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By Robert C. Kelahan
GET REAL. It’s not the pH, it’s the ion flow. Modifying logarithm bases to help calculated titration curves match the pH range of real curves allows PID control to act based on linear ion flow rates, rather than pH, so traditional gain adjustments aren’t needed.
pH control is often studied in control literature because it presents such a unique case of nonlinearity, and nonlinearity can be very problematic in process control. With pH systems, the emphasis on pH as the control variable obscures the fact that what we’re really trying to measure and control is not pH (although the specification may be in terms of pH), but simply ion concentration or ion flow. pH is just a convenient measure of ion concentration by way of electrode potential as described by the Nernst Equation. However, the Nernst relationship between ion concentration (more correctly, activity) and electrode potential is logarithmic–hence the nonlinearity and its representation as pH.
Compensating for pH Nonlinearity
Most discussions of pH control accept pH measurement as the control variable and apply strategies to modify a part of the PID algorithm, usually the controller gain, to compensate for the nonlinearity. This can involve techniques, such as adaptive gain or gain scheduling, with a low fixed-gain region where pH is most sensitive to changes in reagent (high process gain), and with increasing gain as pH departs from this high process gain region. The result is a controller gain function with two breakpoints. In many cases, this can be reasonably effective. Success with this approach depends on how closely the controller gain maps to offset the changing process gain in the titration curve. Breakpoints must be selected, as well as the degree of gain adjustment, and some control instability can be observed around these breakpoints, even if these parameters are carefully selected.
"It’s valuable to keep the control strategy relatively simple with few parameters to change, but adaptive enough to remain effective with changing conditions."
|FIGURE 1: A SIMPLE ALGORITHM|
|Modifying the logarithm base produces a titration curve that can be made to look similar to the real titration curves of complex waste streams. This allows to modified curve to be used as a simple, effective linearization algorithm for pH that’s easy to configure and maintain.|
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