Figure 3: Optimal control actions of the two fed-batch operation
processes without practical constraints. (a) and (c): control actions of
this process are predicted by the hybrid model. (b) and (d): control
actions of this process are predicted by the original kinetic model.
To restrict the solution space and include more practical concerns, a
new offline optimisation problem is formulated by embedding three
constraints: the first being that changes between two adjacent nitrate
inflow rates must be less than 2 mL h-1; the second
being that final culture nitrate concentration must be lower than 600 mg
L-1; and the third being that total lutein production
must be no lower than 4.0 mg L-1. The first constraint
aims to prevent drastic changes of culture environment, the second aims
to reduce raw material cost, and the third aims to guarantee a similar
final production to the theoretical maximum value. The initial operating
conditions are set to be the same as before. Through (computational)
experimental verification as shown in Fig. 4 and Fig. 5, it is concluded
that, once again, the hybrid model well predicted the dynamics of
biomass growth and lutein production. Nonetheless, its prediction
regarding nitrate concentration (Fig. 4(d)) is found to have large
deviations when simulating the experiment designed by the original
kinetic model. This means that directly using hybrid model for long-term
process prediction, monitoring and optimisation may still be unreliable
without adequate online self-calibration mechanism.