Control 12V ZVS Induction heater

I am looking to control 12V ZVS Induction heater both the power output and the duration, ideally I would set a power level and run it for a specific length of time. This would able to be changed easily, maybe using a display with some buttons hooked to an Arduino?
At the moment I have it hooked to a momentary switch and a normal 12V power supply, it usually draws ~4.5A and I run it for 5-10secs to reach the temp I need.

Originally I thought to hook it up to a mosfet with a pwm control, but the little I understand would mean that you should not be switching voltage on and off if its a ZVS. I am guessing I could buy a bench powersupply and control it with that but I was looking to make a much smaller stand alone device.

At this point I am a little stuck as to what the best way to do it would be and am looking for some advice.

Google "MOSFET Arduino".

Very simple and should cover what you need to do.

ZVS schematic

RV mineirin

The instructions I have seen for a ZVS induction heater are that you have to have a sharp turn-on to start the oscillation. If you don't have a switch between the power supply and the ZVS it may power up with both transistors on and fry itself. A MOSFET might work as the ON/OFF switch but I don't think direct PWM will work.

My guess is that you will need some kind of adjustable buck converter.