I found an example circuit in this pdf file:
http://www.produktinfo.conrad.com/datenblaetter/175000-199999/191004-sp-01-en-CCD_Farbkamera_m_Zoom_hochaufloesend.pdf
What I figured out so far is this.
A signal from 0-4V drives the iris open against a spring.
An opamp circuit integrates the difference between lightlevel and setpoint and uses the output as the DRIVE signal.
This would drive the iris to keep the light level constant, but there is a catch.
The mechanical iris has static friction. When the driving force overcomes the friction, the iris would suddenly jump and overshoot the setpoint. It would continuously jump around the setpoint if not compensated.
The break coil provides an inductive feedback signal when the iris jumps, so the drive circuit can break/dampen the output to avoid overshoot.
The feedback circuit does not allow you to simply put the iris in some fixed position. This is why some manufacturers now use a servo type iris on their cameras.
But there may be another approach. I have not tried it, but I think it may work.
Suppose you connect the DRIVE directly to the 5V PWM output of a microcontroller. By carefully choosing the PWM frequency, you can make the iris blades vibrate, removing the static friction while you vary the position by changing the duty cycle.
To reduce wear and audible sound, you could switch to a much higher frequency with the same duty cycle once the iris is in position.
If anyone tried this, please let us know if it works!