Effect of Measurement Span on Loop Performance

The advent of smart transmitters has reduced the effect of large measurement spans on accuracy but most measurement accuracies are still a function of per cent of span, albeit possibly detailed by more sophisticated equations than simply the error being a percent of span. Bigger considerations these days concern the effect of measurement span on controller tuning and the effect of flow meter size on measurement rangeability.

It has been a common practice to narrow the span of temperature transmitters to improve the accuracy of this measurement that in many loops is critical since temperature is often the key to product quality by determining the composition (e.g., distillation tray temperature), the formation of products (e.g., bioreactor and chemical reactor and crystallizer temperature) and the separation of phases (e.g., evaporator and dryer temperature). The advent of smart transmitters reduces the error from span but the practice of narrowing the span is still worthwhile especially in avoiding unnecessarily high scale ranges. The benefit of a separate transmitter to handle lower operating ranges on startup can be valuable. The second transmitter also offers reliability and better online recognition of performance. For pH measurement, triple electrodes and middle signal selection are essential to improve reliability and reduce the effect of a coated electrode or measurement noise that ultimately determines repeatability.

Most flow meters have a low flow limit to their rangeability that is based on fluid velocity in the meter. To get the meter rangeability shown in the catalog necessitates your max flow requirement exactly matching the meter size capacity. This is a rare occurrence. You are better off choosing a smaller size meter than line size that enables a lower flow at the low velocity limit. In some cases, a second meter or second transmitter with a lower range is used. For flow feedforward, which is really flow ratio control, flow meter rangeability is a limiting factor especially for startup when often ratio control is more important. For example, distillation columns run solely on ratio control until the column reaches operating conditions where temperature is an inference of composition and can be used to correct the ratio. A feedforward summer is particularly appropriate for volumes with mixing from agitation or recirculation or boiling like columns and is less sensitive to feedforward scaling and flow measurement problems especially at low production rates as noted in the 5/30/2015 Control Talk Blog “Essential Feedforward Control and Operator Interface Tips”.

Most of the literature talks about a process gain and its effect on tuning. This leads one to overlook the effect of instrumentation on tuning. More appropriate terms are an open loop self-regulating process gain and an open loop integrating process gain. These open loop gains are the product of a manipulated variable gain (e.g., valve gain), a process gain (including a hidden factor for composition, pH and temperature per last month’s blog), and a measurement gain. The measurement gain is the simplest and most linear of all gain calculations (assuming linearization has occurred for differential head meters and temperature sensors) being simply 100% divided by the measurement span in the same engineering units as the process gain. The proper use of units gives an open loop self-regulating process gain that is dimensionless and an open loop integrating process gain with units of 1/sec.

The end result is that if you reduce the measurement span by one half, you have doubled the open loop gain. If your PID gain was much lower than possible, often the case for level and composition control, the performance of the loop will be better in terms of a smaller peak error and integrated error for load disturbances. If the PID gain was close to the maximum, the PID gain should be halved for the halved measurement span. The problem here of more oscillation may only show up at low production rates for composition, pH and temperature control when the process gain is higher due to the hidden factor.

The final message is to realize the effect of measurement span on loop performance in terms of truly knowing what the process is doing (measurements being the window into the process) and enabling the best effect on the process in terms of controller action (feedforward and feedback control being the way of correcting the process). Please don’t skimp on technology and number of transmitters needed to achieve the 5 Rs (rangeability, resolution, repeatability, response time and reliability) detailed in the 9/9/2015 Control Talk Blog “What is Truly Important for Measurements and Valves”. We often don’t give our profession and ourselves enough credit to know and make a case for more and better instrumentation. Most of my mistakes as a user early in my career were the result of a misguided attempt to reduce project costs. This is not me putting on a sales hat. I never have been or can be a sales person. This is my honest plea to not sell yourself or our profession short by focusing on cost to the exclusion of performance. Taking the advantage of new technology is the key to advancement. Better loop performance can provide benefits in many unexpected ways. Just have the confidence to do it. Migration projects that simply translate the configuration and do not upgrade the instrumentation and improve the use of PID features and tuning are doing the plant and our profession a great disservice.

For more details on the use of terms such as process gain that are often misunderstood see the 8/24/2015 Control Talk Blog “Understanding Terminology to Advance Yourself and the Profession”.

For a concise presentation of the concepts and details on the effects of measurements on PID control see my ISA book Good Tuning: A Pocket Guide, 4th Edition. If you are up for a more comprehensive view, see my Momentum Press book Tuning and Control Loop Performance - 4th Edition.