I see the need for four limit switches. Two on each side of the machine along the centerline of the grinder. Label them Left far, Left edge, Right edge, and Right far. Left and Right edge tells you the plate has cleared the grinder.

Left far PLUS Left edge tells you the plate is off the grinder to the left.

Right edge PLUS Right far tells you the plate is off the grinder to the right.

LF & LE & NOT (RE) = Start belt feed to the Right

RF & RE & NOT (LE) = Start belt feed to the Left

LE & RE = Plate in grinder, direction UNKNOWN

You also need manual belt drive controls to load the plate in the grinder, E-stops for operator safety. some sort of counter or limit switch when the plate is done. You will need to set the slew rate and time when reversing the belt direction. Also auto/manual selector, possibly a status light to tell you what mode it is in. How do you set the grinding height.

This sounds like a small PLC would help with the run logic.