please solve 4 questions with full answers and formulas course is control chemical engineering

Question 14 points) 2 2 For the process shown below: a) Define the control objective(s) b) Identify the possible controlled manipulated, and disturbance variables, sensors and actuators used for this process. c) Draw a feedback block diagram for the temperature control loop. a Flue gas rc Feed TC full feel upl system is tomaintain the flowrate at a de afput the temp 2 Question 2 (6 points) For the function f(t) = u(t) - 2u(tl) fu(-2), a) Find Laplace transform of the function f(t). b) For the differential equation dx/dt +x = f(t), x(0) = 0, determine x(1) c) Determine x(0) and x(0) Question 3 (5 points) The transfer function of a process is: 1 1652 +8s + 4 a) Determine the values of K, t, and for the above process T S b) If a step change is introduced into the system, then what will be the response characteristics? Why? Draw a qualitative sketch of the response. day + ZIT d) +y=kx Question 4 (10 pts) Consider the chemical mixing process shown in the drawing, where numeric values mentioned are steady-state ones. Neglecting the dynamics of the mixing tee, answer the following: a) Develop the dynamic mathematical model that describes how the outlet concentration Calt) is related to the inlet concentrations Ca(t) and Ca(t). b) Derive the transfer functions for this mixing process showing all your steps. c) Write the expressions for the time constant and steady-state process gains and evaluate their numeric values. d) Draw the block diagram for the process, Stream 3 Ca=? g/L Mixing tee v3=30 U/min Stream 1 Cal=lgl =10 L/min V=150L Stream 2 C.2=4 g/L Yo=20 L/min To reactor Hul a