It is well known that measurement noise reduces or eliminates the use of derivative action. Since rate is not popular (another story), the exclusion of rate is not seen as a significant disadvantage even though temperature loops could benefit from rate since it can compensate for thermowell and heat transfer surface lags and reduce overshoot. In the 1980s and 1990s many temperature loops suffered from the prevalent use of 12 bit I/O and wide range thermocouple input cards that caused a resolution error of 0.25 degrees in a signal whose true rate of change of temperature was usually much slower than 0.25 per minute. The result was a poor signal to noise ratio. We tried to filter the heck out of the signal so we could use rate but this added another lag. Fortunately, today we have 16 bit I/O systems and smart transmitters so that signal resolution is better than the sensitivity of the sensor – just one of the many reasons to get your automation system into the 21st century.
A wider consequence of measurement noise not so readily recognized is the reduction in permissible controller gain. For loops with a true integrating or “near integrating” response where the process variable ramps when the controller is put in manual, the high limit for controller gain is way above the normal range of consideration. For example, level and batch temperature loops normally have a ramp rate so slow (0.000001 %/sec), that the controller gain could be higher than 50 if there was no measurement noise and the reset time was not too small (a big “if”). Since the peak and integrated errors are inversely proportional to the controller gain, these and other loops could significantly benefit from a smoother signal and better tuning.
What is measurement noise and where does it come from? In my book, measurement noise is any fluctuation in the measurement signal that should be ignored by the controller. If the controller reacts to a fluctuation it really cannot correct, the loop inflicts a disturbance upon itself. If resolution problems are behind us, the biggest sources of measurement noise are inadequate axial (back) mixing, bubbles and foam in liquids, liquid droplets in steam or gas, inconsistent profiles, lqiuid and pressure waves, and insufficient measurement rangeability. Measurement noise is amplified by high process gains (e.g. steep titration curve for pH control) and sensitive measurement ranges (e.g. – 0.25 to 0.25 inches of water column for draft pressure control). The Table in MeasurementNoiseSourcesControlBandAmplitude.pdf provides a summary of my assessment of noise sources, control bands (allowable control error), and noise amplitude (peak to peak) for common loops. The noise amplitude should be less than ¼ the allowable control band for fast disturbances. A reduction in noise amplitude is ideally achieved by eliminating the source of the problem. If the correction is not practical or is not yet implemented, a signal filter is often used to attenuate the noise. The ratio of the amplitude of the filtered signal to raw signal is roughly proportional to the ratio of the period to the filter time when the filter time is greater than the period (simplification of the Bode plot attenuation equation). The filter time becomes effectively additional deadtime in a loop when it is less than the process time constant. If the filter time is considerably greater than the process time constant, the measured process variable amplitude may look better but the real amplitude is worse because you are seeing a very attenuated version of the real world. I have seen where an ISA conference speaker said he almost did not get permission to give his presentation because the improvement was so great it was considered proprietary. He had increased the measurement filter so much he was drawing a straight line no matter what was happening in the process. I have seen where a biochemist withdrew a temperature sensor halfway in its thermowell and proudly said this was the way to run the bioreactor because the temperature reading was so much smoother. Then there were the cases of sand in thermowells and the mounting of extruder temperature sensors in massive blocks of metal giving the illusion of smooth temperature. These are all old stories but I am sure people are being fooled today especially since one can so easily add a filter via the damping setting in the transmitter, the analog input block, and the PID block. Provided the filter setting is not so large it eliminates any recognition of process variability, the key symptom of too large of a filter setting is a long control loop period or recovery time if the controller gain is not so detuned you can’t see the effect of more loop dead time (see Advanced Application Note 5 for estimation of how the detuning of a controller is equivalent to additional deadtime in the loop). To prevent the loop from inflicting disturbances upon itself by reacting to noise, the filter time should be set just large enough to keep the fluctuations in the controller output smaller than the resolution (stick-slip) of the final control element (e.g. control valve). A less desirable but widely used way of keeping the fluctuations in the controller output small enough is to reduce the controller gain.