Dead Time Exceeding Time Constant

The loop dead time can become larger than the largest time constant for in-line mixer installations, because these units provide mostly axial mixing instead of back-mixing. Td can also exceed r1 in several situations: in poorly mixed tanks; when the reagent dip tubes are poorly designed; in systems where transportation time exceeds turnover time; and when electrodes are improperly located or severely fouled. Td can exceed r1 in seemingly well-designed and well-mixed vessels also if the setpoint falls on a particularly steep section of the titration curve because (as was illustrated in Figure 7.40.14), most of the time constant is lost due to rapid movement of pH. Under such conditions, the measurement can actually accelerate and the process can appear to be non-self-regulating to the controller. For this case, dead-time dominance causes the window of allowable gains to close, and loop instability occurs regardless of tuning. Also, for non-self-regulating processes, it is important to maximize derivative or rate action and minimize the use of integral or reset action. Neither of these steps is possible when dead time exceeds the time constant in the loop.

For Td > r1 and when using a PI controller:

where:

Kc = controller gain

Ko = the open-loop steady-state gain (dimensionless) r1 = largest time constant with titration curve effect (minutes)

Td = total loop dead time (minutes) Td = derivative time setting (minutes) Ti = integral time setting (minutes/repeat)

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