# Identification, Control, and Characterization of Peristaltic Pumps in Hemodialysis Machines
## 4 Discussion  
The implementation of the P.I. controller in the peristaltic pump achieved meaningful improvements in flow precision and stability while reducing errors relative to the established setpoints. This study builds upon prior research by advancing the characterization, control, and validation of the system under conditions that closely emulate real-world hemodialysis treatments.  
Experimental results confirmed a non-linear relationship between RPM and volumetric flow rate (mL/min). The first contribution of this study is the robust characterization of the peristaltic pump, achieved by selecting a polynomial function through experimental fitting using the non-linear least squares method, which provided the most accurate representation of this relationship with an RMSE of 0.9193 mL/min. Such precision minimizes deviations from experimental data, critical for ensuring flow stability in medical applications. The P.I. controller reduced the effects of inherent fluctuations in the hose compression and release mechanism caused by the rollers, as evidenced by symmetric deviations of approximately \(\pm 2\) RPM in steady-state conditions. Additionally, the system maintained an RMSE of 1.687 RPM for speed control, demonstrating its ability to respond effectively to deviations and sustain a uniform flow.  
The second contribution of this study is its direct comparison with a commercial hemodialysis machine under identical experimental conditions. The developed system achieved an average flow error of 4.000 mL/min, substantially lower than the 8.9929 mL/min error of the commercial machine. This comparison was made possible using specialized hemodialysis equipment, including synthetic blood, dialysis circuits, and filters. Furthermore, the paired \(t\)-test applied to the error data confirmed that these differences are statistically significant, with a \(p\)-value of 0.021 at a 95% confidence level. This robust statistical validation not only underscores the superiority of the proposed system but also highlights its ability to maintain precision ratios close to the ideal value of 1 (0.9947 vs. 0.9723 for the commercial machine). These results, summarized in Table 6, establish a solid foundation for the system's clinical applicability.  
The use of synthetic blood, dialysis circuits, and filters specifically designed for hemodialysis ensured that the experimental setup closely resembled clinical scenarios.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **Commercial System** & **Our System** & **Interpretation** \\ \hline RMSE (mL/min) & 10.25 & 4.75 & Lower error in the developed system \\ \hline Mean Error (mL/min) & 10.25 & 4.75 &
\begin{tabular}{c} Slightly improved accuracy in the \\ developed system \\ \end{tabular} \\ \hline Standard Deviation (mL/min) & 7.15 & 2.60 & Greater stability in the developed system \\ \hline \(t\)-value & 2.96 & N/A & Confirms that errors are lower \\ \hline \(p\)-value & 0.021 & N/A & Statistically significant difference (\(p<0.05\)) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Statistical metrics and \(t\)-test results.  
This realistic testing allowed the study to capture non-linear behaviors, including flow variations caused by filter resistance and tubing viscoelastic properties. Redundant mass and volume measurement methodologies further enhanced the reliability and representativeness of the data.  
This study advances the control and characterization of peristaltic pumps for hemodialysis. By combining a well-tuned P.I. controller with detailed characterization, robust statistical validation, and realistic testing conditions, it demonstrates significant improvements in flow precision and reliability, contributing to safer and more effective hemodialysis treatments.