1. The schematic below represents a CST composition mixing tank with the following parameters and variables: (F) spee FC F at C F2 0 at C C- the concentration of the component in the mixed stream mol/l) C the concentration of the component in stream 1 (0.5 g mol/l) C- the concentration of the component in stream 2 (1.0 g mol/l) 0 AT Product at C Figure 3.5.7 Schematic of a CST composition mixing process. F the mass flow rate of stream 1 (initially 500 kg/min) F2 the mass flow rate of stream 2 (500 kg/min) t-time (min) V- the volume of the mixer (1000 1) p- the constant density of the feed and product streams (1 kg/1) t, the time constant for the flow controller on stream 1 (2 s). -analyzer deadtime (5 min). At time equal to 5 minutes, a step change in the specified feed rate for stream 1 is made from 500 kg/min to 400 kg/min. A. Derive/write the dyamic model for the actuator(0.2 pts) B. Derive/write the dyamic model for the process (do not skip steps). (0.4 pts) C. Derive/write the dyamic model for the sensor. (0.2 pts) D. Using MATLAB, find the initial composition of the mixed liquid. Hint: to do this, you can solve the steady state portion of the dynamic model for the process and use an in-built function in MATLAB. (0.2 pts) E. Using MATLAB, plot the dynamic response of F1,spec, F1, C and Cs from t=0 to t=100. Plot C and Cs in 1 figure and F1spec, F in another figure. (1.5 pts) Note: You should type or hand write answers next to the questions and compile a PDF. For all MATLAB parts, you need to include a published PDF file which will consist of the code and results. You should then combine everything into 1 single PDF document. Hint: Cs can be plotted with few lines of code as a time shift of C by the amount theta and should look like this: Conc before and after sensor 0.78 0.775 0.77 0.765 0.76 0.755 0.75 20 40 60 00 80 80 100 120 time (s) deadtime C