###### Abstract  
This study is concerned with developing a robust tracking control system that merges the optimal control theory with fractional-order-based control and the heuristic optimization algorithms into a single framework for the non-minimum phase pitch angle dynamics of Boeing 747 aircraft. The main control objective is to deal with the non-minimum phase nature of the aircraft pitching-up action, which is used to increase the altitude. The fractional-order integral controller (FIC) is implemented in the control loop as a pre-compensator to compensate for the non-minimum phase effect. Then, the linear quadratic regulator (LQR) is introduced as an optimal feedback controller to this augmented model ensuring the minimum phase to create an efficient, robust, and stable closed-loop control system. The control problem is formulated in a single objective optimization framework and solved for an optimal feedback gain together with pre-compensator parameters according to an error index and heuristic optimization constraints. The fractional-order integral pre-compensator is replaced by a fractional-order derivative pre-compensator in the proposed structure for comparison in terms of handling the non-minimum phase limitations, the magnitude of gain, phase-margin, and time-response specifications. To further verify the effectiveness of the proposed approach, the LQR-FIC controller is compared with the pole placement controller as a full-state feedback controller that has been successfully applied to control aircraft dynamics in terms of time and frequency domains. The performance, robustness, and internal stability characteristics of the proposed control strategy are validated by simulation studies carried out for flight conditions of fault-free, 50%, and 80% losses of actuator effectiveness. actuator fault-tolerant; aircraft dynamics; heuristic optimization; fractional-order control; non-minimum phase; optimal control +
Footnote †: journal: Applied Sciences  
A. [PERSON] [PERSON]; [PERSON], [PERSON]. nature of dynamics causes physical limitations to the open-loop bandwidth, and thus restricting the benefits of the feedback control system [5]. This can be seen in the tracking control problem, where the feedback controller can track the reference signal perfectly, but the system states can become unstable, which is referred to as the internal stability problem generated by non-minimum phase dynamics [6]. Various methodologies have been proposed to control plants with non-minimum phase characteristics. The main features of these approaches from the transformation of NMP nonlinear systems to approximately minimum phase systems such as approximate feedback linearization (FBL) [7], real-zero elimination [8], and stable inversion [9] approaches, to other approaches that investigate the possibility of overcoming unstable internal dynamics by introducing a dummy output thereby obtaining the desired trajectories via methods such as the output redefinition method [10]. More recent works are rather destined to the inversion-based nonlinear controllers to deal with nonlinear non-minimum phase systems [11; 12]. Although previously proposed approaches in literature showed a strong capability for dealing with NMP dynamics, there still are some inadequacies that make them restricted to certain applications and cases. Among those reported methods, for instance, the approximate feedback linearization method can be classified into two approaches: input-output FBL and input-state FBL. While the input-output FBL cannot cope with NMP dynamics satisfactorily, the input-state FBL can achieve a good asymptotic closed-loop stability. However, in this case, the states of the system must be known precisely [13]. Furthermore, the input-state FBL method suffers from the robustness problem in the existence of system uncertainties [14].