# Identification, Control, and Characterization of Peristaltic Pumps in Hemodialysis Machines
## 3 Analysis of Results
### Validation
When examining the error ranges across different flow rates, it is evident that the system maintains high precision even at the lowest and highest flow ranges. This suggests that the measurement system is highly reliable across its full operational spectrum, a crucial attribute for applications requiring both low and high flow rates. Additionally, the low average errors and tight ratios further support the system's suitability for environments where precision and repeatability are critical, such as in hemodialysis treatments. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Range**} & \multirow{2}{*}{**g/min (Scale**} & \multirow{2}{*}{**Setpoint**} & \multicolumn{2}{c}{**Error (Set**} & \multicolumn{2}{c}{**mL/min**} & \multicolumn{2}{c}{**Error (Set Point**} & \multirow{2}{*}{**Ratio**} \\  & & **Weight** & **(mL/min)** & **Point vs. Scale** & **(Graduated** & & **vs. Graduated** & & **(mL/min)** \\  & & & & **Weight** & **Cylinder** & **Cylinder** & **Cylinder** & **(mL/min)** \\ \hline \multirow{4}{*}{200–300} & 218.1 & 217 & 1.1 & 218 & 1 & 1.0000 & 1.0050 \\  & 263.5 & 263 & 0.5 & 262 & 1 & 1.0000 & 1.0020 \\  & 290.1 & 289 & 1.1 & 290 & 1 & 1.0000 & 1.0030 \\  
In summary, the analysis in Table 3 shows that the measurement system is highly reliable, with minimal errors and ratios close to ideal values. This confirms that both mass and volume measurements are close to the target values, providing confidence in the accuracy and repeatability of the system used, which is essential for ensuring consistent and safe performance in sensitive applications. To validate the polynomial function's superior accuracy in describing the peristaltic pump's behavior, Table 4 compares volumetric flow results from 32 tests conducted at the same setpoints as in Table 3. This comparison includes the potential, linear, and polynomial estimations shown in Figure 11, highlighting the differences in accuracy between the models and identifying the one that best aligns with the target values. A comparative analysis of the flow estimation methods in Table 4 reveals that polynomial estimation provides superior precision and consistency across all flow ranges, as highlighted in bold within the table. This method maintains a consistently low error level, often below 1 mL/min and, in many cases, as low as 0 mL/min, indicating that it effectively captures the non-linear relationship between speed and flow (mL/min). While potential estimation reduces errors more effectively than the linear method, it shows more variability, with errors ranging from 0 to 26 mL/min depending on the setpoint. This suggests that potential estimation lacks the precision of the polynomial approach. In contrast, linear estimation shows the highest error values, reaching up to 37 mL/min, reflecting its limitations in accurately modeling the non-linearities in the speed-flow relationship. The relationship between actual and estimated values clearly supports the accuracy of the polynomial method. Across most setpoints, particularly within the 20-100 mL/min and 100-200 mL/min ranges, polynomial estimation ratios remain close to 1, indicating high consistency in predicting actual values. While potential estimation ratios are closer to 1 than those from linear estimation, they exhibit larger deviations at higher flow rates, fluctuating between 1.0067 and 1.0369, indicating moderate accuracy. In contrast, linear estimation ratios are significantly higher, such as 1.5865 and 1.2102 in lower ranges (20-100 mL/min).