I already have the VFD: Schneider Altivar 312 1.5kW 230V 1ph to 3ph - AC Inverter Drive Speed Controller - AC Inverter Drives (230V)

It seems that I can use LinuxCNC to control the VFD via an RS232 or RJ45. I'm not working on this part yet, but it's good to know that solutions are available.

LinuxCNC Documentation Wiki: VFD Modbus