Abstract: This study is made upon the modeling of a Permanent-Magnet Synchronous Motor PMSM with torque conditions and variable speed in a matrix and simplified way using mathematical transformation techniques applied to electric machines such as Park transformation. Furthermore, it analyses the model’s behavior by making a simulation with the Matlab’s simulink tool, it also designs a Pulse-Width Modulation PWM controller which supplies the D-Q Model of the three-phase electric machine under normal conditions. Later on, different PID control models will be implemented under different reference values in order to bring it’s behavior to reality. The main outcome is the identification of the best control method by comparing the stabilization time of the obtained signals. Finally, as a conclusion, it reviews the importance of the mathematical modeling for designing control techniques for PMSM.