I often say, “Levels are devils to control.” Why? They’re integrating variables; that is, if the level in a vessel is constant, and the valve is opened or closed and then brought back to its original opening, the level will be at a different place in the vessel. Levels are non-self-regulating – they represent an imbalance between the flow of material into and out of a vessel. The tuning challenge is to find the best combination of gain (or proportional band) and integral time (or reset) that attempts to react to material flow imbalances and maintain the level reasonably close to a set point. For a variety of reasons, using derivative is not a good idea for level control. Gain alone or PI control handles PV trajectory changes quite well.
The first question I ask when tuning a level is how important is it that the level be held close to set point? The answer in almost all cases is, “Not very.” After all, what is the vessel for? Normally it’s to hold an inventory of material for downstream processing, so a major portion of the entire volume of the vessel should be available for this use. In addition, the level measuring field device will normally be designed to measure the level well below or above either the bottom or top of the vessel vertical side, depending upon whether the safety objective is to prevent emptying or overfilling the vessel.
The importance of keeping the level close to set point determines how much gain should be used. For a properly designed level control loop, the control valve will fill or empty the vessel at full design flow rates with the valve wide open. If the level is at 50% of capacity and the flow is at 50% of the maximum design rate (and the valve is 50% open), and then the flow increases to 75% of design rate, a gain of 1.0 will open the valve to 75% when the level goes to 75%. So a gain of 1.0 should be the starting point. If it’s really important to keep the level close to set point, use a gain greater than 1.0; less important, less that 1.0. I typically start at 0.5 for most LCs.
Now for the integral time. How important is getting the level back to set point when a disturbance occurs? The answer again in almost all cases should be, “Not very.” Why? Well, think about it. The vessel is being used for inventory between some upstream process and some downstream process. A change in level represents an imbalance between the two processes. How fast do we want the change to propagate from one process to the other? The answer should be: only as fast as it has to be – give the process being asked to accept the imbalance as much time as possible to adjust to the new flow rate.
I typically start with 20 to 30 minutes of integral time. This produces mild reset action with a gradual return to set point with little or no overshoot after a step-type flow disturbance. As an example, in an olefins plant, there are several distillation columns in series. The first column in the series is the demethanizer, which is fed from the cold box, which is ultimately fed from the cracking furnaces. The demethanizer feeds the deethanizer, then the ethylene splitter and the depropanizer, and finally the propylene splitter. These are all super-fractionators with many trays. Small feed rate changes introduce significant disturbances to the column energy and material balances. The major disturbance variable is a change in the rate of cracked gas from the cracking furnaces, due to a furnace being taken down for de-coking or a planned feed rate change.
The optimum tuning constants for the level controllers on all these columns is a combination of gains in the range of 0.2-0.3 and integral times around 45 minutes. This tuning maintains the column levels within ±20% of set point, and returns the level to within 5% of set point within 2-3 hours of the change in column charge rate. But, most importantly, the resulting propagation of the load change to each column is slow enough such that the main product streams (high-purity ethylene off the top of the ethylene splitter and high-purity propylene off the top of the propylene splitter) remain on-spec.
One important thing to take away: the most important control objective of a level controller is often not to control the level!