Applying gain scheduling

Exploring a process scenario that may be a good place to apply a gain scheduling strategy.
February 25, 2011

Dear Control Engineering: I enjoyed your article about gain scheduling. I’m curious as to your thoughts about another variable gain scenario. Suppose a PID loop heats a measured but unregulated flowing stream. The changing flow rate would seem to change the response dynamics of the heating loop, requiring different tuning parameters. Is this a suitable case for implementing a gain schedule based on flowrate similar to your tank level application?

Thanks, Dale Cresap.

Vance VanDoren’s Back to Basics article drew a number of comments including this one. Here is Vance’s response:

Yes, I think it is. The time constant of your heating process probably lengthens as the flowrate goes up since a larger portion of the heat added by your PID loop is carried downstream, thereby increasing the time required to reach the setpoint. And since more heat is required to achieve the same temperature change, your process gain probably drops as the flowrate goes up. A gain schedule in your controller should help you combat those effects by forcing the controller to be more aggressive at higher flowrates.

I talked to Vance about his suggestion to clarify a couple points. First, we’re assuming that the temperature sensor feeds its signal to the PID controller, which modulates the heater. Vance thinks that setting the gain schedule based on flow can probably be done more easily from empirical data based on observation rather than a formula, although either could be possible.

I would add another thought, and ask which measuring device should be operative sensor. If the temperature is the wider variable and flow is less subject to change, then the discussion above is probably the way to go. On the other hand, if temperature is relatively stable and the flow can change more drastically, maybe it should be flowmeter? Of course that suggest a completely different control strategy, which we’ll leave for another time.

Peter Welander,

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