## 5 Results and Discussions
### Proposed LQR-FIC Controller against Pole Placement Controller  
Among the techniques frequently found in literature for controlling civil aircraft [59], UAV [60], and military aircrafts [61; 62] is the pole placement approach. The proposed LQR-FIC controller is further evaluated by comparing it with the pole placement controller in terms of time and frequency responses under faulty and fault-free conditions. In addition, as described previously, the main obstacle in the classical feedback control loop with NMP dynamics is the problem of internal stability even if the system shows optimal transient and steady-stated time responses. Therefore, for a fair comparison, the desired positions of poles (eigenvalues of the closed\(-\)loop system) in the pole-placement controller were selected at the same positions as those captured by the proposed LQR-FIC controller. This, in fact leads to very similar transient responses from both controllers. The forward scaling factor is attached to the pole placement controller at the input of the system to scale the input, and thus force the steady state response to reach the desired level. The value of the scaling factor is selected as the reciprocal of the DC gain of the system to avoid the reversing response of the pole placement controller due to the NMP nature of aircraft altitude control. The main purpose of the proposed controller is to devise a control method to deal with adverse non-minimum phase characteristics in terms of the internal stability problem. It is seen that the proposed method provided better internal stability, which is particularly important in terms of flight quality. The frequency response analysis presented higher gain, phase, and delay margins. Therefore, the evaluation is carried out according to frequency domain analysis to observe the dynamic behavior of the NMP with respect to its internal state stability. As clearly seen in Figure 7, the pole placement controller with a feedforward scaling factor produced favorable time responses for fault\(-\)free and faulty flight conditions. However, as revealed in Figure 8, which represented the Bode plots of the closed-loop system using the pole placement controller, the gain, phase, and delay margins are reduced when compared with the margins of the proposed LQR-FIC controller. Finally, Table 2 presented the results of the pole placement controller that were obtained during the simulation tests. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Controller** & **IAE** & **P1** & **P2** & **P3** & **P4** & **P5** & **Forward Negative Scaling Factor** \\ \hline Pole placement-Fault free & 0.0704 & \(-\)50.117 & \(-\)10.420 & \(-\)14.27 & \(-\)14.200 & \(-\)1.26 & \(-\)627.4238 \\ Pole placement-50\% & 0.0728 & \(-\)50.117 & \(-\)47.777 & \(-\)9.29 & \(-\)14.274 & \(-\)1.21 & \(-\)599.9231 \\ Fault free & & & & & & & \\ Pole placement-80\% & 0.0728 & \(-\)50.117 & \(-\)47.769 & \(-\)9.29 & \(-\)14.274 & \(-\)1.21 & \(-\)599.9041 \\ Fault free & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical performance results of the pole placement controller. Figure 7: Pitch angle step response with and without faults—pole placement controller. Effect of Fractional-Order-Based Pre-Compensators on the Phase and Gain Margins of Open- and Closed-Loop Systems  
It would be more useful and provide a better evaluation of the effects of both pre-compensators that were demonstrated in the frequency domain by comparing the gain, phase, and delay margins of the augmented dynamic (Open-loop response) with the gain, phase, and delay margins of closed-loop response. Moreover, the comparison of the two pre-compensators in the frequency domain to emphasize the effectiveness of the compensators removing the limitations of the feedback control system with the non-minimum phase dynamics should be performed.