Gp1(s) H(s) = 1 (s + 1)(s + 10)' a) Given a choice between P or Pl controller Dei(s), choose the controller (and its' parameters) that will result in a Type 1 system (with respect to steady-state error) and a steady-state error to a unit-ramp r(t)=t u(t) which is less than 1/100. b) Now, assume that there is some attenuation in the feedback path so that H(s) = 0.9 (instead of unity). Assuming the controller remains the same as in part a), what is the steady-state error due to the unit-step and unit-ramp input now? Hint: derive the E(s) (using the definition) and steady-state error for the case when H(s) is not unity feedback! If H(s) = 0.9, will the system remain Type 1?

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1
Gpi(s) =
H(s) = 1
(s + 1)(s + 10)’
a) Given a choice between P or Pl controller De(s), choose the controller (and its' parameters)
that will result in a Type 1 system (with respect to steady-state error) and a steady-state error to
a unit-ramp r(t)=t u(t) which is less than 1/100.
b) Now, assume that there is some attenuation in the feedback path so that H(s) = 0.9 (instead of
unity). Assuming the controller remains the same as in part a), what is the steady-state error
due to the unit-step and unit-ramp input now? Hint: derive the E(s) (using the definition) and
steady-state error for the case when H(s) is not unity feedback! If H(s) = 0.9, will the system
remain Type 1?
Transcribed Image Text:1 Gpi(s) = H(s) = 1 (s + 1)(s + 10)’ a) Given a choice between P or Pl controller De(s), choose the controller (and its' parameters) that will result in a Type 1 system (with respect to steady-state error) and a steady-state error to a unit-ramp r(t)=t u(t) which is less than 1/100. b) Now, assume that there is some attenuation in the feedback path so that H(s) = 0.9 (instead of unity). Assuming the controller remains the same as in part a), what is the steady-state error due to the unit-step and unit-ramp input now? Hint: derive the E(s) (using the definition) and steady-state error for the case when H(s) is not unity feedback! If H(s) = 0.9, will the system remain Type 1?
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