The direct single-phase matrix converter (SPMC) is a topology composed only of switches. This feature makes it extremely important to have complete control of the six bidirectional switches that make up it. This is why this article presents a comparison between two control techniques. A classic, composed of a pulse width modulator (PWM) that together with proportional-integral-derivative control module (PID) make up the closed loop linear controller. Then, a modern technique known as Finite State Predictive Control (FCS-MPC) is presented, which is based on the composite circuit model between the load and the converter. Finally, a discussion is generated regarding the simulation and experimental results obtained in the laboratory for both controllers.