Consider the fermentor problem in Example 23.1. 

(a) Design an IMC controller for the first operating point (dilution = 0.202 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.
(b) Simulate the response of a -12.5% step change in the maximum growth rate (μ_m). How well does the controller perform?
(c) Comment on the observed nonlinearity in the system.

(d) Discuss how the controller design would change if there were a requirement to operate at the lower dilution operating point. What do you need to consider in this case?