Tuning rule bonanza

Control Talk columnists McMillan and Weiner say in order to get good performance, you need to measure and track the process, the controls, and the equipment under actual real-time operating conditions.

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McMillan & WeinerBy Greg McMillan and Stan Weiner, PE

 

Stan: We got a couple of good reasons from George Buckbee why a rotary control valve increased process variability even though the positioner said the step response was fine.

George: I have seen this same phenomenon several times, with at least two different causes. In both cases, bench-testing and setup could not have uncovered or prevented the problem. In the first case, a 9-in. valve was exhibiting this stiction cycle, despite a more-than-adequate positioner. Closer investigation revealed that the air supply was moving through a ¼-in. tube, running almost 200 ft back to the air header! There simply wasn’t enough air supply to make the valve move. This resulted in a classic stick-slip cycle, as the positioner pressure would eventually build up to make the valve move. 

 

 
Technical Backup

Technical Backup



 

The second case involved a butterfly valve in a line with a substantial pressure drop. The force exerted by the flow would push the valve open. The positioner was tuned while the process was down (no flow), so it wasn’t properly tuned for the actual operating conditions. When there was flow, the positioner tuning was not aggressive enough to control the valve position. This puzzler illustrates a very important principle in process and control performance: To get good performance, you need to measure and track the performance of the process, the controls, and the equipment under actual real-time operating conditions.

Greg: The positioner on many rotary valves uses actuator shaft-position feedback instead of ball or disk-stem position. The positioner doesn’t see friction in the sealing surfaces and packing and backlash in the connections between the stem and shaft. Also, the step size introduced in a test may be larger than the dead band from backlash or the resolution from stick-slip.

Controller Tuning Rules
Now, we’re going to talk controller tuning. Most astute control people can devise a case where using their favorite tuning method is best. The Handbook of PI and PID Controller Tuning Rules, 2nd edition, by Aidan O’Dwyer alone offers over 400 pages of tuning rule tables. To help put them all in perspective, I offer the following Top 10 list.

Top 10 Reasons to Devise
Your Own Tuning Rule and Simulation Test

10. Opportunity to present papers at your favorite conference
9. Material to start a blog site
8. Competitive edge to start a consulting business
7. Listing in a book on tuning rules
6. Method named after you (sorry, Ignatius Michael Coolman, the IMC acronym is taken)
5. Simulations tailored to prove your point
4. Linear processes without control valves
3. Speed, since the time to steady state is just a matter of seconds in your simulation
2. Simplicity gained by ignoring the prevalence, size, speed and entry point of unmeasured disturbances in real processes and nonstationary behavior
1. Chance to discount industrial online software for controller tuning as just hearsay

Tuning Rule #1023

What prompted this impromptu column was the realization that diverse tuning rules have a common basis. For example, the equation for controller gain from the Ziegler Nichols ultimate oscillation, the Lambda self-regulating and integrating process, and the internal model control tuning rules, when set for maximum disturbance rejection (that is, maximum transfer of variability from the process-control variable to the controller output), all reduce to the Ziegler Nichols reaction curve rule. The focus here is on processes dominated by a large process time constant.

The controller gain per the Ziegler Nichols reaction curve rule with the gain cut in half per the industrial practice to increase smoothness and robustness is:

Kc = 0.5 / (R * L)

The figure used by Ziegler Nichols for the graphical estimation of R and L showed the process initially lined out, so R is the ramp rate in %/minutes divided by the change in manual controller output. For integrating and disturbance-prone self-regulating processes, the initial ramp rate isn’t zero. If you use the change in ramp rate before and after the change in controller output, R becomes the integrating process gain used in the Lambda integrating process tuning rule and the shortcut tuning method in Good Tuning–A Pocket Guide. Furthermore, if you realize that the process gain (Kp) divided by the process time constant (Tp) is the integrating process gain (Ki) for a slow self-regulating process, you can convert back and forth between the Ziegler Nichols equation and the common equation seen in the literature:

Kc = 0.5/(Ki*Td) = (0.5*Tp) / (Kp*Td)

If you use process dead time (Td) as the Lambda in the Lambda self-regulating and integrating process tuning rules, you get the above equations, but with a larger coefficient for the integrating process rule. Part of the conceptual hurdle is visualizing the initial response before the inflection point of a slow self-regulating process as the ramp rate of an integrating process. For controllers tuned for fast disturbance rejection, the controller works off only the initial part of the response.

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