2. Open loop analysis: For the open loop system: 𝐺(𝑠) = 𝐺𝑣 (𝑠)𝐺𝑝

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2. Open loop analysis: For the open loop system: 𝐺(𝑠) = 𝐺𝑣
(𝑠)𝐺𝑝(𝑠)𝐺𝑔(𝑠) do the following:
a. Determine the poles and zeros of 𝐺(𝑠)
b. Based on the unit step response determine the nature of the
transient response
c. Calculate the open loop steady state error for the unit step
input
3. Closed loop system with 𝑲(𝒔) = 𝑲𝒐 ∈ 𝑹 +: Consider the closed
loop system shown in Error! Reference source not found.. If the
controller gain is constant, then: a. Compute the value of 𝐾, which
yields steady state error:
𝑒𝑇𝑆𝑃 (∞) = 100 (100+𝑅𝑒𝑔#) 𝑘𝐽/𝑚𝑜𝑙 for 𝑅(𝑠) = 1 𝑠 , when 𝐷(𝑠) =
0
b. Compute the following closed loop transfer functions
i. 𝑈0 (𝑠) 𝑅(𝑠) , where 𝑈0(𝑠) is the flow rate (mol/s) of the
inlet gas supplied to the UCG plant by the valve and 𝑅(𝑠) is the
reference/desired heating value (𝑘𝐽/𝑚𝑜𝑙)
ii. 𝑈(𝑠) 𝑅(𝑠) , where 𝑈(𝑠) is the output voltage (V) of the
controller to determine the percentage opening of the valve
iii. 𝐸(𝑠) 𝐷(𝑠) , where 𝐷(𝑠) is the input disturbance (mol/s)

2 Open Loop Analysis For The Open Loop System G S Gv S Gp S Gg S Do The Following A Determine The Poles And Ze 1 (55.35 KiB) Viewed 21 times

Gp(s) = 0.02s + 0.02 / s^2 + 0.2s + 0.01
Gv = Gg = 1/ 2s+1 ,
R(s) E(8) K(s) Controller U(s) U.(s) G(8) Control valve D(s) G₂ (s) UCG Plant C(s) Gg(s) Gas Analyzer Cm(s)