• Error deadband. Many implementations permit specifying separate values for PV > SP (the high deadband, EDBH) and PV < SP (the low deadband, EDBL). This is a desirable capability for level control applications.
• Controller gain within the gap. This sensitivity (KC,LO ) is applied when the control error is less than the error deadband.
• Controller gain outside the gap. This sensitivity (KC,HI) is applied when the control error exceeds the error deadband.
Using these coefficients, we can express the relationship illustrated in Figure 1 as:
M – MR = KC f(E)
= KC,LO E if |E| ≤ EDB
= KC,LO EDB + KC,HI[E - EDB] if E > EDB
= -KC,LO EDB + KC,LO [E + EDB] if E < -EDB
The following expression is also true:
Sensitivity = KC,LO if |E| ≤ EDB
= KC,HIif |E| > EDB
Most modern proportional-integral-derivative (PID) implementations permit specifying a computed value for the controller gain. This suggests the following implementation of the error gap relationship:
• Configure the PID control block as supplied by the manufacturer.
• Specify KC,LO for the controller gain if |E| ≤ EDB and KC,HIif |E| > EDB.
The success of this approach depends on how the PID is implemented. Where the position relationship is the basis for the PID calculations, the result is likely (but not necessarily) that illustrated in Figure 2. When the control error crosses the error deadband, an abrupt change occurs in the controller output — resulting in a "bump" to the process inappropriate for level control applications.
For level control applications, the controller sensitivity within the gap must effectively respond to the "normal" variations in the feeds to the vessel. In effect, the sensitivity within the gap matches that of a customary linear PID control equation tuned without regard for the possibility of trips. The purpose of the nonlinearity within the control equation is to ensure the controller output reaches the appropriate extreme before either a high- or low-level process trip occurs.
At large values of the control error the error gap relationship gives a high sensitivity. However, this high sensitivity is not used to actually control the level. Instead, it serves to avoid a process trip by causing the controller to react quickly to drive the level back into the error gap.
|Figure 5. Equation sensitivity increases linearly with the control error.|
For level control applications, the appropriate EDB value can be determined from the following (values in parentheses are from the previous articles):
• level set point (40%);
• vessel level at the location of the high level switch (95%); and