## 7 Discussions and Conclusions
The ML-MR PID-IM control structure benefits from having an internal model controller design, however it should be noted that its performance is very sensitive to the accuracy of plant and controller models. * Large-time delay systems that set the point and disturbance rejection performance of ML-MR PID-PID-PFA control structures can surpass the disturbance rejection performance of a single-loop optimal FOPID control system. These results reveal that the disturbance rejection capacity of closed loop PID control loops can be exceeded by combining them with ML-MR control structures. ML-MR control structures are a feasible way to resolve performance tradeoff between set-point and disturbance rejection control structures. * Stability analysis of linear ML-MR control structures is relatively straightforward and is performed by obtaining the transfer function of the whole structure and checking for pole placements for left half-plane (LHP) stability. The satiability of a nonlinear ML-MR structure, such as ML-MR PID-MIT control, along with the stability and convergence conditions, are derived on the basis of the bounded input and bounded output stability state of the model error (see Appendix A). * Results in this study are based on simulation models. The reference models perfectly match the controlled systems. It is very important to note that model mismatches due to limitations in mathematical modeling and parametric model perturbations in real systems may have severe effects on the control performance and stability of the presented ML-MR adaptive control structures in real-world applications. The sensitivity of these structures to model mismatching should be carefully investigated in future works. The fragility of the system stability due to model imprecision should be carefully considered when designing real control systems. Moreover, the resolution of sensors and I/O ports of control cards are important in practical applications. * This study is a theoretical demonstration of six different ML-MR adaptive control structures. Future works should address experimental performance evaluations and practical realization issues of ML-MR adaptive control structures. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ML-MR Control** & \multirow{2}{*}{**Character**} & \multirow{2}{*}{**Dependence to**} & **Negative Effects** & \multirow{2}{*}{**Applicability for Time**} & **Indications in** \\
**Structures** & & **Set-Point** & & **on Set-Point** & **Daly Systems** & **Simulation** \\  & & **Level** & & **Performance** & & **Results** \\ \hline ML-MR PID-MIT & Nonlinear & Dependent & None & None & Figures 3 and 4 \\ ML-MR & Nonlinear & Dependent & None & None & Figure 8 \\ PID-MIT-CGM & Linear & Independent & None & None & Figure 10 \\ ML-MR PID-IM & Linear & Independent & None & None & Figure 14 \\ ML-MR & Nonlinear & Dependent & None & Applicable to some degree & Figure 1 The most prominent contributions of the introduced hierarchical ML-MR control structures are:  
1. The proposed ML-MR adaptive control structures can be applied to existing control loops without modifying any parameters of the control loops. These structures do not require online return of the control loop, which may result in instant performance degradation while altering controller coefficients. Therefore, ML-MR control structures provide more consistent control performance than conventional MRAC structures that are used to perform online return of the control loop. 2. The proposed ML-MR adaptive control structures increase the disturbance rejection performance without deteriorating the set-point control quality. This is an important contribution to the solution of performance tradeoffs between disturbance rejection and set-point control. Conceptualization, B.B.A. and A.T.; methodology, B.B.A. and A.T.; validation, E.P. and C.Y. ; writing--original draft preparation, B.B.A. ; writing--review and editing, A.T., E.P., and C.Y. ; supervision, E.P. and C.Y. All authors have read and agreed to the published version of the manuscript.