The pid algorithm

The PID Algorithm

http://www.pidtuning.net/pid-algorithm.php

Resources -> PID Algorithm:

The many flavors of PID Algorithm
There are 3 different types of PID algorithm 1. Ideal (also called "ISA") 2. Series (also called "series" or "interacting" or "analog" or "classical") 3. Parallel (also called "non-interacting", "independent" and "gain independent)

All 3 algorithms can achieve the same result theoretically; however the tuning constants to get that result may well be very different depending on the algorithm used. You should be able to identify the algorithm used from the vendor-supplied instructio n manual. To make identifying your particular algorithm a bit trickier, manufacturers vary on their names for these categories. They won't necessarily stick with the names on the list above. The only way to really tell which algorithm you have is to look at the equation for t he PID Controller. The equation may be written in the "classical" form or the "Laplace" form or as a block diagram. All 3 formats are shown in the following table to help you match it up with what's written in your user guide.

If your user guide does not make it clear which algorithm is being used – then fax th e table above to the guy that sold you the controller and insist he sends it back with the row that contains your controller's algorithm circled.

Understanding the PID Algorithm differences
Don't be freaked out by the complex looking equations – to understand the difference between the algorithms, just look at the block diagrams. The P, I and D blocks all do exactly the same function in isolation (which is described in detail in "The Complete Idiot's Guide to the PID Algorithm". The difference between the algorithms is how the P, I and D gains affect each other. For example in the parallel algorithm, all 3 gains are totally independent, as the block diagram shows. That mean s that the P, I and D terms all act on a fresh, unadulterated error term, and then the results