In the feedback system shown in Figure Q3, the controller and the plant have the following transfer functions respectively (+4) +1(s+2+3) G, (s) -K>0 and G,Is)- Answer the following for this feedback configuration: a) Calculate the cosed-loop transfer function. b) By using the Routh-Hurwitz criterion find the values of the controller gain K such that the closed-loop system is BIBO stable. c) Compute the steady-state error to a unit step reference input as a function of the controller gain K.

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10:36 O
In the feedback system shown in Figure Q3, the controller and the plant have the following
transfer functions respectively:
(s+4)
(s+1)(s+2)(s+3)
G.(s) -K>0 and G,(s)-
Answer the following for this feedback configuration:
a) Calculate the closed-loop transfer function.
b) By using the Routh-Hurwitz criterion find the values of the controller gain K such that the
closed-loop system is BIBO stable.
c) Compute the steady-state error to a unit step reference input as a function of the
controller gain K
d) Assume now a PI controller G.(s) -K. 1+is used instead of the constant gain K.
Calculate the steady-state error to a unit step reference input. Iis your result in agreement
with the "internal model principle?
Ris)
Els
Yls)
G,(s)
Figure Q3: Unity feedback system
Transcribed Image Text:10:36 O In the feedback system shown in Figure Q3, the controller and the plant have the following transfer functions respectively: (s+4) (s+1)(s+2)(s+3) G.(s) -K>0 and G,(s)- Answer the following for this feedback configuration: a) Calculate the closed-loop transfer function. b) By using the Routh-Hurwitz criterion find the values of the controller gain K such that the closed-loop system is BIBO stable. c) Compute the steady-state error to a unit step reference input as a function of the controller gain K d) Assume now a PI controller G.(s) -K. 1+is used instead of the constant gain K. Calculate the steady-state error to a unit step reference input. Iis your result in agreement with the "internal model principle? Ris) Els Yls) G,(s) Figure Q3: Unity feedback system
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