What if you could use at-line analyzers and even off-line analyzers for control of batch and continuous processes without the need to retune the PID despite long and variable cycle times? What if the lab analyzers could be used for closed loop control without having to be concerned about the PID becoming oscillatory or going out to lunch as the cycle time increases or when analyzer results are not available? Here is a simple solution and some guidance on how to get the most out of this opportunity.
The dead time from analyzers can be confusing and disruptive to say the least. If simulation tests have the disturbance arriving just as the analyzer gives an update, which tends to be the case in the module setup for testing, the full effect of the dead time is not seen and some may not even believe the additional dead time exists. In reality, the disturbance can arrive anytime in an analyzer cycle time. On the average it arrives in the middle of the cycle time, creating a dead time that is ½ the cycle time. The corresponding phase shift has been confirmed by frequency response analysis. You also need to add the time to get an analysis result once a sample arrives at the analyzer inlet. This latency is additional dead time. For chromatographs where the analysis result is available at the end of the analyzer cycle time, the result is a dead time of 1.5 times the analyzer cycle time. For a chromatograph with a 20 minute cycle time, the additional loop dead time from the analyzer is 30 minutes. Sample processing and transport and multiplex times create additional dead time as quantified by equations in my comprehensive chapter on the effect of measurement dynamics in Tuning and Control Loop Performance – 4th Edition Momentum Press, 2015.
Now just imagine what the dead time could be from lab samples. The dead time is huge (e.g., hours to days). If there is not an enforced schedule of taking samples, doing the analysis, and entering the results, the dead time is extremely variable. This has typically excluded the direct use of off-line analysis for closed loop control. The creation of neural network, step response, and first principle models that is updated by lab results can be a viable solution here. However, if the model is not very good resulting in large and variable corrections, we are back to an instability problem caused by excessive dead time from an analyzer.
A simple solution enables the use of a PID where the process variable comes directly from an at-line or for even off-line analyzer that has a large and variable time between analysis results. The PID must have the positive feedback implementation of integral action where the integral contribution is via a filter whose input is the PID output or external reset feedback. The filter output (integral contribution) is added to the proportional mode contribution (hence positive feedback). If the contribution of the filter is computed as a first order exponential response to the change in PID output or external reset feedback when there is an analysis update, we have an enhanced PID that was originally developed for wireless applications that I think has even a more significant future for analyzer applications. The derivative mode contribution is also computed based on the elapsed time between updates, but for at-line and offline analyzers, the updates are too discontinuous to enable the use of much if any derivative action. See the InTech July/August 2010 feature article “Wireless: Overcoming challenges in PID control & analyzer applications” for an overview.
Tests have shown that if the dead time from the analyzer is greater than the 63% process response time (i.e. process dead time plus process time constant), the tuning of enhanced PID does not change as the time between analyzer results change. The tuning in fact simplifies to be a maximum PID gain that is the inverse of the dimensionless open loop gain (e.g., product of valve or VFD gain, ratio gain, process gain and measurement gain). The measurement gain is a simple function of the measurement span (measurement gain = 100%/span). If the valve or VFD gain and process gain is known and used to update the maximum PID gain, the actual PID gain can be set relatively close to the inverse. A PID gain as much as 50% larger than this maximum will not be excessively oscillatory for the enhanced PID. If the PID reset time is set to equal the analysis dead time, the PID can make a single correction upon an update that will bring the controlled variable back to setpoint within the repeatability of the analyzer. This capability only holds true for processes with a steady state (self-regulating process response). While an improvement in control exists for a batch process (integrating process response) by the use of an enhanced PID, the results are not as dramatic and excessive oscillations can develop for a large analysis time. So what can we do to extend these remarkable benefits we see for continuous processes to batch concentration control?
If you translate the controlled variable from concentration to rate of change of concentration that is the slope of the batch concentration profile, you have created a pseudo steady state and self-regulating process. This also has the benefit of creating a bidirectional response (the slope can decrease as well as increase) whereas many batch processes have a unidirectional response (concentration can only increase) that excludes the use of integral action in the PID structure. Thus, the use of batch profile slope as the controlled variable provides the benefits seen in the application of the enhanced PID for continuous processes. The only major requirement is that the slope be computed and updated only when an analysis result is available. The slope is simply the change in analysis results divided by the time interval between the analysis results.
While I don’t suggest you be so aggressive as to set the PID gain to be the inverse of the open loop gain, you will not need to retune the PID for extremely large and variable times between analysis results as long as you have a reasonable knowledge of the open loop gain. This is pretty exciting to me because ultimately we want to control concentrations in the process. We almost always have a lab analysis. At-line analyzers may be viewed as too expensive and difficult to support and online analyzers may not specifically and accurately measure the component of interest. Of course more frequent analysis results is desirable to detect and correct for disturbances sooner, but at least we can take advantage of analysis results as they become available giving much more repeatable and accurate compensation than what you would gain from manual correction by operators. Of course analysis results would be screened and if strange values are detected, the analysis that is sent to the PID would not be updated. The enhanced PID has no problem waiting longer for a valid result.
My August 2010 white paper PID-Enhancements-for-Wireless gives test results for various applications focusing on wireless opportunities. I understood the potential advantage for analyzers when I wrote the paper but the excitement was all about wireless at the time. While wireless has a great future in terms of reducing installation costs and enabling portable diagnostics, I think the greater opportunity in terms of immediate process performance improvement is the use at-line and offline analyzers for batch profile and continuous process concentration control by checking a PID options box that turns on an enhanced PID and simply setting the PID gain to be less than the inverse of the open loop gain.