**5. Conclusions**

With the aim of validating, through circuit simulations and experimental results, the proposed mathematical model of the new "full-bridge Buck inverter–DC motor" system, the flatness property has been exploited. Likewise, the steady-state, stability, and controllability properties associated with the dynamic behavior of such a system have been developed.

In the development of the mathematical model of the new "full-bridge Buck inverter–DC motor" system, all components were considered as ideal. This was done with the intention of obtaining a non-complex mathematical model that would still enjoy relatively good accuracy. On the other hand, by applying the flatness concept to the proposed mathematical model, it was found that the flat output of the system is given by *ω*. Therefore, the vector state and the input signal were differentially parameterized, in terms of the flat output and its successive derivatives with respect to time. Thus, with the help of such a parametrization, the validation of the deduced mathematical model was

carried out through circuit simulation and a built prototype of the system. The circuit simulation results (presented in Figures 5–8) and the experimental results (depicted in Figures 11–14) validates the proposed mathematical model despite the small tracking error between system variables and reference variables. It is worth mentioning that such an error could be minimized if the electronic and electric elements were considered nonideal, meaning that energy losses and parasitic resistances should be considered into the mathematical model. However, the advantages of using the model presented in this paper is its simplicity and its accuracy.

Future research will be devoted to the design of feedback tracking controls and their experimental implementation on the prototype of the system that has been built.

**Author Contributions:** Conceptualization, E.H.-M. and R.S.-O.; Data curation, C.A.A.-R., J.R.G.-S., M.M.-M., A.R.-C., and C.M.-S.; Funding acquisition, E.H.-M., R.S.-O., and M.M.-A.; Investigation, E.H.-M., C.A.A.-R., J.R.G.-S., R.S.-O., A.R.-C., and C.M.-S.; Project administration, M.M.-A.; Resources, E.H.-M., R.S.-O., and M.M.-M.; Software, C.A.A.-R., J.R.G.-S., A.R.-C., and C.M.-S.; Supervision, E.H.-M. and R.S.-O.; Validation, C.A.A.-R., J.R.G.-S., M.M.-M., A.R.-C., and C.M.-S.; Visualization, C.A.A.-R., J.R.G.-S., M.M.-M., M.M.-A., A.R.-C., and C.M.-S.; Writing—original draft, E.H.-M., C.A.A.-R., J.R.G.-S., R.S.-O., A.R.-C., and C.M.-S.; Writing—review & editing, E.H.-M., C.A.A.-R., J.R.G.-S., R.S.-O., M.M.-M., M.M.-A., A.R.-C., and C.M.-S.

**Funding:** This research was funded by the Comisión de Operación y Fomento de Actividades Académicas (COFAA) and the Secretaría de Investigación y Posgrado (SIP), both from the Instituto Politécnico Nacional, México.

**Acknowledgments:** This work has been supported by the Secretaría de Investigación y Posgrado del Instituto Politécnico Nacional (SIP-IPN), México. J. R. García-Sánchez and C. Márquez-Sánchez acknowledge the financial support received from the SNI-México. R. Silva-Ortigoza, M. Marciano-Melchor, and M. Marcelino-Aranda acknowledge the financial support received from the IPN programs EDI and COFAA and from the SNI-México. Finally, the work of A. Roldán-Caballero has been supported by the CONACYT-México and BEIFI scholarships.

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