## 5 Conclusions  
In this work, the I/O FBL method combined with the SMC technique was investigated in order to deal with control issues related to model parameter uncertainties and undetermined state disturbances under severe constraints.  
The proposed analytical method provides better outcomes versus the I/O FBL alone. Nevertheless, complete decoupling of the desired output variable from the unmeasured disturbance could not be achieved.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Control Strategy** & **IAE** & **Control Effort** & **ISE** & **Maximum Overshoot** \\ \hline Fuzzy PSO & 0.01 & 1152 & 0.000 & 0.11 \\ SMC-based I/O FBL & 0.15 & 1609 & 0.016 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 4: A comparative analysis.  
Figure 15: Control input signal.  
The need to determine the exact value of the unmeasured state in order to define the manipulated control input for complete decoupling led to the implementation of advanced heuristic techniques to enhance the steady-state performance. In this respect, a novel and advanced nonlinear control strategy based on fuzzy logic combined with PSO has been developed. Using this approach, it was demonstrated that the tracking error could be made equal to zero. In spite of employing SMC, the undesirable chattering did not impact the system dynamics.  
The designed scheme combines the state FBL technique to decouple the disturbance from the system output and an SMC technique to guarantee the robustness of the controller in addition to external disturbance-rejection, fast dynamic response and insensitivity to uncertainties in plant parameters and modeling. Moreover, to alleviate the SMC chattering, fuzzy logic was implemented. Indeed, fuzzy logic enables the tuning of the switching SMC gain, which guarantees the process stability and almost eliminates the effect of chattering. A PSO algorithm was applied to enhance the fuzzy logic control gain tuning, give more flexibility in adjusting the controller gains and reduce the steady-state error. As a result, the accuracy of the output trajectory tracking was significantly enhanced.  
Future development work will focus on applying the proposed methodology in the discrete-time domain. Even though the control strategy made use of real-time application software, the effects of sampling period selection and process delays associated with the use of the control input were not specifically addressed in this work. Moreover, investigating the algorithm performance when exposed to constraints would be a promising research subject.  
Conceptualization, S.C., H.J. and S.B.A.; methodology, S.C., H.J. and A.B.; software, S.C. and S.B.A.; validation, M.K., O.A., S.B.A. and Z.E.; formal analysis, S.C. and H.J.; investigation, H.J. and M.K.; resources, A.B., O.A. and S.B.A.; data curation, S.C. and S.B.A.; writing--original draft preparation, S.C., R.A. and H.J.; writing--review and editing, H.J. and A.B.; visualization, R.A. and Z.E.; supervision, H.J.; project administration M.K., A.B., H.J. and S.B.A.; funding acquisition, A.B. and H.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Research Deanship of Hail University--KSA project number (RG-20 097).  
Not applicable.  
Data availability Statement: Data are contained within the article.  
Authors acknowledge the Research Deanship of Ha'il University-KSA for the administrative, financial and technical support.  
The authors declare no conflict of interest.