Ah, it looks like the RH is a simpler turret, as it only rotates one direction without the complicated and time critical locking/direction reversal of the TOE turrets.
I've got a TOE (or at least all the parts of one after a slight mishap), and I ended up controlling it via a PLC, using my rotary phase converter to power everything.

The issue is although it's quite a small motor, it's pushed hard due to the inertia of the turret. As I said, you'll probably need to add a braking resistor to brake the motor fast enough before reversing it, and possibly increase the current limiting above the rating for the motor to get fast enough acceleration (make sure the thermal switch is wired in to kill things if the motor does overheat) but given the slacker time requirements of the RH, a VFD should handle it quite comfortably.

I'm guessing this is on Denford lathe?
If it is, Denford did use VFDs on some lathes to control the turret, so it could be worth asking over on the Denford forums to see if anybody knows what size of VFD they used, and how it was configured in terms of acceleration/deceleration.