## 7 Conclusions  
A practical constrained model predictive control (MPC) approach is proposed to optimize the real-time transient performance of gas turbine engines for efficient and safe operations. The effectiveness of the algorithm is validated from different points of view by transient simulations of a twin-spool turbofan engine, which is developed by the inter-component volume (ICV) method and validated against Turbomatch, which is an in-house verified gas turbine performance simulation software. Different settings, parameters tuning, and constraints defined for the MPC provide a significant impact  
\begin{table}
\begin{tabular}{l c} \hline \hline \(\omega=0.2\) & 18.04 \\ \(\omega=0.8\) & 19.40 (+7.57\%) \\ \(\omega=0.2\), no overshoot limit & 18.40 (+1.99\%) \\ \(\omega=0.2\), W\({}_{H}\leq 0.32\) kg/s & 17.50 (\(-2.99\%\)) \\ \(\omega=0.2\), SFC \(\leq 0.03\) kg/Ns & 17.56 (\(-2.63\%\)) \\ \(\omega=0.2\), SFC \(\leq 0.02\) kg/Ns & 16.51 (\(-8.47\%\)) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Total fuel consumption (kg) for 130 s simulation.  
on the optimization result of transient performance. However, choosing an appropriate weighting factor value, prediction and control horizons, and implementing a sufficient number of constraints to the engine parameters enables the MPC to control the engine to its best transient performance within the operating and safety requirements.
* The weighting factor is used to adjust the efficiency of the optimization process from the application point of view. A slightly smaller value for the weighting factor ensures that the transient operations can be completed within the specified time for the entire operating range and guarantees the required maneuverability for the engine. However, larger weighting factor values will result in better fuel economy.
* The larger prediction and control length allow the controller to estimate the engine future dynamics with a longer vision. However, the larger the prediction length, the more computational burden to the algorithm. So, a sufficient horizon length should be selected to provide the controller with enough time to plan and realize the control efforts to engine parameters for the satisfaction of the transient time and the performance limitation within the available computing memory.
* Adding constraints to the engine parameters restricts the controller to operate the engine within the operating envelope. The constraints can also be added to improve the performance quality, such as to obtain a fast-transient operation with a limited steady-state overshoot, and to achieve a specific target for fuel consumption (e.g., better fuel economy). However, having more than enough constraints may result in infeasible solutions or huge computational effort.  
This research has shown that the constrained MPC can provide the optimal control inputs with no need for the classic scheduling techniques. The MPC is capable of adjusting the fuel flow to adapt the change of the engine performance to the performance requirements and producing the optimal control solution to obtain the optimal transient performance for the entire operating range.  
Conceptualization, T.N. and Z.L.; methodology, T.N. and Z.L.; software, T.N. and Z.L.; validation, Z.L. and S.J.; formal analysis, Z.L. and S.J.; investigation, Z.L.; resources, T.N. and S.J.; writing-original draft preparation, Z.L.; writing-review and editing, T.N. and S.J.; supervision, T.N.  
This research received no external funding.  
The authors declare no conflict of interest.