How much additional positive phase should we request from a

How much additional positive phase should we request from a DT PID controller with a standard selection of the sampling rate at 6 samples-per-rise-time (assuming ZOH introduces a half-sample delay, and bandwidth is 1.5 times the cutoff frequency): About 6deg. About 12deg. No additional phase. Depends on PI vs PID. None of the above.

Solution

None of above because below explanation written.

Approaches range from simplistic rules of thumb to scientific methods (e.g. NyquistShannon sampling theorem). On the easier end of the spectrum its commonplace to stipulate sample rates of 1 second or faster for Flow loops and 1-2 seconds for Pressure. Such loops react very quickly to changes in Controller Output. Not far behind are rates of 2-5 seconds for many Temperature and Level loops which characteristically possess slower dynamics.

When considering sample rate from a scientific or mathematical perspective, the guidelines are a bit more involved and beyond the scope of this blog post. Still, its generally accepted best-practice for the sample rate to be based on frequency or time based components of the process data. Basic formulas propose the use of data that is either 5-10 times faster than the Process Time Constant or 3-5 times faster than the Process Dead-Time.