I've gone through a control theory course, and after looking back at what we covered and how the subject was taught to us, I still have quite a few questions (which I unfortunately did not ask in class). As such, I thought I'd ask a few of them here, as separate posts, in order to clear up a few points that I don't understand.
Why do we linearize our dynamic equations/transfer functions when doing classical and state-space control? Is this only to allow us to be able to analyse stability and do initial specification design (rise time, overshoot etc.), where we know that the real nonlinear system won't actually act exactly in the above manner? I would have thought that since we'll generally be dealing with nonlinear systems in the real-world, it would be better to test our control implementation on a model that more closely resembles our real system.