If the controlled device already has a 10v source, then possibly a digital pot or a mechanical pot setup might be possible. If the motor controller has accessible parts, you may be able to bypass its pot setup and use the arduino PWM to directly control the current control parts of the motor controller.
I think the OP wants to use the arduino to control the VFD . (Variable Frequency Drive) but I think it's a stretch to think he could hack it if he's asking the question he is asking. But you did inadvertly touch on a very viable solution. Almost all VFDs provide several means of control, one of which the OP mentioned being the analog 0-10V. But what the OP may not know , is that if he
looks at the manual for the VFD, there is a very strong possibility that it also provides a PWM input option, as that is found on almost all VFDs. I don't want to say that it is a standard, but I have seen it on all the VFDs I have worked on. (Baldor, Danfoss)
If he can find the manual or read the model number off the serial number plate we can pull the manual off the web and find out the input pin for the PWM.