This is a Chemical Process Control question from the Chemical Engineering course. Please do not respond if you are not sure.

Consider now that for the feedback control loop (Figure 2) the transfer function

Figure 2. Feedback control loop.

a) Write the closed-loop transfer function and the characteristic equation for the loop for the controller

b) Determine the values of Kc for which the system will be stable.

c) Choose a value of Kc for which the system will be stable, and now I used the PI controller

For what values of I will the system be stable?

d) Determine the closed-loop response to a unit-step variation in the set-point, what happens to the system if when I=20 and the controller gain has values = [1; 3; 5; 7; 9; 11 and 13]. What is the offset value.

e) Determine the value of the offset (stationary error) for a unit step disturbance in the load, using a PI controller with a parameter I=20 and consider a value of Kc from the previous item in which the system is stable.

Where I is:

Gm=s+11 Gc(s)=Kc Gc(s)=Kc(1+ls1) 1