## 3 Results
\begin{table}
\begin{tabular}{l l|c c c c c} \hline \hline \multirow{2}{*}{Transfer Function} & Poles & 2 & 3 & 3 & 4 & 4 \\  & Zeroes & 2 & 2 & 3 & 3 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & Number of & 5 & 6 & 7 & 8 & 9 \\  & Parameters & 3 & 3 & 4 & 4 & 5 \\ \cline{1-1}  & Number of & 2 & 3 & 3 & 4 & 4 \\ \cline{1-1}  & Zeroes & 2 & 3 & 3 & 4 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & Number of & 5 & 6 & 7 & 8 & 9 \\  & Parameters & 3 & 3 & 4 & 4 & 5 \\ \cline{1-1}  & Number of & 2 & 3 & 3 & 4 & 4 \\ \cline{1-1}  & Capacitors & 2 & 3 & 3 & 4 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & \% Fit & 90.15 & 90.15 & 97.09 & 99.65 & 99.65 \\  & Mean Squared Error & 5.275 & 5.275 & 0.04882 & 0.006531 & 0.006531 \\ \cline{1-1}  & Final Prediction & 5.407 & 5.435 & 0.05087 & 0.006793 & 0.00683 \\ \cline{1-1}  & Number of Samples & 201 & 201 & 201 & 201 & 201 \\ \cline{1-1}  & AIC & 1819 & 1821 & \(-\)48.12 & \(-\)865.7 & \(-\)863.7 \\ \cline{1-1}  & AICc & 1819 & 1821 & \(-\)47.78 & \(-\)865.4 & \(-\)863.3 \\ \hline \multirow{6}{*}{Controllability/} & Rank Observability & 2 & 3 & 3 & 1 & 1 \\ \cline{1-1}  & Unobservable States & 0 & 0 & 0 & 3 & 3 \\ \cline{1-1}  & Uncontrollability & 2 & 1 & 3 & 1 & 1 \\ \cline{1-1}  & States & 0 & 2 & 0 & 3 & 3 \\ \cline{1-1} \cline{2-6}  & max log (Hankel SV) & * & * & * & 15.47 & 7.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Summary of model estimation for Ranitidine. \begin{table}
\begin{tabular}{l l|c c c c c} \hline \hline \multirow{2}{*}{Transfer Function} & Poles & 2 & 3 & 3 & 4 & 4 \\  & Zeroes & 2 & 2 & 3 & 3 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & Number of & 5 & 6 & 7 & 8 & 9 \\  & Parameters & 3 & 3 & 4 & 4 & 5 \\ \cline{1-1}  & Number of & 2 & 3 & 3 & 4 & 4 \\ \cline{1-1}  & Zeroes & 2 & 3 & 3 & 4 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & Number of & 5 & 6 & 7 & 8 & 9 \\  & Parameters & 3 & 3 & 4 & 4 & 5 \\ \cline{1-1}  & Number of & 2 & 3 & 3 & 4 & 4 \\ \cline{1-1}  & Capacitors & 2 & 3 & 3 & 4 & 4 \\ \hline \multirow{6}{*}{Electrical Model} & \% Fit & 93.11 & 97.69 & 97.37 & 97.73 & 97.76 \\ \cline{1-1}  & Mean Squared Error & 10.69 & 1.199 & 1.551 & 1.16 & 1.123 \\ \cline{1-1}  & (MSE) & 10.96 & 1.235 & 1.606 & 1.207 & 1.175 \\ \cline{1-1}  & Number of Samples & 201 & 201 & 201 & 201 & 201 \\ \cline{1-1}  & Capacitors & 201 & 20 Figure 9: _Cont._  
For a model to be a minimal state-space representation, the controllability analysis must result in zero unobservable and zero uncontrollable states and the Hankel singular value must be finite. Although all the models provide a reasonable approximation, only one estimation per experiment qualifies as a feasible representation. For instance, using six parameters to model metamizole provides a 98% approximation over the entire measurement frequency range. However, using six parameters does not represent a minimal state-space realization, since the Controllability/Observability analysis reveals two uncontrollable states. In the case of the seven-parameter model for ambroxol, the Controllability/Observability analysis reveals zero uncontrollable and zero unobservable states; however, the Hankel singular value is not finite and therefore does not correspond to a minimal state-space representation. The values of the RC components for the four experiments are calculated in a similar manner for all four test samples as listed in Table 7. The best approximation is obtained for metamizole (94.93%) whereas the poorest approximation is obtained for ranitidine (90.15%). The 90.15% value is probably due to the error induced by a linear approximation to model the electrochemical cell, where only linear time-invariant components are used for modelling. In contrast, in Figure 9D, there appears to be a contribution of approximately \(-45^{\circ}\) at low frequencies for trimethoprim/sulfamethoxazole which may be explained by a Warburg element.