing:
"How to control a servo motor" are not that, they are descriptions of how to control a servo.
In other words, the two terms seem to be commonly conflated on arduino threads. At least, the few that I have found.
What I am looking for is a method to program a arduino uno (for example), to serve the function of the microcontroller board in a standard radio control servo, and use it to control a separate small DC motor.
My intended project is to build a linear servo to move a weight and so shift the CG of an aircraft while in flight, and to control it with a surplus channel on my RC transmitter.
One possibility is to use a threaded rod, powered by the DC motor (not a complete off the shelf standard servo) which should also operate a multi turn potentiometer (or linear pot) to replace the normal pot in a standard servo.
Any leads or advice appreciated.
Thanks,
Jim.

Generally speaking, correct. :grin:

In particular, using a microcontroller to implement a fast servo loop is impractical as you have to involve reading an ADC and generating some sort of PWM output once you calculate the required correction.

The standard servo controller does not use a microcontroller but a linear circuit whose response is far more instantaneous - and uncomplicated.

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Thanks for that correction Paul!

You could use the board from a standard servo to control via a motor driver circuit a bigger motor.

Example

Or example

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