Question

1. A process is known to be first order in the response of the tank temperature, TO, to changes in the inlet flowrate, gi(). The process is at steady state. T) is at 125 °C and gi) is at 50 gpm. An engineer makes a step change of 5 gpm in qi(0. After a period of time, TO) settles at 158 °C Plot the deviation variables for these two variables over time starting from the time of the change until settling. Plot the standard variables for these two variables over time starting from the time of the change until settling. Give the transfer function representing this input to output relationship. Give the equation for TC) for this input change. a. b. c. d.

Answer 1

(c) Let Deviation variables be, T = T(t) - T_s T = T(t) - 125 and q = q(t) - q_x = [q(t) - 50] and Z [T] = T(x) and Z [q] = q(s) = > Laplace transform given that, T(s)/q(x) = (K/tau s + 1) first order system. q(s) = 5/s T(s) = F(s) = (k/tau s + 1) 5/5 = 5/5 (s) - (1) T(t) = 158 degree C t rightarrow infinity i.e. T (t) = 158 - 125 = 33 degree C Applying final value theorem we have lim_t rightarrow infinity T(f) = lim_s rightarrow 0 s F(s) = 158 degree C lim_s rightarrow 0 s middot 5K/s(tau s + 1) = 158 degree C 5k = 158 k = 158/5 \r\n Thus T(s) = 158/s(s tau + 1) T(t) = Z^- 1 [158/s(s c + 1] = Z [tau 158/tau [1/5 - 1/(5 + 1/c)]] = T