Question

Question 4 A control system is shown in Figure 3, where Ge(s) is the controller, R(s) is the setpoint temperature, Tw is the measured water temperature, Ta is the ambient temperature and u(t) is the rate of heat supplied to the heater. The mathematical model of a simple thermal system consisting of an insulated tank of water is given by: dTW = c(1, - Iw) +u dt where c is the heat insulation coefficient. Heater Water R(s) Ta Gc/s) u(1) TW Insulation Figure 3 (a) State if this is an open loop or closed loop system. Justify your answer. (4 marks) (2 marks) (b) Is there any disturbances in the system? State the disturbances that you could find in this system (8 marks) (c) Draw a closed-loop functional block diagram for the thermal system above. Label your diagram correctly. (6 marks) (d) By setting y(t)=Tw(t)-Ta and assuming c = 0.55-1, calculate the transfer function G(s)=Y(s)/U(s) where y(s) and U(s) are the Laplace transforms of y(t) and u(t) respectively.

Answer 1

(a) a Sencor il 10 Gogh feed back element This is a clared loop System because Used to Serpe temperature so sensor is the feed back element which maked the system closed loop. The error in the set point temperature and actual temperature determines the input to heating element and there by regulating the temperature Hence it is a closed loop system. (b) feat Energy can escape through insulation slowly. This results in a decrease in water temperature. Hence it can be distrabance crop in change temperature is also a distrabance plant Tret Grool Heatest ert water tark Temperdue Sonsol None 1199 concidered as a ambient Ta Controller PE ULI Controll no HCC) 1

ten!! (d) y tl = TW(t) - Ta dy diw dt (Assuming Cambient temperter is constant ) NOW Oce dow de dt dy dt c (Tar Tw) & u dy = c(ta - Twilt), ) + u(t) = c(-y. (t)) + ule groue Apply Laplace Laplace transform syu) - cy(s) + UCD YESH Saclaucs) Yus) Tucs) 30 1 et biopien du SM Given (=0.5 6-) YES) S+0.5 ull y box Top ole tuo HOUL