PID controller modelling
"C" and "P" aren't  constants or fixed gains - but functions of time (or by Laplace transf. -> on complex "s").  In other words, are dynamical systems - where the output depends not only on actual input, but also on its past values. To be short: A input change not reflects immediately on output (instead, need to pass through "C" and "P" blocks) in order to be sensed and compared. This "lag" is reflected by the poles and zeros of transfer functions. The controller "C" is created by design, but the plant "P" does not depend on you - it has its own features. If you want Y = R all the time, then you do not need a control system.