# Identification, Control, and Characterization of Peristaltic Pumps in Hemodialysis Machines
## 3 Analysis of Results
### Validation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Range**} & **Sepular** & **Linear** & **Ponential** & **P Polynomial** & **Emax** & **Linear (Ponential)** & **Error Polynomial** & **Ratio (Linear)** & **Ratio (Ponential)** & **Ratio (Ponential)** & **Ratio (Ponential)** \\  & **(mL/min)** & **Flow Rate** & **Flow Rate** & **Flow Rate** & **Estimation** & **Estimation** & **Estimation** & **Estimation** & **Estimation** & **Estimation** & **Estimation** \\ \hline \multirow{3}{*}{20-100} & 80 & 35 & 46 & 85 & 20 & 9 & 0 & 1.586 & 1.176 & 1.0000 \\  & 87 & 74 & 79 & 86 & 13 & 8 & 1 & 1.167 & 1.1013 & 0.9847 \\  & 65 & 78 & 84 & 94 & 17 & 10 & 1 & 1.1202 & 1.1203 & 1.0000 \\  & 99 & 90 & 90 & 90 & 9 & 9 & 1 & 1.1000 & 1.1000 & 1.0002 \\ \hline \multirow{3}{*}{100-200} & 109 & 100 & 100 & 110 & 9 & 9 & 1 & 1.0000 & 1.0000 & 1.0283 \\  & 185 & 185 & 185 & 125 & 188 & 2 & 10 & 9.9452 & 1.1871 & 1.0054 \\  & 195 & 196 & 185 & 194 & 1 & 10 & 1 & 9.9989 & 1.0841 & 1.0838 \\ \hline \multirow{3}{*}{200-300} & 217 & 217 & 217 & 205 & 218 & 0 & 12 & 1 & 1.0000 & 1.0855 & 1.0873 \\  & 203 & 260 & 265 & 262 & 3 & 18 & 1 & 1.0155 & 1.0755 & 1.0934 \\  & 277 & 277 & 265 & 290 & 0 & 12 & 1 & 1.0000 & 1.0453 & 1.0209 \\  & 299 & 237 & 275 & 277 & 2 & 14 & 0 & 1.0012 & 1.0007 & 1.0775 \\ \hline \multirow{3}{*}{300-400} & 304 & 305 & 299 & 301 & 6 & 2 & 0 & 1.0003 & 1.0007 & 1.0853 \\  & 305 & 305 & 259 & 304 & 0 & 2 & 1 & 1.0000 & 0.0857 & 1.0856 \\  & 307 & 307 & 309 & 308 & 0 & 2 & 1 & 1.0000 & 0.9994 & 1.0857 \\  & 309 & 309 & 309 & 309 & 0 & 0 & 1 & 1.0000 & 1.0000 & 1.0850 \\  & 309 & 309 & 309 & 309 & 0 & 0 & 1 & 1.0000 & 1.0000 & 1.0850 \\ \hline \multirow{3}{*}{400-500} & 411 & 413 & 489 & 411 & 2 & 2 & 0 & 9.992 & 1.0000 & 1.0213 \\  & 441 & 440 & 445 & 441 & 1 & 4 & 0 & 1.0233 & 0.0991 & 1.0213 \\  & 443 & 461 & 462 & 463 & 2 & 1 & 0 & 1.0433 & 1.0232 & 1.0009 \\  & 477 & 479 & 478 & 480 & 2 & 1 & 3 & 0.9988 & 0.9970 & 1.0486 \\ \hline \multirow{3}{*}{500-600} & 500 & 500 & 489 & 502 & 3 & 4 & 1 & 1.0000 & 1.0000 & 1.0006 \\  & 527 & 535 & 520 & 522 & 2 & 7 & 1 & 1.0018 & 1.0153 & 1.0153 \\  & 565 & 539 & 539 & 567 & 6 & 6 & 2 & 1.0107 & 1.0107 & 1.0153 \\  & 561 & 568 & 579 & 591 & 23 & 12 & 0 & 1.0455 & 1.0203 \\ \hline \multirow{3}{*}{600-700} & 643 & 590 & 605 & 615 & 25 & 10 & 0 & 1.0424 & 1.0165 & 1.0082 \\  & 644 & 613 & 623 & 641 & 25 & 18 & 0 & 1.0457 & 1.0259 & 1.0079 \\  & 679 & 643 & 609 & 678 & 36 & 10 & 1 & 1.0560 & 1.0419 & 1.0074 \\  & 665 & 658 & 671 & 691 & 37 & 24 & 4 & 1.0562 & 1.0158 & 1.0153 \\ \hline \multirow{3}{*}{200-720} & 713 & 679 & 649 & 710 & 34 & 24 & 3 & 1.0011 & 1.0480 & 1.0153 \\  & 731 & 695 & 705 & 729 & 36 & 26 & 2 & 1.0518 & 1.0209 & 1.0097 \\ \hline \multirow{3}{*}{Average} & & & & & 10.7000 & 9.6666 & **1.3831** & 1.0566 & 1.0411 & **0.9999** \\ \cline{1-1}  & & & & & & & & 5.1829\% & 4.1170\% & **0.8807\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Flow rate comparison between linear and non-linear estimation. Although these ratios stabilize closer to 1 at higher ranges, this variability suggests that linear estimation may not be ideal for accurately modeling this dataset. The efficacy of each estimation technique is contingent upon the flow range in question. In the low flow range (20-100 mL/min), polynomial estimation demonstrates near-perfect accuracy, exhibiting consistently lower errors than both linear and potential methods. As flow rates exceed 500 mL/min, all three estimation techniques demonstrate enhanced ratio consistency. Nevertheless, polynomial estimation remains the most accurate, followed by potential estimation, while linear estimation is the least accurate, particularly at the highest flow rates (600-730 mL/min). In this upper range, polynomial estimation exhibits the lowest error rates, demonstrating robust performance across the entire data series. While the RMSE values for all estimation methods illustrated in Figure 11 are relatively low, even minor discrepancies can have a considerable impact on experimental outcomes.