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(ProQuest Information and Learning: ... denotes formulae omitted.)

Pl control of level

In two items in InTech (Process Control Basics letter, June 2006; and "Mind Your Ps," August 2006), statements were made to the effect that the use of Pl control for level would lead to sustained oscillation

I have no problem with the statement that level is an integrating process, nor do I have a problem with the use of proportional-only control for level control loops. I do have a problem with the assertion that the use of Pl will always lead to sustained oscillation or failure.

If the vessel is of significant size so that its dynamics are large compared with the dynamics of the level control valve or cascaded flow loop (this is a reasonable assumption for most industrial level control applications), and if the level control valve (without cascade) is free of hysteresis, then the process can be considered a pure integrator. In that case, whether or not the loop oscillates (see August 2005 DeltaTech, supplement to InTech for related information) depends upon the value of the parameter group...

Where:

K^sub C^ is the controller gain

T^sub I^ is the integral time, minutes (per repeat)

T^sub L^ is the vessel hold-up time in minutes (quantity between O and 10% level transmitter range, divided by maximum outflow in compatible units)

If this parameter group is:

* Greater than 4, the response will be overdamped.

* Equal to 4, the response will be critically damped.

* Less than 4, the response will be underdamped.

* Equal to 0.2 (special case of less than 4), the response will be a quarter cycle decay.

Under the "ideal model" conditions stated above (negligible dynamics of valve or cascaded flow loop, no valve hysteresis), a level loop at most will exhibit a very slightly decaying oscillation-it cannot go into sustained oscillation.

Now for a reality check. Most level control loops are not afforded the luxury of a cascaded flow loop, and there is probably some amount of hysteresis in all level control valves. In this case, the use of Pl will always result in a sustained oscillation. I suspect that is what the authors of both of these articles have observed. But notice the real culprit is the valve hysteresis, not the fact that integral is part of the control algorithm.

I advocate that, wherever possible, the level controller should be cascaded to a flow loop. Then many of the disturbances that would otherwise affect the level loop, such as valve hysteresis, upstream or downstream pressure effects, etc., are contained within the secondary loop, and Pl control for level is perfectly acceptable. Many of the times, the flow is already measured-it's just a matter of closing the secondary loon within the DCS.