Figure 3 repeats Figure 2 with a TI of 24 min, which hopefully is close to the period of the cycles in Figure 2. Consistent cycles of a sinusoidal nature no longer are evident in the vessel level or controller output. However, this comes at a cost. As the controller is made less aggressive, deviations in vessel level from its set point (SP) increase, as shown in Table 1.
Reducing Kc has a larger adverse effect on performance than increasing TI.
For the process in Figure 1, the level controller moves the variance from the process variable (PV), the vessel level, to the flow through the control valve. This raises two issues:
1. What are the consequences of variations in vessel level? Often the answer is "none." However, there are exceptions -- one being thermosiphon reboilers. The flow through a reboiler is by natural convection, which is affected by the liquid head, which in turn depends on the bottoms level.
2. What are the consequences of variations in the flow through the control valve? If discharge flow in Figure 1 is to a large storage tank, the consequences are nil. However, when the discharge flow is to another process unit, throughput changes usually are major upsets.
LEVEL CONTROL IN SURGE VESSELS
The purpose of a surge vessel is to provide averaging or smoothing so that changes in discharge flow are less rapid and less extreme than changes in feed flow. Tight control of level is counterproductive -- very quickly translating any change in feed flow to a change in discharge flow. Instead, vessel level is allowed to vary "within reason," that is, as long as it doesn't cause process trips on high and low level. The appropriate tuning is the lowest possible Kc that doesn't result in process trips. However, especially in large vessels, reset action in the controller can lead to a discharge flow cycle with a very long period.
If the vessel in Figure 1 is a surge vessel, maintaining as smooth a discharge flow as possible is the primary objective. This suggests low controller gains and long reset times.
In addition, variations in vessel level don't pose consequences, provided no process trips are initiated by the high and low level switches. This suggests two requirements on the controller output:
1. Before the high level switch is actuated, the control valve should be fully open.
2. Before the low level switch is actuated, the control valve should be fully closed (or the flow to the downstream process should be at its minimum acceptable value).
From these requirements, you can compute values for Kc.
In a proportional-integral (PI) controller, the equation for the proportional mode is the following proportional-plus-bias equation:
M = Kc E + MR
where M is controller output, %; E is control error, %, which equals PV – SP for a direct acting controller and SP – PV for a reverse acting controller; and MR is controller output bias, %.
When the reset mode is present, MR is the output of the reset mode. If E is zero (PV = SP), M equals MR. Some, but not all, commercial controllers will display the value of MR. If the controller won't show this value, you can obtain it either by computing via MR = M – Kc E or temporarily setting SP = PV -- because E then is zero, the value of M is MR.