# Design of PIDD(r) Controller for Robust Performance of Process Plants
## 1 Introduction
### Power Electronic Applications
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Ref.** & **Year** & **Controller** & **Parameters** & **Comparison** & **System** & **Tuning** & **Measures** & **Simulation/Practical** & **Software** \\ \hline
[6] & 2023 & Fuzzy PIDD2 & 8 & PID, Fuzzy PID & Conventional and hybrid two-area & Gradient-based optimization & ITAE & Simulation & MATLAB \\ \hline
[1] & 2023 & PIDD2 & 5 & PID & \
\begin{tabular}{c} AVR of synchronous \\ generator \\ \end{tabular} &
\begin{tabular}{c} Constrained \\ optimization problem \\ via an iterative \\ procedure \\ \end{tabular} & IAE & Practical & MATLAB \\ \hline
[20] & 2023 & FPIDD & 6 & \begin{tabular}{c} GRO tuned ID-T, \\ FPDD \\ \end{tabular} & \begin{tabular}{c} Two-area hybrid \\ system \\ \end{tabular} & \begin{tabular}{c} Gradient-based \\ optimization \\ and undershoed, ITAE \\ \end{tabular} & \
\begin{tabular}{c} rise time, settling \\ time, max overshoot, \\ Practical \\ \end{tabular} &
\begin{tabular}{c} Simulation and \\ Practical \\ \end{tabular} & MATLAB/Simulink \\ \hline
[22] & 2022 & PIDD2-PD & 9 & PID-TID, ID-T & \
\begin{tabular}{c} Two-area linked \\ power system \\ \end{tabular} & Wild horse optimizer &
\begin{tabular}{c} Stillting time, \\ maximum overshoot, \\ and undershoed \\ values \\ \end{tabular} & Simulation & MATLAB/Simulink \\ \hline
[10] & 2022 & PIDD2 & 4 & \begin{tabular}{c} WO-PIDD2, \\ PSO-PIDD2, \\ OBAS-PIDD2, \\ ASO-PIDD2 \\ \end{tabular} & \begin{tabular}{c} AVR system \\ \end{tabular} & \
\begin{tabular}{c} Coronavirus herd \\ immunity \\ optimization \\ \end{tabular} & ITAE, ITSE &
\begin{tabular}{c} Simulation and \\ Practical \\ \end{tabular} & MATLAB \\ \hline
[7] & 2022 & PIDD2-PD & 6 & \begin{tabular}{c} PIDD-ISO, \\ FPDD-SCA, \\ PIDD-WAO \\ \end{tabular} & \
\begin{tabular}{c} Arithmetic \\ optimisation \\ algorithm \\ \end{tabular} &
\begin{tabular}{c} overshoot, rise time, \\ settling time, phase \\ margin, bandwidth \\ \end{tabular} & Simulation & MATLAB \\ \hline
[9] & 2022 & PIDD2 & 6 & \begin{tabular}{c} PIDD2, FIDA, \\ FOPID, PIDD2 \\ \end{tabular} & \begin{tabular}{c} AVR system \\ \end{tabular} & \
\begin{tabular}{c} Improved Range \\ Kutta optimiser \\ \end{tabular} &
\begin{tabular}{c} rise time, settling \\ time, percent \\ overshoot \\ \end{tabular} & Simulation & – \\ \hline
[12] & 2022 & PIDD2 & 4 & PID, FOPID, RFID, \\ SFD & & \begin{tabular}{c} APDD, RFID, \\ algorithm \\ \end{tabular} & \begin{tabular}{c} AVR system \\ \end{tabular} & \
\begin{tabular}{c} Archimedes \\ optimization \\ \end{tabular} &
\begin{tabular}{c} settling time, rise \\ time, overshoot \\ voltage \\ \end{tabular} & Simulation & – \\ \hline
[18] & 2022 & PROND2N2 & 7 & \begin{tabular}{c} FOPID, PID, PIDA, \\ PIDD2 \\ \end{tabular} & \begin{tabular}{c} AVR system \\ \end{tabular} & \
\begin{tabular}{c} Coyote optimization \\ algorithm \\ \end{tabular} &
\begin{tabular}{c} transient response \\ and disturbance \\ rejection \\ \end{tabular} & Simulation & MATLAB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of recent developments and applications of PIDD2 controller in various fields.