## 6 Conclusions  
This study presents a significant advancement in the control of DC-DC boost converters by effectively addressing the non-minimum phase behavior, a common challenge in such systems. The main contribution of this work is to examine the limitations of utilizing horizon-one FCS-MPC exhibiting non-minimum phase behavior and to propose a solution that addresses these issues without extending the prediction horizon. Unlike traditional PI-MPC approaches, where the PI controller manages both dynamic and steady-state transitions, the proposed method separates these roles. The FCS-MPC is solely responsible for a fast dynamic response, while the PI controller is only tasked with fine-tuning the reference  
Figure 18: FFT analysis of the output voltage and inductor current with sampling steps of 1 \(\upmu\)s and 5 \(\upmu\)s.  
current calculated by the IRC block, ensuring steady-state accuracy. This decoupling enables the system to handle dynamic load changes more efficiently and maintain high-speed operation, as the PI controller does not interfere with the fast responses of the FCS-MPC.  
Simulation results show that the system effectively mitigates the non-minimum phase issue, maintaining the desired output voltage with minimal deviation and quick recovery from load changes. The method's practical viability is demonstrated through comprehensive simulation and HIL experimental tests, showcasing its ability to handle real-world conditions effectively. In particular, the smaller sampling step (5 \(\upmu\)s) achieved in this study significantly contributes to the faster response of the system compared to other FCS-MPC methods. Notably, in the HIL tests, both the controller and the converter's discretized model are implemented inside the same FPGA. This integration eliminates clock mismatch issues and negates the need for additional blocks such as ADCs for interfacing between these components, thus simplifying the experimental setup.  
The steady-state error is comparable to long-horizon FCS-MPC and conventional PI-MPC methods, but smaller compared to short-horizon FCS-MPC thanks to the offset tuning mechanism employed. With a negligible undershoot and rapid settling time, the system is suitable for industrial applications requiring precise voltage regulation and adaptability to changing load conditions. Furthermore, the proposed dual control strategy can be extended to other power electronic systems facing non-minimum phase issues, broadening its applicability. Future work will focus on optimizing the control algorithm and exploring its application to more complex power electronic systems.  
Conceptualization, A.M. and E.Z.; methodology, A.M., A.V. and A.d.C.; software, A.M. and M.P.; validation, J.T.D., E.Z. and D.M.; formal analysis, A.M. and E.Z.; investigation, E.Z.; resources, A.d.C.; data curation, M.P.; writing--original draft preparation, A.M. and E.Z.; writing--review and editing, A.d.C. and A.V.; visualization, A.M. and E.Z.; supervision, A.d.C.; project administration, A.d.C.; funding acquisition, A.d.C. All authors have read and agreed to the published version of the manuscript.  
This research was partially funded by the project PID2022-137593 OB100, financed by the Spanish Ministry MCIN/AEI/10.13039/501100011033/FEDER, UE, and FSE+.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.