Hi again,
Sorry, plus or minus 3ms is much higher than that. It puts the turn on/turn off time at 180*0.003/0.010=54 degrees, of which the sine is 0.81 which is 81 percent of peak, and that's assuming 50Hz (60Hz would be even worse). I think you did something wrong there in the calculation, although if you want to explain i'll certainly listen and compare your results to mine.
Controlled current is where you control the current rather than the voltage. Let me explain a bit more...
The relay coil is rated in voltage but really the physics of the coil has a current limit and only a voltage limit if that voltage is constant. The manufacturer assumes a constant voltage, so they rate it in voltage units rather than current. It's easy to get the current rating, just measure the current while it is operating at nominal voltage. I assume also that you uare using DC coil relays, not AC coil relays as i dont think the AC coil relays would work very well for this.
Ok back to the current rating...
Say you measure the current at 100ma. That would mean the max current should be kept to around 100ma or maybe a little higher for short periods if the relay does not have to turn on and off very frequently. Holding the current at 100ma means you can either apply 120vdc (or whatever the coil voltage is) and wait for the current to build up, OR, you can apply a current. Interestingly, the magnetic field is related to the current, not the voltage, and the armature pulls in due to the current causing the mag field, not the voltage. This means if we can get the current to build up much faster then we can get the relay to pull in faster. You still didnt say if you need to turn it on or off at the zero cross though, but i'll assume turn on for now. To get the current to build up very quickly, you would use a current generator rather than a voltage supply. Unfortunately the current generator has to be constructed and the voltage will be limited so we cant get 1us turn on for example, but we can improve it. With twice the voltage (as a limit that is) we might get 1/2 the response time, which could reduce 3ms to 1.5ms, which would be a pretty good improvement. It also depends partly on the inertia though.
So it all boils down to how far you are willing to go to get this to work. You'll need to make a power supply that can put out at least twice the voltage and you'll need to make it current and voltage limited. It could be as simple as making a voltage doubler with regulated output, but that's a bit of a task too, so i'll have to wait until you get back here and mention what you think you would be willing to build to get this to work.
So until then a couple questions too:
1. Are you turning on or turning off?
2. How many relays do you have to operate?