It sounds like you don't yet have a strong grasp on how that chiller works. Chiller control is not something that should be attempted by someone who doesn't understand chillers, unless you really do have money to replace it. If you don't understand it you will very quickly be replacing the compressors. If my assessment is accurate then I suggest that you engage the services of a local refrigeration expert who is well versed in chillers to help you create the control design parameters and to check your work - otherwise by the time you are done you may pay for a new chiller yet still have the old one.
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Knowing the age of the chiller helps in that it narrows down how the chiller capacity is controlled. At that age you have two kinds of capacity control 1)Hot gas bypass. 2)Cylinder unloading.
Does this chiller have semi-hermetic compressors or hermetic compressors? (if its a hermetic compressor then you can have hot gas bypass only for pressure control)
If it has semi-hermetic compressors, is there a solenoid valve mounted directly on the top of one compressor head? (If yes you probably have an unloader valve for capacity control. In this case you may or may not also have a hot gas bypass valve. Each kind of valve cuts cap
How many solenoid valves are in the refrigerant lines? A sketch or photo would help.
You said 2 x 4 stage chillers. Do you mean two completely separate chiller systems?
Or is this two chillers on a single pump tank? If so, do the two chillers operate as redundant chillers, or are both required for capacity?
Because chiller cooling capacity is constant, and because compressors cannot be time proportioned, setpoint deviation and staged timers is the best way to go. Where your possible capacity steps are 0, 25%, 50%, and 100% (75% is not an achievable capacity for a conventional compressor configuration - and it has yet to be determined if 25% is achievable for your configuration) and where compressors must stay on for a minimum amount of time, and once switched off, stay off for a minimum amount of time, PID control would just add headache over and above the simplicity of just using set point deviation and staging timers without improving the quality of control significantly.