Q1 [50 pts] Consider the following block diagram: (a) Define the transfer function of the process, disturbance, valve and sensor. What type of controller is used? (b) Is the process itself stable? And why (c) Drive the closed-loop transfer function relating the output, C to the set point R and the disturbance, L. (d) For the set point case, take ke = 5, calculate the zeros R + K Re L and poles of the closed-loop transfer function. Is the closed-loop system stable? (e) What values for ke makes the closed-loop system stable? (f) What value for ke makes the closed-loop response oscillatory? s+10 C 91.01 91. C AC Q2 [50pt] Consider the mixer shown in figure where two streams with different flow rate and concetrations are blnded isothermaly without reaction. It desired to control the outlet concentration by manipulating 42. PI controller will be used. The exit concentration is measured by a sensor that has fast dynamics and emits a signal between 4 and 16 mA when the concentration is between 2-14 lbmole/ft³. The penumatic control valve has a negligible dynamic and receive a signal between 12 and 7 psi to allow for flow rate between 10 and 20 ft³/min. The process model is given as follows: AT 93.0 V dc3(t) dt 91(t)c₁ +92(t)c₂-93c3(t) Consider feed concentration to be constant [a] Develop the transfer function for each control compoenent and substiute numerical values [b] Draw a block diagram for the composition control system. [c] Explain why q2 is beter to use as MV than qi. [d] What are the disturbances [e] Drive the closed-loop transfer fucntion for set point only. What os the order of the closed- loop system [f] What is the value of the overall static gain? Is is bigger than the porcess static gain? [g] During set point change of 1, c3 showed an overshoot of 23%, what Is the corresponding value of ke if t₁ = 0.1. Data: at steady state: V-15 ft³, q=10 ft³/min, q=15 ft³/min. q3=25 ft/min. c₁ = 2 lbmole/ft³, C2-7 lbmole/ft³, c3-5 lbmole/ft³. T= period of oscilation = 2πτ 1-32 OS = exp(- -πζ 11-32°