The main objective of this work revolves around the design of second order sliding mode controllers (SOSMC) based on the super twisting algorithm (STA) for asynchronous permanent magnet motor (PMSM) fed by a direct matrix converter (DMC), in order to improve the effectiveness of the considered drive system. The SOSMC was selected to minimize the chattering phenomenon caused by the conventional sliding mode controller (SMC), as well to decrease the level of total harmonic distortion (THD) produced by the drive system. In addition, the literature has taken a great interest in the STA due to its robustness to modeling errors and to external disturbances. Furthermore, due to its low conduction losses, the space vector approach was designated as a switching law to control the DMC. In addition, the topology and design method of the damped passive filter, which allows improvement of the waveform and attenuation of the harmonics of the input current, have been detailed. Finally, to discover the strengths and weaknesses of the proposed control approach based on SOSMC, a comparative study between the latter and that using the conventional SMC was executed. The results obtained confirm the effectiveness of SOSMC over the conventional SMC under different operating conditions.