Hello there!
We are looking for a solution which is commonly known as a variable-frequency-drive...
There are some hurdles to be overcome, but let's see first what this thing has to do...
The principle idea is in a first step to soft-start a 3-phace AC motor to it's regular RPM.
As a second step, the RPM shall be matched to the supply-frequency, so the motor can then be directly hooked to the power-source and the electronics be shut-off and bypassed by a relay.
The whole thing is to avoid that brute switch-over from star to triangle when starting the motor.
So all-in-all, it's just a soft-start for an electric motor.
There's no need to control the frequency in regular operation.
Motor is around 6kW...
What I was wondering, if anyone already did some brainwork or prototyping of any kind for such an application?
We're a team of aircraft-maintenance-engineer and a software-engineer and are aware of the problems, dangers and solutions.
Re-inventing the wheel sometimes is cool, but when it comes to high-power applications, we rather take the experiences from others into account...
Yes, I know, there are only a few companies that make VFD's, and those are expensive.
Some people say that thus, it's too complicated to make one on your own.
Let's just say this is an attempt in the sense of "Everybody said it's not possible. Then there was that guy who did not know that, and then did it."
So yes, I could buy one. I would have a bunch of functions I do not need, as well as an empty account...
But isn't arduino about doing things on your own?
Let's hear your take on the subject!

Cheers from switzerland,
Dany