Answer Happy

Question 3 (25 marks) In the feedback system shown in Figure 03, the controller and the plant have the following transfer functions respectively: (+4) Ges) >0 and G (s) (5+1)(3+2)(3+3) Answer the following for this feedback configuration: a) Calculate the closed-loop transfer function. (5 marks] b) By using the Routh-Hurwitz criterion find the values of the controller gain K such that the closed-loop system is BIBO stable. (10 marks] c) Compute the steady-state error to a unit step reference input as a function of the controller gain K. 15 marks] d) Assume now a Pl controller Ge(s)=K, is used instead of the constant gain K. Calculate the steady-state error to a unit step reference input. Is your result in agreement with the internal model principle"? [5 marks] R(S) ES Y(s) G(s) G, (s) Figure Q3: Unity feedback system