Help choosing the right platform for a real-time PI-lock

I have recently stumbled upon the Arduino microcontrollers and was intrigued by its accessibility, from the point of view of someone, who has no experience with microcontrollers. However, I am not entirely sure whether it is the right platform for solving the problem that I have at hand.

The idea is to use a microcontroller to lock an interferometer. The requirements are that I should be able to do the following with a frequency of ~5kHz (or higher):

  1. signal input (analog)
  2. perform calculations (simple PI control scheme)
  3. signal output (analog)

As far as I can see the Arduino DUE has a clock speed of 84MHz and the maximum analog reading speed is 10kHz (analogRead() - Arduino Reference). And even if I assume the same writing speed (I was not able to find any information on the writing speed), I might already be pushing the 5kHz that I am aiming for.

My question is thus whether or not Arduino DUE (or a different board) is the right choice for me, or if I should be looking into a different approach.

EDIT: After searching for a little while, I found the following thread, showing how to crank up the analog read speed (and I assume write speed as well):

If my assumption about the analog write speed is correct, my requirements for the interferometer lock should be feasible.
But is there any advantage in choosing the Arduino DUE over the other boards? Any advice would be much appreciated!