3.2 Open-loop optimal control (offline optimisation)
To further assess advantages of this hybrid model, it is first used in
offline optimisation to test its ability in long-term process predictive
modelling and optimisation. The objective function is to maximise the
final lutein production over a 5-day fed-batch operation system in which
incident light intensity (100 μmol m-2s-1 to 800 μmol m-2s-1) and nitrate inflow rate (0 to 17.5 mL
h-1 with a concentration of 0.1 M so that total added
liquid volume is negligible) can change once per day. Once optimal
control actions were estimated by the hybrid model, they were
implemented and verified in the computational experiment (using the
original complex kinetic model). In addition, the original model was
also used to search for the theoretical maximum lutein production in
this fed-batch process. This is used as a benchmark to evaluate the
hybrid model’s predictive capability. Initial operating conditions of
this process are listed in Table 1.
Fig. 2 and Fig. 3 shows the model prediction result and experimental
verification results. From Fig. 2, it can be observed that the hybrid
model can well predict the dynamic process behaviour over the entire
operating time course before executing the process. This directly speaks
of the predictive capability of the hybrid model. Furthermore, through
(computational) experimental verification, the hybrid model is found to
provide the same lutein production as the maximum theoretical value
estimated by the original kinetic model, indicating its high performance
in offline optimisation. The two processes (designed based on the hybrid
model: Fig. 2(a), 2(e), 3(c); designed based on the original model: Fig.
2(b), 2(f), 3(d)) have the same trajectory for biomass growth, lutein
production, and control actions of incident light intensity. However,
culture nitrate concentration (Fig. 2(b) vs. Fig. 2(d)) and nitrate
inflow rate (Fig. 3(a) vs. Fig. 3(b)) deviate substantially between the
two processes. This indicates that this process is not sensitive to the
change of nitrate concentration as long as it is sufficient (400 to 900
mg L-1). It also suggests that multiple optimal
solutions exist for this offline optimisation problem.