Question

Question A1 A single tank process has first order dynamics. When the inlet flow rate is chosen as the input and the level as the output, the transfer function is as follows. 5 G(s) - H(s) 2. (S) S +1 91(t) h(t) *7 q:(0) q2(t) Fig. Q.Al schematic of the liquid level process (a) Determine the system constant t and steady state gain K. [6 marks] (b) For a unit step input q, (t) = 1(1), determine the time response of the process h(t), with the inverse Laplace transform of H(s). [9 marks] (c) To achieve zero steady state error for a constant level set-point, a unit feedback control with a P+I controller is applied. The controller transfer function is (S+2) G(S) = s (i) Draw the block diagram of the closed-loop control system. [5 marks] (ii) Determine the closed-loop transfer function Glace(s). [5 marks]

Answer 1

conrider an open loop System.Windows goo 900 > het) het) = Q(+] *g(t). g(t) — Laplace inverse of Ges). ht) — of MCs). OVED -> ~ of gas). Since system transfer function Gas) = GCS) = a @ from 0 $ ®, Ho C=; K=185 >>K=s. b) when. 91, (+) = 11t), 0,15)= HCS) = Ges) 0,cs) = se g - - stj]'s Laplace inverse fransform HS) 돐 Thet) =5(l-e-t) 1X5 IS HCS) SOSHI 5 Stl.

Gc G) is S let a constrolled with transfer function added with unity tud back. 60, +-744.592 kcal Gas . X H 1X5 S+) - The close loop - G (s) = fransfer function GCSS.Cclosed) . Gc (S) Ges) 1+ GeCSJ GCS) Gelose (s) = 6 cs+ 2)xs 52+5 + 3065+2) = 360 + 2) 52+375 +60 - 30 (5+2) Gclose (s) = Les $2+315760.-