Somethink like:
t=0; all valves off
t=1 ; valve 1 on
t= 2; valve 1 on
t=3; valve 1 on
t=4; valve 1 on
t-5; valve 1 on; valve 2 on
t=6 valve 1 off; valve 2 on
So, if the interval were seconds. Each valve would stay on for say 5 sec, and the next valve would turn on at the 5 second mark so at one point in time, you would have two valves on and then onto the next one?
Would those times be totally fixed. i.e. would
Time on and (sequential 2-valve dwell time) define the system?
e.g.
all valves off V(*) = 0
for v=1 to 199 (# of valves -1)
V(v) =1; on
wait ( 4 sec)
V(v+1) =1; on
wait (1 sec)
V(v) =0; off
Next v
I didn't deal with the repeat, nor the 200 valve being of while the 1st one being on which i would assume that you would want. Basically a ring counter.
That could make the programming simple.
Thinking out loud:
If only two valves can be on at one time, you might consider two matrixes. Say a 14 x 14 matrix which is 196 valves, one on at a time and another matrix for the other valve. I'm not sure it's possible though. It MIGHT be possible to turn on 196 valves, 2 at a time with 56 I/O points. I need to think about it.
But again, you may have to employ solid state switching because of the number of activations/year. I'm also not sure you can save $1500 either.
If your going to make bunches of these things, then it may be possible to do it in an entirely different way.
So, far the code seems minimal. The hardest part is getting the amount of digital outputs. If this thin is operating 24/7/365 then relays are out the door/window. If you need a user interface that adds complexity. If you can hard code the delays, that makes it easy. A test mode also adds complexity. e.g. Turn on valve 180 indefinately. Then possibly a double display for which valves are on.
Can the valves be purchased with a DC coil voltage such as 24 VDC?
For giggles, when you try to get intimate with a small micocontroller and want 200 ports, even that gets tough. This device,
https://www.gravitech.us/i2c16gpex.html would allow 128 I/O pins on a I2C bus. I2C is Inner IC communications and it's standard on many microcontrollers. Its my understanding that you could multiplex the bus, so you could conceivably increase the pin count.
Each relay, if we go one at a time, might need a triac for AC and an adequate heatsink or one or two big ones. It would need a snubber and drivers for each as well. Even 200 * $3.00/channel is $600 and I'm not saying a channel would cost $3. You may need a LED indicator as well.
What, exactly, is an aeroponics system?
Meanwhile, go get your feet wet.