# Identification, Control, and Characterization of Peristaltic Pumps in Hemodialysis Machines
## 3 Analysis of Results
### Validation  
Figure 10 shows nine random tests performed for in situ characterization and control. Each sub-image shows the applied setpoint at the bottom, with the corresponding mass and volume measurements displayed within the image. Both the volume and mass measurements are close to the target values. The images also include the results of the tests using the polynomial function, which demonstrated the best performance in experimental trials. Detailed measurements from these tests are presented in Table 3.  
Figure 9: Estimation of a linear function for the experimental characterization data in Table 2. **Caption:** Comparison of the linear estimation with experimental data, showing significant deviations at key points. This highlights the need for a non-linear model for better representation. Figure 10: Characterization and control test with volume and mass measurement. Caption: Results of nine random in situ characterization tests. Includes mass and volume measurements close to target values, validating the accuracy of the polynomial model in experimental applications. Note: Red dye was added only to visualize the synthetic blood. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Range**} & \multirow{2}{*}{\begin{tabular}{c} **g/min (Scale** \\ **Weight)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Setpoint** \\ **(mL/min)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Error (Set** \\ **Point vs. Scale** \\ **Weight)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **mL/min** \\ **(Graduated** \\ **Cylinder)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Error (Set Point** \\ **vs. Graduated** \\ **Cylinder)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Ratio (g/min)** \\ **(mL/min)** \\ \end{tabular} } \\ \hline \multirow{4}{*}{20–100} & 54.4 & 55 & 0.6 & 55 & 0 & 1.0110 & 1 \\  & 85.7 & 87 & 1.3 & 86 & 1 & 1.0090 & 0.9942 \\  & 93.6 & 95 & 1.4 & 94 & 1 & 1.0090 & 0.9947 \\  & 98.1 & 99 & 0.9 & 98 & 1 & 1.0090 & 1.0050 \\ \hline \multirow{4}{*}{100–200} & 108.5 & 109 & 0.5 & 110 & 1 & 1.0140 & 1.0090 \\  & 136.4 & 137 & 0.6 & 138 & 1 & 1.0120 & 1.0070 \\  & 185.5 & 185 & 0.5 & 185 & 0 & 1.0000 & 1.0030 \\  & 194.5 & 195 & 0.5 & 194 & 1 & 1.0120 & 1.0263 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Flow rate characterization in mL/min vs. RPM. Table 3 presents a detailed analysis of the accuracy and control of the measurement system over different flow ranges, from 20 to 100 mL/min to 700-730 mL/min. For each range, both the target values and the actual measurements obtained using a weight scale and graduated cylinder were recorded. This approach allows the system's accuracy to be evaluated by comparing the measurements to the target values. It is important to note that the values tested were randomly selected and not the same as those used for characterization to assess generalization. The analysis of the measurement errors shows that the deviations between the actual measurements and the target values are generally minor, indicating a high level of accuracy in the system's performance. In the case of the weight scale, the errors range between 0.06 and 8.8 g, showing that the mass measurements are very close to the setpoints. Similarly, the errors observed when comparing the setpoints with the graduated cylinder data range from 0 to 7 mL, reflecting remarkable consistency in the volumetric measurements. In addition, the calculated ratios between the mass per minute (g/min) and volume per minute (mL/min) measurements are close to 1 in most cases. This indicates that the conversions between mass and volume are consistent and accurate across the different flow ranges. The average ratios for g/min and mL/min are 1.0013 and 0.9999, respectively, indicating excellent system control. The deviation observed in the ratio complements of 0.1314% for g/min and 0.001% for mL/min further supports the idea that the system is robust and capable of maintaining consistent accuracy.