Various types of micro-vortex generators (mu VGs) are investigated for control of a supersonic turbulent boundary layer subject to an oblique shock impingement, which causes flow separation. The micro-vortex generators are embedded in the boundary layer to avoid excessive wave drag while still creating strong streamwise vortices to energise the boundary layer. Several different types of mu VGs were considered including micro-ramps and micro-vanes. These were investigated computationally in a supersonic boundary layer at Mach 3 using monotone integrated large eddy simulations (MILES). The results showed that vortices generated from mu VGs can partially eliminate shock induced flow separation and can continue to entrain high momentum flux for boundary-layer recovery downstream. The micro-ramps resulted in thinner downstream displacement thickness in comparison to the micro-vanes. However, the strength of the streamwise vorticity for the micro-ramps decayed faster due to dissipation especially after the shock interaction. In addition, the close spanwise distance between each vortex for the ramp geometry causes the vortex cores to move upwards from the wall due to induced upwash effects. Micro-vanes, on the other hand, yielded an increased spanwise spacing of the streamwise vortices at the point of formation. This resulted in streamwise vortices staying closer to the floor with less circulation decay, and the reduction in overall flow separation is attributed to these effects. Two hybrid concepts, named 'thick-vane' and 'split-ramp', were also studied where the former is a vane with side supports and the latter has a uniform spacing along the centreline of the baseline ramp. These geometries behaved similar to the micro-vanes in terms of the streamwise vorticity and the ability to reduce flow separation, but are more physically robust than the thin vanes.