How to Tune Self-Regulating Control Loops

I’ve highlighted a few Emerson presentations for this week’s ChemInnovations conference in New Orleans. Emerson’s James Beall, a 30-year veteran in process control and chairman of the ISA 75.25 committee on control valve performance testing, shared his ChemInnovations presentation with me as well. The subject is a look at the fundamentals of modern loop tuning.

With a high demand for automation professionals and more new engineers joining the ranks every day, James’ primer is well timed. I’ll highlight some of the guidance he offers. He opens by defining the proportional, derivative, and integral terms of a PID loop:

Proportional – output contribution is “proportional” to difference between Set Point and PV (error). Therefore, output contribution is “gain” times error. Will have “offset” between Set Point and PV. Action expressed in gain.

Integral – output contribution is “integration” of the difference between Set Point and PV (error). Therefore, always tries to make PV = Set Point (eliminates offset). Action expressed in integral time, Tr, in seconds/repeat.

Derivative – output contribution is based on the derivative (rate of change) of the difference between Set Point and PV. Actually usually based on PV, not error. Action expressed in seconds.

James noted that the PID algorithm comes in different forms—parallel, series, standard. The form significantly impacts the actual tuning values. The tuning rules he presents are based on the series and standard form of the PID algorithm.

Historically, the older tuning methods try to tune as fast as possible and loops were tuned independently without coordinating the impact of the associated process dynamics. James advised a 4-step approach.

First, determine the basic type of process, such as integrating or self-regulating. Next, determine the process dynamics. Next, choose the desired closed-loop response time, known as Lambda, λ. Finally, calculate the tuning constants.

Self Regulating Process

Click to enlarge

James first looked at a self-regulating process. To determine the process dynamics, first put the controller output in manual mode and bump the controller output. This change in output gives you the % change in output (Δ%output), deadtime, Td, from when the change is made until the output reaches the asked for new output level, the time, T98, until the process variable PV reaches 98% of its final value, Δ%PV. The illustration shows how to arrive at these values and calculate the process gain, Kp, and time constant, Tau.

He offers the Lambda tuning rules for a self-regulating process. A recommended starting point to ensure robustness is 3 * (larger of Td or Tau). This results in stable tuning if the deadtime and process gain double. The closed loop “Time to Steady State”, T98 for a set point change is approximately 4*Lambda, assuming “P” is on error. Tr, the reset time is equal to Tau. The controller gain, Kc, is calculated with the formula Tr / (Kp * (λ + Td)). James notes that Tr stays the same and only Kc changes with Lambda.

James addressed a concern that Lambda tuning is slow by noting, “Compared to what?” We addressed some of these concerns in an earlier post, Lambda Tuning-Yeah or Neah?

Now that we have a handle on the process for a single self-regulating loop, what do you do about interacting loops? The key is to coordinate the loop tuning based on the Lambda values from lowest to highest. This animation shows a distillation column example beginning with a couple of flow controllers, moving on to level controllers, and finally a temperature controller.
Self-regulating process

I’ll save James’ discussion of tuning integrating processes for another post. I hope if you’re new to process automation that this helps. I’d also suggest visiting the Control Loop Foundation site for more background.

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