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I got something working. I put a splitter in the HVAC so that the coils were separate from the humidifier. One side has a fan, cooling water coil, and heating water coil. The other side has a fan and a direct evaporative cooler. Then I used some energy management objects to turn on and off the availability schedule of the evaporative cooler based on the humidity of the computer room. I try to avoid EMS objects when I can, but in this case they are working pretty well. Having the availability of the evaporative cooler lag by a timestep probably won't cause a problem anyway.

Putting the humidifier before the cooling coil didn't work since the coil condensed most of the moisture out of the air.

Putting the humidifier after the cooling coil didn't work because the air coming into the evaporative cooler was 15C so the air couldn't hold much water. The air coming out of the evaporative cooler was almost 100% relative humidity, but once it got into the data center, the relative humidity couldn't get above 45% since the data center air was 28C.

I also tried using controlling objects from some energyplus example files, but those controlling either don't directly control the direct evaporative cooler objects of just didn't work that well.