## 6 Results
### Comparison of the Results  
After completing the research on both applied integration methods, the analogue and digital methods, aimed at comparing the estimated associated flux waveforms with the reference waveforms generated by simulation, an attempt was made to perform a comparative analysis of the results for both integration methods. Comparing the results of both methods, the accuracy (convergence) of the results, the speed of convergence and the stability of the solution were analysed. Comparing both methods with each other, as well as with the reference waveform, it was found that both methods do not allow for correct estimation of the constant component of the flux waveform. This is an expected consequence of using a differentiator and an additional resistor in the feedback loop of the differentiator of the analogue system. Similarly, for the digital method, this is a consequence of using mean value filters that eliminate the constant component, both at the input and output of the algorithm. Both methods allow for the estimation of the periodic component of the flux waveform but with different amplitude and angular accuracy. In the case of the analogue method, as the frequency of the input voltage signal decreases, the angular shift of the signal relative to the expected delay by 90\({}^{\circ}\) also decreases. Therefore, the accuracy of the integration operation decreases. Below the frequency of 10.26 Hz, the integration process stops completely, and the response of the analogue system is similar to the differentiation operation (the output signal leads the input signal in phase). This characteristic explains the change in the dynamics of the estimated slowly changing component in the flux course (Figure 20). The integrating term used in the digital method allows for the correct estimation of the periodic component for low frequencies, but the added average value filters, with the measurement window width set to 25 Hz, cause the estimated flux signals with a frequency lower than 25 Hz to be strongly distorted (Figure 25). This results from the oscillating responses of the average value filters at signal frequencies lower than the filter cut-off frequency (too narrow a measurement window of the filters). These oscillations, although with a much smaller amplitude, will also appear when the input signal frequency is not an integer multiple of the 25 Hz frequency. This feature is a source of estimation errors for the digital method.  
The digital method was characterised by a faster, although nonlinear, elimination of the constant component (convergence to the steady state). The analogue method allows for a shorter elimination time of the constant component but at the cost of the angular accuracy of the integration operation.  
Figure 25: Comparison of the reference flux curve (grey, dashed) and the curve estimated with the proposed numerical integration algorithm with offset elimination (red) for the capacitance \(C_{0}=9\) nF.  
Due to better integration properties for low frequencies, the applied analogue method allowed for a more accurate representation of the periodic components of the flux waveform. The digital method, although less accurate, turned out to be faster. The use of average value filters with a wider measurement window (e.g., for a frequency of 12.5 Hz) would improve the accuracy of the estimation but at the cost of extending its time.