Process Control & Dynamics

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the figure is the transfer function that have given

QUESTION 2 [33 MARKS Consider an electrical heated stirred-tank system as shown in Figure 1. The volumetric flowrate, q for all streams are kept constant. The density and heat capacity of the liquid in the tank are constant. The electrical power, Q1 and Q2 are the possible manipulated variables and inlet temperature, TO is disturbance variable. Figure 1 The transfer functions of the process are given below: 3 To'cs) T's) Q:'(s) 5 T(S) Tics) 3 108 +1 155 +1 129 +7 Assume the standard closed-loop block diagram with the following information are used for temperature control development: (1) Temperature transmitter has been identified as first order (ii) Control valve has gain value of 0.5 with negligible time constant (iii) Set-point transmitter has gain value equal to unity a) If an engineer wants to control the outlet temperature T2 using Proportional control, determine the suitable manipulated variable. Assume magnitude of set-point changes in the range of 5 to 20. Prove with calculation. State your assumptions clearly. (20marks) b) The process engineer aim to improve the process stability by tuning the Proportional Integral (PI) controller parameters. Determine the values of controller parameters. The closed-loop time constant of 1 minute is desired for this process. (Hint: Use the process transfer function obtained in (a)). (6 marks) c) Analyse the closed-loop stability using the PI setting calculated in (b). (7marks)