# An Analytical Design of Simplified Decoupling Smith Predictors for Multivariable Processes
## 4 Conclusions  
In this paper, a new structure of a Smith predictor was proposed for multivariable systems by combining the SP with a simplified decoupling network. The general formulation of simplified decoupling was derived from previous works. However, in this study, the PSO algorithm was adopted to approximate model transfer functions and solve the problem of realizability. Multi-loop PI/PID controllers in series with first-order lag filters were used and the general tuning rules were also derived for the delay-free parts of some standard forms of industrial processes. The proposed  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**OR (+20\%)**} & \multicolumn{2}{c}{**OR (-20\%)**} \\ \cline{2-5}  & **IAE** & **TV** & **IAE** & **TV** \\ \hline Proposed & 22.5028 & 6.6492 & 19.1277 & 6.2967 \\ [PERSON] and [PERSON] (2013) & 31.5263 & 4.7536 & 26.7030 & 4.1616 \\ [PERSON] and [PERSON] (2010) & 72.5965 & 10.8927 & 46.7938 & 7.0285 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Robustness analysis for the OR column under \(\pm 20\%\) parametric uncertainties in all parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Tuning** & **Loops** & \(K_{ci}\) & \(\tau_{Hi}\) & \(\tau_{Di}\) & \(\tau_{Fi}\) & \(\lambda_{i}\) & \(\mu[\mathbf{M}]\) & **IAE** & **TV** \\ \hline \multirow{3}{*}{Proposed} & 1 & 5.0586 & 9.8126 & 0.4244 & 10.723 & 2.0 & & & \\  & 2 & \(-\)0.363 & 1.8804 & 0.4253 & 1.0 & 2.0 & 0.1220 & 17.907 & 5.302 \\  & 3 & 73.665 & 25.560 & 2.2486 & 19.787 & 0.2 & & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON]} & 1 & 1.383 & 3.535 & — & — & 5.0 & & & \\  & 2 & \(-\)0.148 & 1.666 & — & — & 5.0 & 0.1506 & 25.388 & 3.594 \\ \cline{1-1}  & 3 & 5.00 & 9.979 & — & — & 0.68 & & & \\ \hline \multirow{3}{*}{[PERSON] and [PERSON]}  
approach is straightforward, easy to implement, and effective when the size of systems is increased. The time-domain simulations demonstrated the superior performance of the proposed structure with, fast and well-balanced closed-loop time responses for both the set-point and load changes. Robustness was investigated by SSV analysis in multiplicative output uncertainty. In order to guarantee robust stability, perturbation uncertainties of \(\pm 20\%\) were inserted in all three process parameters, and the simulation results showed that the proposed method afforded superior robust performance in the plant-model mismatch case.  
The individual contributions of authors: conceptualization, T.N.L.V., V.L.C.; methodology, V.L.C., T.N.L.V.; writing of original draft preparation, V.L.C.; writing of review and editing, V.L.C., N.T.N.T.; supervision, J.H.J., T.N.L.V.; funding acquisition, J.H.J., T.N.L.V.  
This research was supported by Ho Chi Minh City University of Technology and Education, and the \"Human Resources Program in Energy Technology\" of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), with financial resources from the Ministry of Trade, Industry & Energy, Republic of Korea. [No. 20174030201760].  
The authors declare no conflict of interest.