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.