Transfer functions for controls

Lets look at a very general control scheme:

with the block and signals:

• $F$ : feedforward controller
• $C$ : feedback controller
• $P$ : the plant
• $r$ : reference signal, global input
• $e$ : tracking error
• $u$ : control signal
• $d$ : input disturbance
• $v$ : disturbed input
• $\eta$ : plant output
• $n$ : output disturbance
• $y$ : disturbed output, global output

I'm sure you're now able to do this, but I'll do it for you, the algebraic expressions for the error and output are $$ e = \frac{F}{1 + PC} r + \frac{-1}{1 + PC} n + \frac{-P}{1 + PC} d = G_{er}r + G_{en}n + G_{ed}d \text{, and}$$ $$ y = \frac{PCF}{1 + PC} r + \frac{1}{1+PC} n + \frac{P}{1 + PC} d = G_{yr}r + G_{yn}n + G_{yd}d.$$ You might recognise the fractions as transfer functions and this reveals the robust control problem they might tackle in the master course: how to reject noise, but follow the reference?