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Effect of measurement lag over time constant

Hola Greg, how important is to determine the lag caused by my measurement system?

At a bump test I will note the associated delay time and the change in my process variable; any lag in my measurement will be already be acting over the observed dynamics. Since the computed tuning parameters will be based on these, they will be already acounting for such measurement lag; will it make a difference determining how much is coming from such source?

When will it be important to determine the measurement lag?



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  • Excellent question that really made me think. The motivation to identify the size of the measurement lag is in the knowledge whether the lag is causing a significant deception in the view or delay in the correction of process variability. Excessive lag in many cases can be fixed by an adjustment, replacement of the sensor, or redesign of the installation. The solution is often within the responsibility and capability of the automation engineer.  Since the measurement is the window for analyzing and controlling the process, your knowledge and solution can be essential.

    Deception occurs when the measurement lag is greater than the ultimate period of the loop. The large measurement lag acts as a filter attenuating process variability. The measurement amplitude of an oscillation is less than the actual amplitude. Doing the wrong thing (i.e. making the measurement lag larger), makes the trend chart look better in terms of less variability. If the measurement lag becomes the largest time constant in the loop, an increase in the lag enables an increase in the PID gain furthering the deception that the measurement lag is beneficial. Normally, the reset time cannot be decreased and may in fact need to be increased to stop a reset cycle. So the clue may be a slower more oscillatory response. The ratio of the measured to actual process variable amplitude is the period of the oscillation divided by 6.28 times the lag. This simple relationship enables one to estimate the degree of deception and the actual process variable amplitude from the observed amplitude for a given oscillation.

    A noticeable effect of measurement delay occurs when the measurement lag is more than 10% of the PID reset time. The effect is seen in terms of an increase in the measurement peak and integrated error for a load disturbance and the rise time for a setpoint change. The effect becomes intolerable if the additional delay from the lag increases the total loop dead time to the point where the PID must be re-tuned. This occurs when the additional dead time from measurement lag increases the total loop dead time to be greater than the implied dead time based on the old tuning. The result is often an oscillatory response from excessive integral action. The implied dead time is ½ and ¼ the sum of lambda plus the original loop dead time (dead time with no measurement lag) for self-regulating and near or true integrating processes, respectively.   If the measurement lag is smaller than the process time constant, the additional dead time comes from the larger measurement lag itself. If the measurement lag is greater than the process time constant, the additional dead time comes indirectly from a greater fraction of other time constants becoming effectively dead time.  A clue as to whether the measurement lag has increased is a process variable that oscillates with a larger period. Due to attenuation /deception, the amplitude may look less.

    If the measurement lag becomes the largest time constant in a loop for an integrating process or even worse for a runaway process (e.g. highly exothermic reaction), the deterioration is huge. Setting the PID rate time equal to a large measurement lag is important. For runaway processes a large measurement lag can make the maximum allowable PID gain approach the minimum allowable PID gain needed to prevent the process from accelerating and reaching a point of no return. The window of allowable PID gains can close in a runaway process due to a large measurement lag ( a serious safety risk).

    How do you identify the measurement lag? How do you know the primary or secondary time constant identified by software is in the measurement, process, or final control element (e.g. control valve or variable frequency drive)? There are few easy cases. The PID process variable filter time and transmitter damping should be checked and reduced if they are causing deception or deterioration per above guidelines. The settings should be minimized if the settings are larger than 10% of the reset time. There is a chicken and egg possibility, in that the reset time may be large due to a large measurement lag.

    If a step change in flow can be made to a process input, the open loop response of the measure variable will exclude the effect of the final control element lag from its rate limited exponential response and inherent time constant (another story). Also, the time constant for a small sliding stem valve or a variable frequency drive with insignificant rate limiting in the drive setup is negligible for small changes (e.g. <2%) in PID output.  This still leaves us with the quandary of how to know if the primary or secondary time constant identified is in the process or the measurement.

    For fast process where there is negligible back mixing the process time constant is small. The process time constant is less than 1 second for gas flow reactor and furnace composition and temperature control by manipulation of feeds or fuel, liquid or polymer pressure and flow control, and inline pH control.  A primary or secondary time constant much larger than 1 second in these loops is most likely a measurement lag.  The electrode time constant is about 2 to 6 seconds for a new clean electrode and reasonable velocity (e.g. > 5 fps). An aged or coated glass electrode can increase the measurement lag from a few seconds to minutes, even hours.  A loosely fitted temperature sensor in a thermowell or even worse a thermocouple in a ceramic protection tube will cause the measurement lag to increase from seconds to minutes due to the air gap or ceramic tube acting as an insulator.

    Transmitters and electrodes can be tested in the shop to determine the measurement lag excluding any installation effects. The transmitters and electrodes should not be cleaned, which would eliminate the effect of coatings. Electrodes are inserted into buffer solutions or even better process samples at operating conditions. Temperature sensors still in their thermowells can be inserted into temperature baths. Velocity affects the electrode and thermowell response, so a stirrer should give about the same velocity as in the process installation.  The measurement lag is ½ the 86% response time assuming the measurement delay is negligible. Waiting for a more complete response (e.g. 95% response time) especially for pH electrodes causes less relevant and more inconsistent results.

    Greg is a retired Senior Fellow from Monsanto-Solutia and an ISA Fellow. Greg was inducted into the Control “Process Automation Hall of Fame” in 2001 and received the ISA Life Achievement Award in 2010.