I guess we are no longer interested in a simple approach?
Personally, my preference is for the engineer to perform the calculation based on the mechanical system. Afterall, the control system is really trying to "control" the mechanical process - whatever it may be (flow, pressure, cell growth, pH, temp, etc.).
However, I've found very few engineers, even ME's, who can appropriately complete the calculation for the method employed by the controller that they are using. Additionally, few even remember how to complete the series transformation in order to determine the actual mechancial system's response based on the nature of the system (e.g. viscosity, pipe size,
So, for our friend who is trying to just get a good start on tuning a loop, using the AB/Rockwell system (which approaches the Z-N method; but, doesn't follow when it comes to derivative or damnpening especially), I maintain - start with P, and as nessasary, employ some I. My suggestion with regards to D still holds as well. MOST loops that I've re-tuned have been critically dampened with D, apparently as a solution to a poorly tuned loop. Is it a crutch? Only when mis-applied. Is it nessasary sometimes? Absolutely!!!
When everyone is ready to "hang" it over the edge and compare size, I suggest we move over to flight controls. Forget PLC, DCS, loop controllers, and let's move into the real world.
So, our friend from WA is correct. You should know your system! But, if you can't calculate the coef, then you need to start somewhere....especially for your first shot!
Also, the gains entered are an approximation. Often, in truely well tuned loops 3 sets of coef can be used and you can perform a linear interpolation between. Again, we can get into the differential calculus that applies here; but, we were just trying to be helpful weren't we?
PS: After 12 years in controls, and tuning on tens of loops using everything from PLCs (Mitsi, AB, GE, Modicon, Koyo, Siemens...etc), DCS (Fisher and Landis) and C based systems, I might have a bit of a clue. And, I HAVE worked on flight controls....