By F.G. Shinskey
ALMOST HALF OF the controllers in a typical process plant are flow controllers, and the next most common regulate liquid level, many of which set flow in cascade. Level loops differ from others in their economic objectives, in that there may be no economic penalty associated with a particular deviation from set point–yet a loss of level control can shut down an entire plant. They also differ in that their task is to regulate a process that is fundamentally non-self-regulating. This characteristic leads to limit-cycling of a PI (proportional + integral) controller in the presence of any deadband in the control valve, avoided by using either a valve positioner or a cascade flow loop. This combination of properties results in the need for different rules for tuning level controllers than are applied to flow, temperature, pressure and composition controllers.
There are different categories of level loops based on the vessel being regulated, and different tuning rules apply to each. Four categories are suggested here:
- Surge tanks feeding critical processes
- Material-balance regulators between process stages
- Levels affected by shrink-swell and inverse response, such as boiler drums
- Levels with resonance (manometer effect)
|FIGURE 1: LOAD RESPONSE UNDER PROPORTIONAL AVERAGING LEVEL CONTROL
Surge Tanks Serve to Deliver
A surge tank accumulates feedstock from one or more sources–some may be batch–and serves to deliver a smooth average feed rate to a critical downstream process such as a reactor, evaporator, distillation column, or recovery boiler. To minimize disturbances to the downstream process, its feed rate should be constant, but must represent the average value of the total flow entering the surge tank.
Averaging takes place over the closed-loop time constant of the surge tank–typically 20 minutes to several hours–and this application is called “averaging level control.” The tank accumulates volume based on the integral of the difference between total inflow and manipulated outflow rates. Its integrating time constant (WHAT SYMBOL?) is the time required to empty the tank from 100 to 0% level with zero inflow and 100% outflow (or by any other percentage level with the same percentage difference between inflow and outflow rates).
Simply Proportional Only
The simplest method of averaging level control is proportional-only. Consider the case of 100% proportional control, where the controller at 100% level sets outflow at 100%, and at zero level sets outflow at zero. This produces a closed-loop time constant equal to the integrating time of the tank. The outflow at any point in time consequently represents the exponentially weighted average value of the inflow, averaged over the integrating time constant of the tank. The closed-loop time constant of the tank is that portion of the tank volume covered by the proportional band P of the controller:
It could only exceed (WHAT SYMBOL?) by setting P beyond 100 %, but then outflow could not be manipulated over its full range, and the controller could not prevent the tank from overflowing or emptying. In most cases, operators choose a safety margin such as 10% at both ends of the tank, which requires a proportional band of 80%.
A proportional control algorithm manipulates outflow m in relation to the deviation of controlled level c from set point r:
where <i>b<i> is an adjustable output bias also known as “manual reset.” Ideally, <i>m<i> should be the set point of a linear flow controller.
If r = 50 and b = 50, then the proportional band will be distributed uniformly across the level measurement. One drawback of proportional control is that the level will almost never be at set point, leading operators to suspect that the controller is not working properly. One way of avoiding this misconception is to set r at the desired low limit of level, and b at zero, so that flow is zero when the level falls to that low limit. Full outflow is then reached when the level rises to
r + P.
Some digital controllers are unable to execute pure proportional control, in that bias b cannot be fixed, but floats, changing every time the controller is transferred between automatic and manual. Such a controller cannot be used in this application. But a proportional controller can be made from a digital scaler or calculation block, performing the function:
where cl and ch are set low and high limits respectively.
The maximum rate-of-change of outflow following a step change to inflow fi occurs immediately following the step, as shown in the lower set of curves in Figure 1. The initial steady state is at 50% flow and level. Because the proportional band of the controller is 80%, the level change is 80% of the steady-state flow change. The maximum rate-of-change of outflow is
Its value can be reduced by inserting a first-order lag at either the input or output of the controller. The upper set of curves in Figure 1 shows the effect of a lag whose time constant (WHAT SYMBOL?) f = 0.4(WHAT SYMBOL?). This is about the highest value recommended, in that it produces a second-order closed loop with a damping factor of 0.707–note the slight overshoot in flow and in level. At the same time, it reduces the maximum rate-of-change of outflow to a factor of 0.65 of what is calculated in Equation (4). It also effectively filters noise and other high-frequency transients.