Answer the (e) point

In an industry there is a continuous stirred reactor tank (CSTR). This CSTR operates at a constant temperature (T) and has a volume V(!). Then, the reactant A is fed to the tank with a flow rate of Fo and a molar concentration of Co to the reactor. Next, the liquid solvent is flowed into the reactor through a second stream with a flow rate of F1. The molar concentration in the reactor is CA. The outflow rate from the reactor is F2 with the molar concentration being CA. Symbol Fo: liter/second VA F1 liter/second CA: molar/liter FZ: liter/second In the reactor, component A reacts and forms product B. The reactions that occur are: 2A B The reaction rate for component A is: rA=-k[A]2 (mol/liter second). Where, the kinetic rate constant k=0.25 (liter mole/liter.second) and A is the molar concentration of A. Assumption: 1 The content in the STR is mixed well/evenly. 2. Incompressible flow with constant density in all streams 3. The output molar concentration of C2 and the volume of V in the tank is to be controlled by manipulating the inflow rate of Fo and the outflow rate of F2 4. It can be assumed that all flows are manipulated using a pump 5. There is a sensor to measure the concentrotion of C2 QUESTION (if you need other information to answer the question please add/assume) a) Identification of input and output variables in the system. b) Develop a dynamic model for the control system c) Is the dynamic control system linear or nonlinear? d) Calculate the molar concentration of A at steady state in the CA reactor, if V = 10 (1), co = 0.5 (mol/liter), c1 = 0.45 (mol/liter), FO = 0.7 (liter/second), F1 = 0.8 (liters/second). e) Linearize the control system at steady state (point d), state the linearization system in the form of deviation and calculate the transfer function related to the molar concentration at the output of the C2 reactor, Inlet flow rate Fo, F2 outflow rate (in deviation form) . Assume that Co and Fi are maintained at steady state (should be treated as constants)