Consider the fermentor problem in Example 23.1.

1. Design an IMC controller for the first operating point (dilution = .202 h^-1), and simulate the response to both a +0.5 [g/L] and a -0.5 [g/L] change in the biomass concentration set point. Then, simulate the response to both a +1 [g/L] and a -1 [g/L] change in the biomass concentration set point.
2. Simulate the response of a -12.5% step change in the maximum growth rate ( μ_m). How well does your controller perform?
3. Comment on the observed nonlinearity in the system.
4. Discuss how your controller design would change if there was a requirement to operate at the lower dilution operating point. What do you need to consider in this case?