## 6 Discussion  
With all the control weights, predictions, and horizon length as well as constraints set-up, the MPC can operate the engine under variable environmental conditions (Figure 17). The MPC accelerated the engine from EPR 1.18 to 1.83 (corresponding from PCNL from 60% to 100% at sea level) within five seconds and maintained the EPR output as close to the final steady-state level as possible while the environmental and the flight condition keeps changing. In addition to the transient time optimization, fuel economy can be optimized by constraining the maximum fuel flow, the fuel rate, or increasing the control weight to the MPC. However, all of these methods attempt to introduce the actions, which directly influence the input of the fuel value. Figure 16: (**a**) The transient performance of output gross thrust ratio (GTR) with the limitation of TET; (**b**) the close-up view. Figure 17: Transient acceleration under increase of Mach number and altitude. It was found that the value of SFC could be controlled (below 0.03 kg/N\(\cdot\)s) by only limiting the maximum value of fuel flow (Wff \(\leq\) 0.32 kg/s; Figures 18 and 19). Instead, the SFC can be directly added to the constraint, as listed in Table 2. The SFC value was taken as the ratio between the measured fuel flow and the estimated thrust from the engine. The maximum SFC value can be reduced by more than half to the highest peak value given by the transient operation without the limit of SFC. Figure 18 shows that the SFC is successfully kept below the threshold (SFC \(\leq\) 0.03 kg/N\(\cdot\)s and SFC \(\leq\) 0.0  
Finally, Table 4 shows the total fuel consumption after the 130 s engine operation test. When the SFC is limited below 0.03 kg/N-s, the fuel consumption reduces by 2.63%. This value becomes 8.47% when the SFC is limited by a further 0.01 kg/N-s (SFC \(\leq\) 0.02 kg/Ns). Alternatively, limiting the maximum value of the fuel input means reducing a similar percentage of fuel consumption as well (similar to the results from the constraint of the maximum SFC (0.03 kg/N-s)). The total fuel consumption has been increased by 7.57% if a higher value of the weighting factor (\(\omega=0.8\)) is used in MPC, due to a longer time in transient states (Table 5). However, if only the first two transient cycles are considered (Figure 19), 0.55% of fuel can be saved by increasing the weighting factor to 0.8. Consequently, the above results and analyses state that:  
The maneuverability of the engine could be achieved by decreasing the weight factor in the designed controller (e.g., 0.2). It will reduce the response time of the engine with the penalty of higher fuel consumption. The fuel economy will be enhanced by increasing the weighting factor. In this case, the engine response time will be increased as well. A relatively smaller weighting factor can be applied by the MPC for the parameters, which have a wider cut-off frequency (e.g., GTR and EPR). In contradictive situations, the designed MPC chooses to satisfy the input limit and compromises the output limit. In other words, the input limits have a higher priority than the output limits. With a moderate horizon length (70 steps), the controller is capable of allowing the transient operation to be completed within 5 s (\(\leq\)5% overshoot) as well as saving the computing memory by reducing the columns and rows of constraints in matrix \"F\". Adding more constraints increases the possibility of having less control freedom or a higher chance of contradiction among the constraints. Therefore, it should be taken into account that the definition of a huge number of constraints is not necessarily a positive point in the engine control. The minimum number of required constraints should be defined and formulated. By utilizing the methodology and results presented in this paper, future studies could be focused on:  
* Defining and exploring other constraints, and investigating the effects of ambient temperature and weather conditions.