## 5 Results
### Discussion and Potential Applications
of calculation resolution on switch performance. As demonstrated in Figure 17, reducing the sampling step from 5 \(\upmu\)s to 1 \(\upmu\)s leads to greater precision, effectively mitigating the low-frequency subharmonics observed in earlier tests with the sampling step of 5 \(\upmu\)s. The smaller sampling period allows for more frequent updates to control inputs, improving prediction accuracy and reducing oscillations in the control response. The correlation between the sampling step and harmonics spectrum is clearly illustrated in the spectra of the inductor current and output voltage in Figure 18. As shown in the subfigures, the amplitude of subharmonics is significantly larger when a sampling step of 5 \(\upmu\)s is used compared to 1 \(\upmu\)s. Increasing the _Ts_ results in additional low-frequency subharmonics that may negatively affect system stability and performance. The maximum achievable switching frequency (\(f_{sw,\text{max}}\)) is determined by the relationship given by (9); therefore, with _Ts_ set to 5 \(\upmu\)s, the \(f_{sw,\text{max}}\) is limited to 100 kHz. However, in this application, switching generally follows a pattern of one _on_-cycle followed by two _off_-cycles, a behavior attributed to the differing slopes of increasing and decreasing current, as described by (3). This results in a more commonly observed switching frequency of approximately 1/(3_Ts_). Consequently, with _Ts_ = 5 \(\upmu\)s, the main harmonic appears at 67 kHz (displayed as 68 kHz due to resolution limitations), while reducing _Ts_ to 1 \(\upmu\)s shifts this primary harmonic to around 333 kHz (observed as 342 kHz). This shift to higher frequencies with reduced _Ts_ allows for more effective filtering by the converter, enhancing performance by mitigating low-frequency subharmonics and stabilizing the system. \[f_{sw,\text{max}}=\frac{1}{2\cdot T_{s}} \tag{9}\]  
The integration of the MPC controller with a PI-based reference current offset tuner provides a versatile control mechanism that can be adapted to any non-minimum phase power converter. In such cases, the MPC controller may help simplify the regulator implementation, particularly when compared to linear controllers like PI or PID. This would be the case for boost-derived topologies, such as the buck-boost, four-switch buck-boost, Cuk, SEPIC, or ZETA converters, which are frequently used in low-power battery chargers (below 100 W). These converters, especially the Cuk topology, benefit from inherent current ripple reduction on one of their ports, making them ideal candidates for this control approach. Figure 17: Performance of the proposed FCS-MPC method with a 1 \(\upmu\)s sampling step, showing the response to a load change from R1 = 45 \(\Omega\) to R2 = 22.5 \(\Omega\), captured by the ILA. The extension to AC-DC single-phase active rectifiers would also offer potential advantages over traditional controllers, reducing the complexity of implementation. For example, flyback, flyboost [29], or boost AC-DC power factor correctors [30] could benefit from the MPC strategy. Additionally, some applications impose non-linear behaviors in the control stage, as seen in quadratic boost power converters [31], coupled inductor boost-derived topologies [32; 33], Maximum Power Tracking strategies for photovoltaic panels [34], multi-port boost converters [35], or partially saturated inductor boost converters [36; 37]. These non-linearities add complexity to the control stage beyond voltage or current regulation. In these cases, the proposed strategy could simplify implementation and reduce computational burdens compared to linear regulators.