• vessel level at the location of the low level switch (5%).
When a discharge stream controls level its flow must be the maximum permitted, usually control valve fully open, before a high-level trip occurs. Similarly, the discharge flow must be the minimum permitted before a low-level trip occurs. Here we assume a valve fully closed — but some applications, such as pumping a starch slurry, cannot tolerate zero flows.
For the relationship in Figure 1, we can determine the controller output values for the PV values at each level switch:
High level (PV = 95%). The controller output attains 100% (control valve fully open) just before the vessel level reaches 95%. This meets the requirement for a fully open control valve should a process trip occur on high vessel level.
Low level (PV = 5%). The controller output is more than 50% at a vessel level of 5%. This does not meet the requirement for a fully closed control valve should a process trip occur on low vessel level.
The error gap relationship illustrated in Figure 3 satisfies these requirements. The sensitivity within the error gap is the same as in Figure 1. The differences are:
• The controller gain outside the gap is 10 %/%. For this sensitivity a change of 10% in level would drive the output from 0% to 100% or vice versa.
• The error deadband high (PV > SP) is 45%, which makes the transition to the high sensitivity occur at a level of 85%. This provides a 10% change in level to drive the control valve fully open.
• The error deadband low (PV < SP) is 25%, which makes the transition to the high sensitivity occur at a level of 15%. This provides a 10% change in level to drive the control valve fully closed.
In Figure 3, the switch to the high sensitivity happens at a vessel level 10% on the safe side of the trip. This can be thought of as "elbow room." How much is required depends on how quickly the vessel level responds to a change in the flow in or out.
When using the error gap relationship for the proportional mode, the integral or reset mode serves the same purpose as in the customary PID control equation — to shift the controller output bias so the vessel level is controlled at its set point. In surge vessels with frequent changes in the flows in or out, the vessel level will not line out at the set point. However, it should vary around the set point, with approximately equal excursions above and below.
|Figure 6. The control equation provides low sensitivity above the set point.|
The previous article covered the response of the standard PI control equation for a controller gain of 0.4 %/% and a reset time of 120 min. The control equation provided a relatively smooth discharge flow without initiating any process trips on high level or low level.
Figure 4 shows the performance of the error gap control equation for a controller gain of 0.2 %/% within the gap and 10 %/% outside the gap. The discharge flow is even smoother. However, the vessel level occasionally makes brief excursions outside the gap — once above the upper deadband and once below the lower deadband. On each excursion the gain abruptly increases from 0.2 %/% to 10 %/%. This causes both the controller output and the discharge flow to change rapidly.
Rapid changes in the discharge flow have the desired effect of avoiding a process trip on high or low level. However, this is at the expense of an upset to the downstream unit. A process may tolerate occasional occurrences, especially if they are associated with a major upset or other abnormal event. However, if such excursions happen regularly you must increase the sensitivity within the gap.