## 1 Introduction
Therefore, the constrained MPC method is the most suitable one for gas turbine transient process control and performance optimization, as it is fully capable of determining the control inputs and seeking the optimal route based on the prediction of engine dynamics to optimally satisfy all the engine constraints [25]. Consequently, it could be concluded that the next generation of GTE controllers must have:  
* Higher flexibility to deal with control requirements and constraints at different flight and weather conditions. So, a lower coupling between the control channels has become a developing trend to improve the performance of classic scheduling technique (e.g., the min-max algorithm) [26]. * More robustness to cope with system uncertainties in order to adapt dynamics of the GTEs to the wide operating range requirements as well as varying working conditions. This study contributes to the advanced constraint-based optimal control strategy development for the new generation of GTEs in the following ways:  
* Practicality considerations: the control strategy and laws are designed based on realistic assumptions with respect to the implementation considerations, engine, and aircraft flight range, and designer requirements such as the maneuverability (to satisfy the control requirements of short-range aircraft engines) and fuel economy (to satisfy the long-range civil aero engines control requirements). * System dynamics considerations: the dynamic behavior and frequency responses of different parameters such as the pressure, rotational speed, and thrust are considered in controller structure design, and a weighting factors regulation procedure is proposed to achieve a realistic optimal performance for the engine at different flight conditions. * Implementation considerations: the implementation considerations are considered in two ways: from the simplicity of the controller structure to implement, and from the computational effort point of view to achieve the capability of real-time simulation and optimization. * Constraints definition: a modular form of constraints definition and implementation will be considered in the control structure as well. The effects of adding more constraints to the system on performance behavior of the engine will be analyzed in detail. * Controller characteristics: the effects of different controller parameters will be considered on the engine transient performance:
* Effects of weighting factor on maneuverability and fuel economy. * Effects of system dynamics and parameters frequencies on the controller weighting factors selection. * Effects of prediction length and control horizon on the controller performance. * Effects of adding constraints on the system performance and computational efforts. For this purpose, a thermodynamic model for a twin-spool turbofan engine, as a case study, is developed by using the inter-component volume (ICV) method to simulate the engine's transient performance. In order to use the model in a real-time mode, a model identification approach is implemented to develop a recursive least square with varying stabilizing factor (RLS-SV) model for the engine. Then, a model predictive controller (MPC) is designed to deal with engine control modes, where the Lagrangian multipliers and Hildreth's quadratic programming methods are utilized to deal with constraint inequalities and selecting the controller weighting values, respectively. The designed controller is tested in several operating conditions, and different criteria are discussed comprehensively followed by the conclusions.