Refer to the bioreactor example discussed in class but with a constant volume of 1000 liters. Assume the same set of conditions as in the "base case" (Part B) and that the cell growth rate is substrate inhibition kinetics: u=umaxS/(K+S+(S2)/Ki) 1. For D=0.15h1 what are the values of X and S at the three possible steady states? 2. For open-loop operation: a. Find a couple sets of initial X and S values that result in the reactor reaching the stable steady state. b. Repeat for different initial X and S values that result in washout. 3. Implement a closed-loop control system that measures outlet cell concentration, X, and manipulates the feed flow rate. Make sure the model contains the line of code that limits the feed rate to only zero or positive values. 4. Implement proportional control with the desired operating point being the open-loop unstable steady state. Use the disturbances (initial X and S values) from \#2 and your choices of Kc to obtain transients that results in satisfactory control atear the desired goal. 5. Pick one case from \#4 and analyze the responses to changes in the feed substrate (reactant) concentration Sf. Part B: Inhibition Kinetics Here is Polymath code for the same reactor geometry but with inhibition kinetics \# bioreactor open loop inhibition kinetics (plot of u vs S might be helpful) d(X)/d(t)=(uD)Xd(S)/d(t)=D(SfS)(uX/Y)Y=0.4X(0)=1S(0)=0.5D=0.15u=umaxS/(K+S+(S2)/Ki)K=1.0Ki=3t(0)=0t(f)=30S=10.0umax=0.5