## 3 Control Techniques
### CVOA Based PID Controller
While the good performance indicates the recovered population from corona antivirus. \[J_{t}=\frac{(j_{1}+j_{2}+j_{3}+j_{4})}{4} \tag{11}\]  
\[J_{1}=\frac{|t_{r}-t_{rd}|}{t_{rd}} \tag{12}\]  
\[J_{2}=\frac{|t_{s}-t_{sd}|}{t_{sd}} \tag{13}\]  
\[J_{3}=\frac{|t_{ess}-t_{essd}|}{t_{essd}} \tag{14}\]  
\[J_{4}=\frac{|OS-OS_{d}|}{OS_{d}} \tag{15}\]  
where (\(t_{rd}\)) is the desired rise time and (\(t_{r}\)) is the measured rise time, (\(OS_{d}\)) is the desired maximum overshoot and (\(OS\)) is the actual overshoot, (\(t_{sd}\)) is the desired settling time and (\(t_{s}\)) is the determining settling time, and (\(e_{ssd}\)) is the desired steady-state error and (\(ess\)) is the estimated steady-state error. It can be noted that objective function attempts to satisfy the designer using four sub-objective functions. The first sub-objective function focuses on improving the rise time of the overall drive systems. The second sub-objective function attempts to reduce the settling time. The third sub-objective function measures the steady-state error. The fourth sub-objective function investigates the required overshoot. The value of each sub-objective function ranges from zero to one. So, the overall objective function considers the average of the sum of four sub-objective functions. Figure 4 shows the CVOA offline tuning system with the BLDC motor drive system. Figure 4: The CVOA tuning system with BLDC motor drive system. The first step investigates the Probability of travel If \(P_{t}=0\) then the type of spreading is \(S_{R}=(0\) to \(0.5)\). In case of \(P_{t}=1\) then the type of spreading \(S_{RR}=(0.5\) to \(1)\). In the second step, the zero infected patient If \(P_{t}=0\) will become as follows:  
\[X_{FO}=L_{X}+(U_{X}-L_{X})S_{R} \tag{16}\]  
If zero infected patient If \(P_{t}=1\). \[X_{FO}=L_{X}+(U_{X}-L_{X})S_{RR} \tag{17}\]  
The third step investigates if \(J_{t}>P_{DIE}\) then this patient is dead and generates a newly infected patient. In the case of \(J_{t}<P_{DIE}\) then the newly infected patient will be as follows:  
\[X_{new}=X_{old}\pm X_{old}\left[ \begin{array}{c}J_{1}.D_{R}\\ \frac{1}{2}(J_{2}+J_{3}).DR\\ J_{4}.D_{R}\end{array} \right] \tag{18}\]  
The optimization will be stopped if \((X_{new}=X_{old})\) where the newly infected populations cannot infect new individuals. If the number of iteration ended before this previous condition. the CVOA cannot give the optimal solution. Therefore, to obtain the optimal parameters of PID controller must be \((X_{new}=X_{old})\) to guarantee the global solution. Table 2 demonstrates the used CVOA parameters through offline optimization. The objective function has been minimized subjected to:  
\[ \begin{array}{c}K_{pmin}\leq Kp\leq K_{pmax}\\ K_{\text{imin}}\leq K_{i}\leq K_{\text{imax}}\\ K_{dmin}\leq K_{d}\leq K_{\text{dmax}}\end{array}  \tag{19}\]  
The upper and lower limits of PID controller parameters as the following. \[L_{X}=[K_{pmin}\ K_{\text{imin}}\ K_{dmin}] \tag{20}\]  
\[U_{X}=[K_{pmax}\ K_{\text{imax}}\ K_{dmax}] \tag{21}\]  
Best Fitness values are plotted against generations or number of iterations to get the convergence characteristic shown in Figure 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **CVOA Parameter** & **Symbol** & **Value** \\ \hline
1 & Probability of Death & \(P_{DIE}\) & random value from 0 to 1 \\
2 & Death Rate & \(D_{R}\) & random value from 0 to 1 \\
3 & Spreading Rate & \(S_{R}\) & random value from 0 to 0.5 \\
4 & Super Spreading Rate & \(S_{RR}\) & random value from 0.5 to 1 \\
5 & Probability of travel & \(P_{t}\) & random binary value 0 or 1 \\
6 & Lower boundary & \(L_{X}\) & \([0.1,0.1,0.1]\) \\
7 & Upper boundary & \(U_{X}\) & \([100,100,10]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The CVOA parameters. The sequence flow chart of optimization as shown in Figure 6.