3. (35 points) Problem 2 A reaction, A+BC, takes place in a CSTR. The liquid reaction occurs at a constant volume (V) with a constant flowrate (F) under a constant temperature in the reactor. CA, CA,in, and CB represent the steady state value of CA,CA,in, and CB at time zero, respectively. We plan to design controller to control CA by adjusting both CB and CA,in. In addition, we need to change design parameters like F and V to make the system respond faster or increase CA in the reactor. Please answer the following questions and show the detail of your work. (1) (10 points) Linearize the model at the steady state condition (i.e., CA,CA,in, and CB ). Please represent the linearized model using CA,CA,in, and CB. Use CA,CA,in, and CB as the initial value of CA,CA,in, and CB. (2) (10 points) Derive two transfer functions, one relating CB to CA, and the other relating CAin to CA. (3) (5 points) If there is a unit step change in CA,in from CA,in, please estimate the time for CA to reach a new steady state. (4) (10 points) CA will reach a new steady state due to the unit step change in CA,in. Assume that we can change the value of CB over time in the reactor. To keep CA unchanged (i.e., staying at the old steady state value), please determine the magnitude of the step change we should make for CB. 3. (35 points) Problem 2 A reaction, A+BC, takes place in a CSTR. The liquid reaction occurs at a constant volume (V) with a constant flowrate (F) under a constant temperature in the reactor. CA, CA,in, and CB represent the steady state value of CA,CA,in, and CB at time zero, respectively. We plan to design controller to control CA by adjusting both CB and CA,in. In addition, we need to change design parameters like F and V to make the system respond faster or increase CA in the reactor. Please answer the following questions and show the detail of your work. (1) (10 points) Linearize the model at the steady state condition (i.e., CA,CA,in, and CB ). Please represent the linearized model using CA,CA,in, and CB. Use CA,CA,in, and CB as the initial value of CA,CA,in, and CB. (2) (10 points) Derive two transfer functions, one relating CB to CA, and the other relating CAin to CA. (3) (5 points) If there is a unit step change in CA,in from CA,in, please estimate the time for CA to reach a new steady state. (4) (10 points) CA will reach a new steady state due to the unit step change in CA,in. Assume that we can change the value of CB over time in the reactor. To keep CA unchanged (i.e., staying at the old steady state value), please determine the magnitude of the step change we should make for CB