## 5 Conclusions and Discussion  
This experimental study investigated the use of multi-loop MRAC-FOPID control with NARX reference modeling in the disturbance rejection control problem of ML systems. Simulation and experimental studies were conducted and it was observed that NARX reference modeling enables more intelligent realization of multi-loop MRAC-FOPID control structures. Simulation and experimental studies reveal that NARX modeling can be utilized for online modeling of nonlinear, unstable dynamical systems and it can be a feasible solution for real-time modeling requirements of intelligent control systems. This study also shows that the recurrent artificial neural network serves for improvement of classical control loops. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Control Structure** & \begin{tabular}{c} **Peak Values** \\ **of\(|y(t)-r(t)|\) in** \\ **Disturbance** \\ **Resposes [m]** \\ \end{tabular} & \begin{tabular}{c} **Settling Time** \\ **after Step** \\ **Disturbance** \\ **[s]** \\ \end{tabular} & \begin{tabular}{c} **Cumulative** \\ **Absolute Control** \\ **Error (Additive** \\ **Disturbance**)** \\ \end{tabular} & \begin{tabular}{c} **Cumulative** \\ **Absolute Control** \\ **Error (Harmonic** \\ **Disturbance**)** \\ \end{tabular} \\ \hline \begin{tabular}{l} FOPID control loop \\ (MRAC disabled) \\ \end{tabular} & \(3.603\times 10^{-3}\) & 1.23 & 8.6403 & 28.6592 \\ \hline \
\begin{tabular}{l} Multi-loop \\ MRAC-FOPID control with NARX reference model \\ \end{tabular} & \(2.021\times 10^{-3}\) & 0.43 & 3.6240 & 8.2300 \\ \hline
\begin{tabular}{l} Multi-loop original \\ PID control with NARX reference model \\ \end{tabular} & \(5.552\times 10^{-3}\) & 1.08 & 16.3261 & 18.4087 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of experimental performances of control systems with the MRAC loop disabled and enabled. Figure 16: Sine wave disturbance responses of MRAC system with original PID control loop. It is remarkable that in this study, three major components were considered, which can be used independently to formulate a robust and well-performing control system: (1) the NARX-based control loop with a PID controller that was tuned separately from the FOPID control in the main loop that can be used as an accurate reference model of the controlled process; (2) the retuning FOPID control which replaces the dynamics of another existing PID controller; (3) the MRAC loop which together with the reference model results in improved disturbance rejection in the overall control loop. Indeed, the resulting multi-loop MRAC-FOPID control with NARX reference modeling combines robust stability and set-point control performance of the FOPID control loop with adaptation skills of MRAC loop. Disturbance rejection control is a major concern for practical control applications. To maintain optimal control performance in real-world application, disturbance rejection control performance should be improved in addition to set-point and stability performance. The multi-objective control structures with specialized loops can provide more robust control performance than single control loops in real-world applications. Moreover, this multi-loop control structure can be easily applied to existing closed-loop control systems and this can give an opportunity to upgrade existing classic control loops to multi-loop MRAC loops without changing any parameter or any block of the existing control loops. The NARX reference model facilitates this upgrade process by performing real-time closed-loop model identification of the system and makes the multi-loop MRAC-FOPID control structure more adaptive and intelligent by providing it with benefits stemming from contemporary machine learning. The MIT rule presents a shortcoming of being sensitive to output amplitude of the reference input [5; 11]. Very high amplitudes may cause instability of the system [5] and very low amplitudes diminish effectiveness of MIT rule to respond disturbances [11].