Not sure what you mean by adjustable on/off. Why not just program the output to be at the relay voltage when you want it on. For instance: If PID = 75 then AO = 12vdc else AO = 0vdc. This is assuming your analog outputs are 0 - 12 volts.
It's a Mickey Mouse way to cycle on a spray pump and tower dampers on what is intended to be a cooling tower bypass. The "control contractor" left it with just a common solid state relay doing the switching, and at certain combinations of load and ambient, the relay "stutters".