I have done some research on this item on how to drive a single phase induction motor or an 3 phase motor.
How I would like to do this is as follow.
For driving a 1 phase induction motor I want to build something like this that controll de sinus wave from.

The first problem is that I need to shift phases 90 degrees. I need to do this because of the condensator. This condensator cannot take High frequenties it will short out.
This is only to start the motor. What I like to do is to control the speed by frequentie not by changing the voltage. I'm not sure how to do this.
I have downloaded some files form that explain how to make a lookup table for sinus waves I have attached that file.
Maybe you can help me to figure this out.
Here are some pics of the motor that I want to control.







