# A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors
## 4 Experimental Validation
### Experimental Results  
We designed three distinct experiments to compare the performance of our proposed observer against other observer implementations. (1) Case 1:In this case, we focus on evaluating the robustness of our proposed observer (Equation (19)) against parameter uncertainties, comparing it to a standard open-loop observer (Equation (12)). To simulate a realistic scenario where component parameters may deviate from their nominal values, we introduced deviations of 10% and 20% in the capacitance value within the system parameters. For this experiment, we charge the system using a constant current (CC) source at 2 A, with all three switches deactivated. Our focus is on the first supercapacitor cell, initialized at a voltage of 0.1 V, corresponding to an initial SOC of approximately 3.67%. The proposed observer and open-loop observer are both initialized at 15% SOC. We switched the switch to start charging the supercapacitor at t = 8 s and stopped charging again at at t = 124 s.  
Figure 6 presents the experimental results. As evident from the plots, while the proposed observer exhibits an initial lag behind the true SOC, it rapidly converges and maintains its tracking error within 1% within approximately 5 s. In contrast, the open-loop observer struggles to achieve accurate tracking, as shown in Figure 6a, where a persistent error is observed with a 10% capacitance deviation. In Figure 6b, when the parameter deviation reaches 20%, the error worsens further. Table 2 contains SOC data at the end of charging. This highlights the superior robustness of our proposed observer in the presence of real-world parameter uncertainties. Figure 6: \(Cont.\)  
_(2) Case 2:_ In this experiment, we evaluated the observers' ability to adapt to changing operating conditions and accurately estimate the SOC during dynamic charging scenarios. As depicted in Figure 7b, to achieve this, we still used the first supercapacitor and switched the circuit again one minute after stopping the charging in case 1, at t = 184 s, and continued charging until t = 270 s. A capacitance deviation of 10% was maintained, while the initial voltage and observer states remained consistent with the previous experiment. \begin{table}
\begin{tabular}{l c c} \hline  & **10\% Capacitance Variations** & **20\% Capacitance Variations** \\ \hline
**True Value** & 33.02 & 33.07 \\ \hline
**Proposed Observer** & 33.02 & 33.11 \\ \hline
**Open-loop Observer** & 46.92 & 50.95 \\ \hline \end{tabular}
\end{table} 
Table 2: SOC (%) at the end of charging in case 1. Figure 6: Comparison between the proposed observer and the open-loop observer. (**a**) SOC estimation with 10% capacitance variations. (**b**) SOC estimation with 20% capacitance variations. (**c**) Changes in the switch. Figure 7: _Cont._  
The classical non-switching Luenberger observer, defined in Equation (23), was incorporated into this evaluation, alongside the open-loop and proposed closed-loop observers. \[\left\{ \begin{array}{l}\dot{\mathsf{SOC}}=A_{1}\mathsf{SOC}+B_{1}i+L_{1}(v- \vartheta)\\ \vartheta=C_{1}\mathsf{SOC}+D_{1}i\end{array} \right. \tag{23}\]  
As depicted in Figure 7a and Table 3, the proposed observer exhibited rapid convergence, achieving a tracking error of less than 1% by t = 7 s. This highlights its ability to quickly adapt to changing system dynamics. The open-loop observer, as expected, continued to exhibit significant tracking errors throughout the experiment. The classical observer, while demonstrating improved performance compared to the open-loop approach, exhibited slower convergence initially and a noticeable error spike after the resumption of charging. This suggests that the non-switching nature of the classical observer limits its ability to effectively handle dynamic changes in the system.