[...] this circuit will be able to dimm R,S,and T all at once,
with just one potentiometer?
Yes, either with "just a potentiometer" (plus resistors or trimmers) or by the attached circuit.
The max. and min. voltages can be set or VR1 and VR2 respectively...
Use either a plastic trimmer tool/"screwdriver", or, if you plan to change them regularly, a potentiometer with isolate shaft(!)
If you only plan to set it once, a resistor can be calculated to replce it.
As is, both levels can be adjusted around 32% (min. 0V..3.8V and max. 8.2V to 12V).
C1 and C2 helps against noisy potentiometers and short slips of the wiper contact - values can vary quite a bit without changing the behaviour radically (anything from say 47pF to eg. 4.7nF should do (although it will change the responce times, you probbly won't notice in use.
Next comes the buffers/voltage followers, which doesn't load the trimmers, but keep a low output impedance for driving POT1.
POT1 is the fader proper and it's driven by the min/max voltages you set.
R3protects the buffers, in case you had eg. the POT1 all the way up and the maximum level set to the full 12V when using the Kill switch.
R4/C3 holds the time constant for a slow(-ish) fade in. By using this, your (probably very expensive) lamps will have a longer life - the worst case scenario for a glow lamp is to be turned on at a dimmer setting of 50% with no slow start - like if somebody forced you to do hard excersize the momet you wok up.
With the Soft Start switched in (by shorting X1-1 to X1-2), it will start from 0%light and reach the set level in a few hundred ms (with the values shown - more like if you get a nice breakfast in bed to wake you up.
Finally, a Kill Switch can be used on terminals X2-1 and X2-2. When they're shorted together, the light will turn off immediately and stay off as long as they're shorted.
Mind you, the circuit is still live, it's only the light you kill. I'm not sure if this would be needed or even useful in your application, but the terminals can be left out if not needed.
This is a bit more involved than the simple solution, but I think the streamlined setting warrants the op-amp.
To set minimum light (for all 3 phases):
Turn POT1 all the way down
Adjust VR2 to the level you need
Done
To set maximum light:
Turn POT1 all the way up
Adjust VR1 to the level you need
Done
The potentiometer- and trimmer values was chosen arbitrarily and it could be adapted to almost any other value (although a too low value will be a bad idea, due to the transformerless power supply, as there's not that much current to go around.
If you have to buy new components, it won't matter, but if you either have some existing potentiometers in a box or have some very nice ones in your collection (we all have "our precious ones

), tell me the values, and I can work it/them in.
I'll make the other changes I mentioneed (in a day or two, it's too late now) and when done, I'll recommend building it with just one power module first, as it will be simpler to comprehend - and the power modules can be made be 100% interchangeable, which means that a single spare module could be made for a swift repair (which won't be needed if you have it, to paraphrase on Murphys Law).
Check out the attached circuit and just ask if there's something you don't quite get.
Just reread your original post...
the 3 channels must be controled with just one potentiometer on control panel
Done

It needs to have a timer (with ci 555 would be nice) with a potentiometer on control panel too.a 0 to 15 seconds timer its fine.
Oops, didn't notice before - hav to add that.
Luckily, there's a vacant comparator that'll make a good timer, so no need to add more chips
We gotta have a serious talk about timing though...

a 0 second timer is no timer at all.
The timer will ,in effect, appear to work with a step size of 10ms (on 50Hz mains), due to the nature of the control method.
If you use a log(arithmic) taper potentiometer for the timer, it may be easier to set, as the distance between 1 and 2 seconds will be about the same as the distance between 5 and 10 seconds.
If precise adjustment is needed, it's easy to add an extra potentiometer to have coarse and fine adjustment. However, don't expect super precision from an analog timer of this simplicity.
A start input (and test button) from a magnetic sensor to activate the cycle.Its going to do hundreds of cycles per day.
I am assuming that the test button should replicate the magnetic sensor for a test run?
Do you have some info on this sensor?
Reed switch, hall effect (and if so, switch or linear) or what?
And what's the detection distance - or do you have some sort of switch/sensor in place already?
I'll implement the functions I overlooked and make the ramp generators adjustable in the next day or so - Until then...
Edit: Being too tired to check everything several times, so characters may be missing or double - my wireless keyboard is a joke with poor keys and apparently a will of its own.