I received an email about how the DeltaV PID algorithm was derived. I received a message back from the DeltaV technology team and wanted to capture the answer in this post. Here's what's in Books Online:
Here's the derivation beginning with the PID Standard forn:
Thanks to the DeltaV Technology team for giving me the OK to share this!
First of all, thank you for the very helpful derivation of the PID equation.
I had a question related to the implementation of the external reset. I noticed that in addition to the L(s)-F(s)/(Trs+1) term, you multiplied the rest of the equation excluding the feedforward by Trs/(Trs+1). What is the purpose of this and how would this manifest itself in terms of the block diagram? Could you provide more details on exactly how the external reset is implemented in DeltaV?
In reply to Zachary Hochhalter:
Zachary,
The diagram below shows how DeltaV implement Integral action using positive feedback from the PID/OUT or an external source via BKCAL_IN (generically called "external reset feedback"). The “Forward Path” has the P and D caculations. Note that there are a lot of calculations to take care of downstream statuses such as Limited or not Selected. I’ll work with my colleague, Todd Maras, next week to clarify the equation.
I conferred with my colleague Todd Maras, and here is our answer to your specific question about the TrS/(TrS+1) term.
This is a result of using the "postive feedback" mechanism to create the integral action which provides the ability to perform "external reset feedback" (we call it "dynamic reset limit", see the picture I sent previously). However, if the Dynamic Reset Limit is not used (most often not), then L=OUT; Feed foward F=0, and PID on Error; then equation 3 simplifies to the following. This exactly match the "textbook" equation for a Standard Form PID that includes a first order filter on the signal going to the derivative function.
For convenience, I have included the bock diagram of the Positive Feedback Integral implementation and the connection for external reset. Note that DeltaV uses a "postional" implementation as opposed to a "velocity" (aka incremental) implementation of the PID algorithm. You might look at this reference for more info on external reset feedback and positional PID www.controlglobal.com/.../