It is desired to control the exit concentration of c3 of the liquid blending system shown in Figure Q3. Using the information given below, do the following:
a. Develop the dynamic model for this system as functions of time for any given variation in inputs.
b. Perform a degrees of freedom analysis. Identify all input and output variables.
c. Draw a block diagram for the composition control scheme. (Use the symbols in the figure as much as possible.)
d. Derive an expression for each transfer function
e. Determine the overall transfer function of the block diagram.
Available information:
1. The tank is perfectly mixed.
2. The volumetric flow rate and solute concentration of stream 2, q2 and c2, vary with time, while those of stream 1 are constant.
3. The flow-head relation for the valve on the exit line is given by;
4. The densities of all three streams are identical and do not vary with time.