a very basic explanation:
with the “Dependent” form of the PID equation, the amount of Integral action - and the amount of Derivative action – both DEPEND upon the setting you’ve entered for the Proportional action ...
with the “Independent” form of the PID equation, the various settings (Proportional, Integral, and Derivative) are all INDEPENDENT of each other ...
going further:
first suppose that you’re tuning a loop using the INDEPENDENT form of the PID equation ... suppose that you’ve decided that you need more Proportional action – but you do NOT want to change the existing amount of Integral action or the amount of Derivative action ... no problem, just change the Proportional setting ... the amount of Integral action and the amount of Derivative action will both remain unchanged ...
on the other hand ...
now suppose that you’re tuning a loop using the DEPENDENT form of the PID equation ... once again, suppose that you’ve decided that you need more Proportional action – but you do NOT want to change the existing amount of Integral action or the amount of Derivative action ... this time you COULD have a slight problem ... because whenever you make a change to the Proportional setting, then the amount of Integral action and the amount of Derivative action will both be changed also ... in this case, you’d have to make “compensating” changes to the Integral setting – and to the Derivative setting – in order to accomplish the stated goal ...
finishing up ...
at first glance it seems to be a “no brainer” to go with the INDEPENDENT form (if it’s available) – and keep the tuning task as simple as possible ... I personally won’t enter the debate on which form is “better” ... but here’s something to think about before you make your choice ... MANY controllers ONLY allow the DEPENDENT form ... so ... IF you’ll ever have to work with any of those types of controllers in the future, then consider whether or not you might be “painting yourself into a corner” by starting out with the INDEPENDENT form ... specifically, if you concentrate all of your initial “learning curve” on mastering a feel for tuning the (“somewhat easier”) INDEPENDENT form, then you MIGHT have a problem when you’re eventually forced to deal with the (“more challenging”) DEPENDENT form ...
anticipating your next question:
as long as both forms are properly tuned, then one method doesn’t offer any “better control” for the same process than the other ... specifically, I’ve often had my students tune a system ONE way – and then print out a “test run” of the process ... next we retune the system for the OTHER way – and again print out a “test run” ... when you “stack” the two printouts and hold them up to the light, the traces will essentially be superimposed ...
final thought:
IF (big IF) your process requires a very large amount of Integral action, then the INDEPENDENT form might have a significant advantage ... that’s because with the INDEPENDENT form, the range of values that can be entered for the Integral setting is USUALLY able to crank in more Integral action ...
basic reason: for most controllers using the DEPENDENT form, a LOWER number gives MORE Integral action ... but ... for most controllers using the INDEPENDENT form, a LOWER number gives LESS Integral action ... this has perplexed many people – who quite often “go the wrong way” with their Integral settings – when switching from one form of equation to the other ... (another “gotcha” for the unwary) ...
hope this helps ... please keep us posted on your progress ... printouts of the PID response are always appreciated ...