Need some direction before jumping into LinuxCNC.

I have an older (1996) CNC fabric cutter (Carlson Design - Simplicity · Precision · Performance) that I'm wanting to upgrade with new motors, controls and software (linuc cnc or similar). I can figure the standard XY side of the motors and controls however the machine uses an air solenoid to move the cutting head up and down (speed controlled by needle valves and dwell settings) as well as a pen. The "Z" motor actually steers the cutter in the direction it needs to roll the blade. For the cutter, think of a pizza wheel cutter. It uses a 28mm round razor blade that has to track in the direction it's headed and then lift up, turn and drop back down for corners or angles that exceed its steering limit.

Looking for info pointing me in the right direction for where to start searching this type of controls. Right now I don't even know where to start searching.

Thanks for the help!