If you want to control a system (with a loop controller), why actually do you need to know anything about the system itself (its dynamics or the transfer function or impulse response or whatever)? Isn't it enough to just have a feedback loop that can compensate any disturbance and ensure the target value?
No, it sometimes isn't enough to just have a feedback loop. An understanding of the underlying system will let you know before you put in a lot of effort what the best you can do is, or whether a system is controllable at all, to let you know if its worth trying. After that, you could compare a system to it's ideal behavior to let you know if you're getting the results you should.
That said, there are a variety of systems that are not tricky, and where you don't expect many irregularities. Such systems can usually be satisfactorily controlled with off-the-shelf devices with confidence.
No it's not.
All real systems will have frequency limits and/or time delays in the path. This leads to frequency dependent phase offset between input and output eventually reaching 180 degrees.
A 180 degree phase offset turns negative feedback into positive feedback. If your control loop still has gain at that frequency you end up with an oscilator.
Picture yourself at Acapulco watching those guys diving into the water from the top of the cliffs. Then ask yourself what the diver is waiting for before he dives and why he can't just randomly dive at any particular moment?
Without knowledge of what the "system" naturally does, a diver may be lucky or he might end up with a broken neck or worse. Why? Timing, timing and timing.
In this example the "system" is simply the drop between the cliff top and (hopefully) the sea. The main factor is the time delay i.e. the several seconds it takes to hit the water.
Another factor that might affect things is wind speed and direction so, to avoid scraping down the sides of the cliff, incurring a few more seconds, receiving plenty of cuts and bruises and finally landing in three inches of water, you take this into account.
The catch is that the physical system that you're trying to servo, becomes a part of the loop. It contributes to the loop's overall gain and phase shift.
And that's what the Nyquist's stability criterion applies to. If across the whole spectrum, you can find a point where gain is > 1 and the phase shift is an integer multiple of 360 degrees, the loop will diverge.
Physical systems that "don't need to be taken into account, and a feedback loop will handle them easily" really are systems that don't contribute much gain or phase shift, or are too fast (or too slow) in their response compared to the "useful bandwidth" of your control circuitry...
The above academic rules are best demonstrated in systems that are "linear" or at least continuous. In systems with some components responding step-wise or showing hysteresis, things get interesting :-) But that's probably out of scope here... (a whole different fairy tale).