**4. Conclusions**

The purpose of this paper was to improve the performance of the PEM fuel cell system via the application of a predictive module controller (MPC). The proposed controller scheme was designed based on a global minimum cost function for a two-step horizon in order to enhance the efficiency and the convergence tracking speed of the power delivered by the PEM fuel cell system.

A real-time implementation of the MPC method compared with a PI controller was realized to reveal the advantages of this proposed approach, where the robustness was tested via the application of large load variation through an advanced electronic variable resistance device.

Experimental results have clearly demonstrated the effectiveness of the proposed MPC method over the conventional PI controller. The latter showed an undershoot of 2.1 A, an overshoot of 3.65 A, and a response time of 6.8 and 7.25 s, respectively, for the first and second load variation. On the other hand, results of the proposed MPC showed an undershoot of 1.73 A, an overshoot of 3.15 A, and a response time of 1.3 and 0.51 s, respectively, for the same first and second load variation applied to the PI controller. Hence, the controlled stack current signal has achieved significant improvement in the convergence speed with an average value of 86.9% and a reduced overshoot around 15.65%. Therefore, high tracking accuracy with a fast and robust response as well as global stability of the closed-loop system are obtained via the application of the proposed MPC method.

Finally, the experimental results obtained in this work are quite encouraging, and they pave the way for further advanced research in the performance improvement of PEM fuel cell systems.

**Author Contributions:** Conceptualization, M.D.; methodology, M.D.; software, M.D.; validation, M.D. and O.B.; formal analysis, M.D. and A.C.; investigation, M.D., A.C. and C.N.; resources, O.B.; data curation, M.D.; writing—original draft preparation, M.D. and A.C.; writing—review and editing, M.D., A.C., O.B. and C.N.; visualization, M.D.; supervision, O.B.; project administration, O.B.; funding acquisition, O.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors wish to express their gratitude to the Basque Government, through the project EKOHEGAZ (ELKARTEK KK-2021/00092), to the Diputación Foral de Álava (DFA), through the project CONAVANTER, and to the UPV/EHU, through the project GIU20/063, for supporting this work.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The authors want to acknowledge the UPV/EHU for supporting this work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


