To add two points to the question:
In the context of a know disturbance $d(t)$ in a *discrete* control loop, what is the $dt$ at which the control loop has to be executed *in order to function*?

If you know the system output for the case of no controller for an ordinary control loop (see the pictures). Lets say you want to have a constant system output of 380. Is there a general rule how fast a discrete control loop has two operate in order to achieve this?

If there is no general rule for an arbitray controller, we can restrict the question to an ordinary PID-Controller.

![Control loop][1]([source][2])

![Example-Plot][3]


  [1]: https://i.sstatic.net/bQB60.png
  [2]: http://en.wikipedia.org/wiki/Control_theory
  [3]: https://i.sstatic.net/fbT3H.png