Consider the process control block diagram below:
D
Ua
Gd
SP
E
P
Pa
U
Gc
GFCE
Gp
Gs
a) Write the closed-loop transfer functions for set point tracking in terms of the transfer functions of the individual components. Identify explicitly the input and the output.
b) Write the closed-loop transfer functions for disturbance rejection in terms of the transfer functions of the individual components. Identify explicitly the input and the output.
c) For the following values of the gains, what value must the controller gain have? (i.e., Kc < 0, Kc = 0, Kc > 0.) Write out the relevant equation(s). Justify your answer. Ka < 0, KFCE < 0, Kp < 0, Ks > 0.