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

Consider that a process is represented by the transfer function:

G(s) = 6(1 s)/( (s + 1)(0, 5s + 1))

and that the process is in a closed loop with a proportional controller Gc(s) = Kc, and with transfer functions Gf=Gm=1.

a) Write the closed-loop transfer function and its characteristic equation. Is the system stable?

b) For what values of Kc will the closed-loop response of the system be stable?

c) Determine the offset value if there is a unit-step disturbance at the set-point, using a Kc so that the system is stable. Does the system exhibit critically damped behavior or what kind of behavior?