A feedback control system is defined by the transfer function, 𝑌(𝑠) 𝑅(𝑠) = 22(𝑠

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A feedback control system is defined by the transfer function,
𝑌(𝑠) 𝑅(𝑠) = 22(𝑠 + 3) 𝑠 2 + 8𝑠 + 36
(a) For a unit step input 𝑅(𝑠) = 1/𝑠, determine: the steady
state error 𝑒𝑆𝑆(𝑡) and the steady state output response
𝑦𝑠𝑠(𝑡).
(b) Determine the poles and zeros of the system and draw them on
an s-plane diagram.
(c) If a third root was added to give the following transfer
function, what the smallest value for 𝛼 that will allow the complex
conguate poles to be dominant? 𝑌(𝑠) 𝑅(𝑠) = 22(𝑠 + 3) (𝑠 + 𝛼)(𝑠 2 +
8𝑠 + 36)