Modeling and Control

Last week we discussed how a resolution limit (stick-slip) in a control valve can cause a saw tooth oscillation in the controller output for a self-regulating (steady state) process. For a flow or liquid pressure loop where the process time constant is small, the oscillation in the process variable (PV) is a square wave. For a gas pressure loop where the process time constant is significant, the oscillation in the PV is rounded. Note that if the resolution limit was zero, dead band in itself would not cause this oscillation for a self-regulating process. In real systems, the resolution limit is never zero, so oscillations exist but may be so small that they are lost in the noise or upsets.

For integrating processes such as level, a dead band will create a limit cycle independent of whether a resolution limit exists. In an integrating process, there is no steady state. The PV ramps unless the controller output exactly balances the load, which only occurs for a perfect valve and no disturbances or noise. The lost motion of the control valve from dead band (backlash) causes the PV to ramp until it has worked through the dead band. The result is a saw tooth in the PV whereas for self-regulating processes the saw tooth was in the controller output. While the dead band is never zero, the amplitude of the saw tooth of the PV can be so small it is lost in the noise or upsets.

Whether a valve limit cycle affects the product quality depends whether there is a back mixed volume down stream that filters (attenuates) the oscillation. The analogy in circuit theory works well here where the filtered amplitude for large filter times is proportional to the period of the oscillation and inversely proportional to the filter time.

For a well agitated vessel, the filter time is the vessel residence time (volume divided by throughput flow). Even if the vessel does not have agitation, turbulence of boiling mixtures, the entrance and recirculation of flows, and the migration of compounds from low to high concentrations results in significant smoothing of the oscillation. Thus, for chemical processes involving blend tanks, columns, evaporators, and reactors, the limit cycles typically have little economic impact for reasonably good valves (e.g. resolutions and dead bands less than 0.5%). The exception of course is pH, where the process gain and thus the amplification of a resolution limit can be extremely large for strong acids and bases. In fact, a reagent valve with exceptional resolution combined with advanced control techniques can eliminate a stage of neutralization and the associated equipment, piping, and instrumentation costs.

For pipeline composition control or sheet thickness control, limit cycles are not attenuated because there is essentially no back mixed volume. Oscillations readily appear in the final product and the impact of the valve response plays a more important role. Consequently, the pulp and paper industry is much more sensitive to valve problems.

For split ranged valves, the topic for next week, all bets are off.

Any process with split ranged valves is prone to limit cycling for many reasons. The periods are unpredictable. Some are process related. For example, the transition between steam and coolant creates a severe discontinuity. There is a change of phase and disruptive change in magnitude and sign of the effect. There is no happy medium for a small cooling or heating requirement. When the steam replaces the coolant in the jacket or coils or vice versa, by the time the controller sees that the consequence of its action is too large, it is too late.

The real behavior of control valves also make the transition at the split range point less than smooth. The resolution (stick-slip) at the seat at process conditions is often an order of magnitude larger than the stated resolution of the valve. Tight shutoff specifications and designs, high temperatures, solids, and fouling increases the friction and stick-slip as the valve trim, ball, or disk tries to break free of the seat or seal. Tests done by the manufacturer are usually done far away from shutoff (e.g. 50%). There are exceptions as noted in the blog “Control Valves on the Skids” on May 10 in the Plant Design category.

The slope of an installed characteristic of a control valve is also typically largest near shutoff and smallest near the wide open position. So besides the difference in valve gain due to valve capacity, there is also a change in valve gain due to the installed characteristic.

When a small control valve is split ranged with a large control valve, there may be an improvement in rangeability when you are throttling just the small valve but there is the increase in stick-slip in the transition to the big valve and a loss of sensitivity when throttling the big valve. Model predictive control can eliminate the need for this split ranging by simultaneously manipulating both valves as described in Advanced Application Note 2 available at http://www.easydeltav.com/controlinsights/

When the split ranged valves are for different streams that have opposite effects, the limit cycle across the split range point poses a significant loss in process efficiency. The cycling between coolant and steam wastes energy and the cycling between acids and bases waste reagent. Here not only is there difference in the valve gain, but also in the process gain, dead time, time constant, and sign. Adding a dead band in the split ranged point adds dead time in all processes and creates a limit cycle for integrating processes.

A buffet of techniques that is free to boot (Texas Talk) is available as an E-Book on my Control Insights website.

http://www.easydeltav.com/controlinsights/controltechniques/default.asp

While the title is Continuous Control Techniques for Distributed Control Systems, the techniques are applicable to batch processes and in fact were based in some cases on batch loops. It follows in the foot steps of my first free E-Book A Funny Thing Happened on the Way to the Control Room. While I emphasize technical detail more than humor in the latest E-Book, I still tried to present and conceptualize the techniques in a friendly and interesting way.

If you are a mature adult (e.g. old person) like me, you probably remember the days of analog computing modules and the fun and games of scaling potentiometer for engineering units and sorting through a maze of wiring. I can’t even talk about the days of pneumatic modules, bellows, links, and levers. Even with a broad line of computing modules such as lead-lags and signal characterizers besides the multiplier-dividers and summer-subtractors, you were “awfully limited”. I was going to say “pretty limited” but there was nothing pretty about the installation. One of the many problems with a total hardware solution was the design had to be frozen in time because of footprint, wiring, delivery, and installation requirements. Continuous improvement was difficult at best.

I was lucky enough to part of a beta test of one of the first distributed control systems that had a powerful set of functions some of which I wish I had in newer systems today. I spent the next 10 years exploiting as much as possible these functions in a series of challenging applications many of which are documented in the 2 E-Books and on this web site. I could go straight from conceptualization to implementation. The only limit was my imagination.

My next E-Book will be Biochemical Measurement and Control! No way! Way!

Enjoy.

I write wherever I get the inspiration. Headphones are a given. Right now I am listening to Crosby, Stills and Nash’s “Déjà Vu”, which seems especially appropriate since this is a flashback to my career in instrumentation. When I am in a groove, I enjoy the detail of every note and lyric and the thoughts flow to the page as fast as the music.

I seem to get better insights when I can get away to places particularly beautiful and relaxing. For the November 1998 issue of Chemical Engineering I wrote the feature article “Trouble free Instrumentation” from Pensacola Beach while enjoying the sugar white sand, emerald waters, and tropical drinks as shown on the attached cover.

From the Beach

The article is a summary of everything I learned installing, checking out, and starting up automation systems while in instrument construction and tackling dynamically challenged process control loops for Engineering Technology during my career at Monsanto and its spin off Solutia. The article is a core dump of 11 pages on the selection, installation, maintenance, and troubleshooting of instrumentation and control valves. The article lists major causes of measurement and valve errors and failure, best practices, dos and don’ts of maintenance, diagnostic and knowledge based monitoring techniques, and rules of thumb.

Stay tuned for an electronic copy. If you want to hear about the highlights and lowlights of my career that lead to this article, checkout my “Control Talk” column starting in the August issue of Control magazine titled “One Man’s Story.”

http://www.controlglobal.com/articles/2007/234.html