The Good, the Bad, and the Ugly

Most of the literature makes valve nonlinearity seem bad or just plain ugly. However, if you take into account process dynamics and valve stick-slip, you might actually consider valve nonlinearity as good in some applications. So before we continue on to a discussion of the implications of mixing on tuning next week, let’s consider the role played by the valve.

If we consult the last page of Advanced Application Note 4, we see the controller gain is proportional to the process time constant and inversely proportional to the open loop gain and dead time for maximum disturbance rejection. If we further consider that this same note shows that the open loop gain is the product of the valve gain, process gain, and measurement gain, we have the principles to be more intelligent in our valve trim choices and gain scheduling. Most people call the “open loop gain” a “process gain” even though it depends upon the valve flow characteristic and measurement scale besides the process.

The equal percentage trim has an inherent flow characteristic whose valve gain (curve slope) is proportional to flow. A lot has been published on how bad this is for controller tuning. For flow loops, this is true, but for temperature and composition (including pH) control in pipelines, static mixers, and heat exchangers (plug flow), this valve gain helps cancel out the process gain that is inversely proportional to flow. If you further consider the dead time is inversely proportional to flow, this valve nonlinearity is good.

How about well mixed vessels? Well the valve nonlinearity does the same thing so far as canceling the effect of flow on the process gain. However, since the residence time becomes a time constant rather than a dead time for a back mixed volume as discussed last week, the numerator for the controller gain is inversely proportional to flow so the benefit of canceling it out of the denominator is not such a good deal. Now the dead time from mixing is set by the turnover time and is only a weak function of feed flow. If there is a pipeline or dip tube with a significant transportation delay or poor mixing, then we are back to the case of the dead time being inversely proportional to flow. So for vessels, an equal percentage characteristic may be good or bad from a controller gain view point. There are other considerations that make this trim choice the right choice.

While a linear trim supposedly has the greatest rangeability based on best conformity of the flow coefficient to a designated curve, if you consider the effect of stick-slip which is greatest near the seat, the equal percentage trim has the best turndown (smallest controllable flow), which is more important to me than conformity of the trim characteristic. If you also consider that this trim can deal with the diminishing valve pressure drop caused by higher piping system pressure drops at higher flows and can thus prevent the installed characteristic from flattening out at large lifts, you have clues as to why an equal percentage trim is so popular.

In my book, quick opening trim is mostly ugly because the valve gain is so high near the seat it accentuates stick-slip and the process gain nonlinearity for temperature and composition control. This trim also hastens the premature flattening of the installed characteristic from a diminishing valve drop. However, for liquid pressure control, the process gain is proportional to flow so you can make a case a quick open trim is good for this loop. In fact pressure regulators tend to have this characteristic. Also, for anti-surge control and pressure relief, quick opening trim is used to establish a vent flow as quickly as possible.

Finally, I have to admit quick opening trim can help flush solids out of the seat. However, I would rather preprogram some kicker action in the DCS configuration to provide this burst so I can have a good flow characteristic to work with. I can also switch to pulse duration control for small controller outputs to prevent small flow areas that would plug.