I have found questions similar to mine in the forum but none were quite answered to my full satisfaction. I have two questions:
1) Why is controller design is traditionally done with the open-loop system? Is it simply that if the system responds in a stable and desirable manner in an open loop setting (e.g., step response), it will similarly do so with a changing input once the loop is closed? What if the system's feedback is not unity, but contains some transfer function?
2) Why is it that open-loop characteristics are always analyzed for a system? I understand that stability margins/crossover frequency are properties exclusive to the open loop, but I'm talking about more descriptive concepts. For example, a closed loop bode plot describes how the system will actually respond to a given forcing function, so why not report on the closed loop phase lag and system gain?
Thank you in advance.