## 6 Discussion  
This section summarises the results from previous sections.  
The application addressed by the FPR controller is framed considering a VC-VSC with an output LC coupling filter. The control scheme is then based on two nested control loops, assuming the inner loop is negligible for the stability analysis. The defined range of the fractal component is \(\alpha\in(0,2]\), considering only causal implementation forms of the controller.  
Firstly, using classical techniques such as the Nyquist criterion allows to face the stability challenge. The Nyquist trajectories analysis concludes that \(\alpha\) values above 1 hold system stability. On the contrary, decreasing \(\alpha\) under 1 must be cautiously performed to avoid instabilities. This permits us to deduce that the FPR controller on voltage-controlled application can be valid if \(\alpha\) is well selected.  
Secondly, considering a tuning procedure to obtain a specific gain margin allows to compare different controllers with the FPR controller for voltage applications. Under this assumption, the sensitivity analysis conclusion is that FPRs with \(\alpha\) values below 1 present a better phase delay tracking and disturbance rejection. This statement should be considered valid when the same phase margin at a specific frequency is used as a tuning criterion. On the contrary, \(\alpha\) values above 1 result in the opposite but present lower undesired amplification gains and accomplish better robustness and stability margins. Thirdly, compared to traditional control methods such as PR controllers, fractional tuning of certain parameters can enhance tracking accuracy, decrease phase delay, and improve disturbance rejection. However, fractional-order proportional (FPR) controllers add extra parameters due to their fractional-order elements, increasing the complexity of the tuning process. Optimally selecting these fractional parameters can be challenging, particularly when balancing performance with stability and robustness. In this direction, implementing the FPR on a processor will require analysis of the discretisation procedure to ensure a proper correspondence between the continuous and the discrete-time domain, paying special attention to the sampling time and discretisation strategy used.  
Finally, ideal PRHC controllers (no damping or phase margin compensation) could have better tracking capabilities for individual tones. However, it is at the cost of potentially worsening the interharmonic control, lessening the stability and robustness margins, and increasing computational burdens when a wide range of frequencies want to be controlled.  
The spider diagram depicted in Figure 19 helps to rapidly compare the proposed FPR with the PR or PRHC alternatives according to the relevant points studied: execution time, stability, disturbance rejection, controllability and complexity.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Controller Type** & **Execution Time (μs)** & **Program Memory (Bytes)** \\ \hline PR & 0.321 & 85 \\ PRHC (3 HC) & 0.788 & 141 \\ FPR (\(\alpha=0.75\)) & 0.802 & 116 \\ FPR (\(\alpha=1.5\)) & 0.913 & 134 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Controller type comparison. Execution time and program memory data.