## 5 Results
### Discussion and Potential Applications  
The proposed dual control strategy effectively addresses the non-minimum phase behavior in horizon-1 FCS-MPC for DC-DC boost converters by integrating a PI-based reference current offset tuner. In conventional PI-MPC methods, the PI controller is directly involved in generating the reference current and managing both dynamic and steady-state transitions, which often limits the fast response capabilities of the MPC due to the slower reaction time of the PI controller. In contrast, the proposed method decouples the roles of the PI controller and the FCS-MPC. The PI controller is only responsible for correcting small steady-state errors, while the FCS-MPC handles all fast dynamic responses, resulting in improved stability and faster voltage regulation without limiting the use of short-horizon FCS-MPC, even in applications with non-minimum phase issues. Moreover, the flexibility of the MPC control makes it applicable to a wide range of power electronic systems facing similar non-minimum phase challenges. Table 3 summarizes the key performance characteristics of the proposed dual control strategy (PI + FCS-MPC) compared with other control methods such as Long-Horizon FCS-MPC [26], Adaptive-Horizon FCS-MPC [12], and conventional PI-MPC [18; 19; 20]. The comparison includes factors such as response time, the need for sensors or observers, system complexity, and the sampling step. The Long-Horizon FCS-MPC [26] offers a fast response but comes with significantly higher complexity due to the longer prediction horizon. Its ability to handle non-minimum phase behavior depends on the converter dynamics and the number of horizons considered, but it does not require observers or any extra sensors for detecting the load. The Adaptive-Horizon FCS-MPC [12] also provides a fast response. However, it demands very high complexity for implementation without requiring additional sensors. The PI-MPC method shows a slower response due to the nature of the PI control in comparison with Long/Adaptive-Horizon FCS-MPC. This method introduces low algorithm complexity without the need for additional sensors or observers. The proposed dual control strategy (PI + FCS-MPC) achieves a fast response time, similar to both long/adaptive-Horizon FCS-MPC, due to the isolation of the proposed PI controller from the dynamic response of the converter. The steady-state error is similar to other methods thanks to the offset tuning method. It effectively handles non-minimum phase behavior with relatively low complexity and achieves high performance with the additional help of a sensor or observer for correcting the reference current. In FCS-MPC, reducing the sampling step has been shown to significantly improve controller performance. The proposed method's 5 \(\upmu\)s sampling rate offers precise and rapid control, especially when compared to the 10 \(\upmu\)s step used in the adaptive-horizon method by [PERSON] et al. [12] and the much longer 100 \(\upmu\)s step in the long-horizon approach by [PERSON] et al. [26]. While the proposed method can achieve sampling steps as low as 100 ns, such high-frequency sampling introduces the risk of damaging power electronic switches due to the limited maximum switching frequency. To prevent this, applying a switching frequency control method, such as the Period Control Approach (PCA), is essential [27; 28]. However, the focus of this paper is on the proposed control strategy rather than the impact \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Response Time** & **Sensor/Observer** & **Complexity** & **Sampling Step** \\ \hline Long-Horizon FCS-MPC [26] & Fast & No & High & 100 \(\upmu\)s \\ \hline Adaptive-Horizon FCS-MPC [12] & Fast & No & Very high & 10 \(\upmu\)s \\ \hline PI-MPC [18; 19; 20] & Slow & No & Low & 50, 12.5, 10 \(\upmu\)s \\ \hline Proposed Dual Control [PI + FCS] & Fast (2 ms) & Yes & Low & 1 and 5 \(\upmu\)s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of MPC-based control methods for boost converters.