The lower relative gain of this structure has two benefits: less cycling and tighter control. Cycling brings with it an economic penalty associated with the nonlinear relationship between energy consumption and either product composition (Figure 4).
Figure 4 (above). Boilup/feed ratio varies inversely with impurity level.
When a PID controller is cycling continuously, its integrated error will tend to be zero, so that the average product composition over time will be equal to the set point. However, due to the nonlinear relationship shown in Figure 4, the average level of energy consumed is higher than that required for a constant composition at that same set point in proportion to the amplitude of the cycle. For example, more energy is used to reduce the impurity to 0.8% than is saved at 1.6%—the cycling penalty.
The relative gain for a particular structure varies with the open-loop process gain, the numerator in Equation (1). For example,
Now if we change the structure of the top-composition loop, lowering the RG, the open-loop gain of the bottom-composition loop decreases by the same factor:
Dividing Equation (3) by Equation (4) gives a gain reduction in the bottom-composition loop by a factor of about five when the top loop is restructured. There is a similar reduction in that of the top loop.
This allows the proportional bands of the two temperature controllers to be reduced by the same factor of five, thereby reducing the deviation following disturbances by a factor of five—tighter control! This has been proven by field experience. Tighter control means that the set points for the composition (temperature) controllers can be moved that much closer to specification limits, resulting in further savings in energy.
There is one more economic factor that can be of major importance in refinery columns. They’re all limited in how much vapor traffic they can carry at the reboiler, at the condenser and in the column itself. Reducing the V/F ratio as described in Figure 4 allows the potential for increased feed rate F within the limits placed on V.
With some columns, the high purity demanded of the products results in relative gains exceeding 100, such as shown in the example of Figure 5, which are typical of benzene and toluene columns. Note how all the operating curves collapse into one, with only the material-balance line separate. An RG of over 1,000 guarantees that the structure of Figure 1 will fail to control both product compositions. The only way to succeed here is to manipulate one of the product flows to control its own composition, called “material-balance control.” The relative gain of 0.626 recommends distillate flow to control distillate composition.
Figure 5 (above). High-purity columns have high relative gains.
The structure used to accomplish this is shown in Figure 6. Feed flow is sent as a feed-forward signal to both composition loops, as all flows in the column must move in ratio to the feed rate. Moving distillate flow affects top temperature (composition) only indirectly, for the first result of any change appears in the liquid level in the reflux drum. Reflux flow must change by an amount equal and opposite to the change in distillate flow to force the external material balance on the internal vapor-liquid balance. If the overhead LC is left alone to adjust reflux flow in response to distillate flow, there will be a lag equal to the residence time of distillate in the drum, multiplied by the proportional band of the LC. This could amount to several minutes lag and substantially delay the top temperature loop. Dynamic response is even worse when separating close-boiling mixtures, like propane-propylene, where the temperature gradient is so small that its measurement isn’t useful for control, and the analyzer controllers have to respond to load changes.
The dynamic response of the top composition (temperature) loop is greatly enhanced by the simple decoupler shown as a summing block [∑] in Figure 6. It converts changes in distillate flow to opposite changes in reflux flow, eliminating any delay. The output of the LC then becomes (L + D), from which the measured flow D is subtracted to produce the set point L for reflux flow control.
Figure 6 (above). Material-balance control is needed for high-purity columns.
It’s imperative that the material-balance loop remain closed all the time, for if it’s left in manual, then neither composition can be controlled. The withdrawal of distillate must match the amount of the light component entering in the feed, and this requires that the top composition (temperature) feedback loop be closed. No amount of adjustment to boilup can overcome an incorrect distillate flow.
Material-balance control has the added advantage of protecting the column against heat-balance upsets. Any change in heat input, feed enthalpy or reflux temperature is prevented from affecting the distillate flow, and therefore disturbing distillate composition. With an L-V structure, these disturbances are magnified by the L/D ratio and passed on to the material balance.
The Role of MPC
Having imposed the appropriate control structure on the column to provide tight temperature control, there’s little work for the analyzer controllers to do. An MPC applied at that level will probably perform satisfactorily and can be used for optimizing set points.
While MPCs are capable of constraint control, these need to be applied at the lowest level, rather than at the highest. For example, the column needs to be protected against flooding and overpressure—the former represents a column limit and the latter a condenser limit. The flooding limit is most reliably imposed by a column differential-pressure controller overriding steam flow through a low-signal selector at the steam valve; a second pressure controller can also override steam flow in the same way. This method of applying constraints is simple, reliable, dynamically effective, and proven over many, many years. Protection against integral winup is described in my May 2006 article in Control, “The Power of External-reset Feedback.”
In conclusion, as Y. Z. Friedman suggests, controlling multivariable processes is more than simply throwing the latest matrix-based MPC at them—sound engineering principles must also be applied. [end]