**New "Full-Bridge Buck Inverter–DC Motor" System: Steady-State and Dynamic Analysis and Experimental Validation**

**Eduardo Hernández-Márquez 1, Carlos Alejandro Avila-Rea 2, José Rafael García-Sánchez 3, Ramón Silva-Ortigoza 2,\*, Magdalena Marciano-Melchor 2, Mariana Marcelino-Aranda 4, Alfredo Roldán-Caballero 2 and Celso Márquez-Sánchez 5**


 Estado de México 52005, Mexico; j.garcia@correo.ler.uam.mx


Received: 18 September 2019; Accepted: 20 October 2019; Published: 24 October 2019

**Abstract:** A mathematical model of a new "full-bridge Buck inverter–DC motor" system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

**Keywords:** motor drives; power converters; full-bridge Buck inverter; DC motor; mathematical model; differential flatness; time-varying duty cycle; circuit simulation; experimental validation
