What Have I Learned? – Cost and Source of Oscillations (Part 4)

I need to minimize the time delay to dinner so I will minimize this discussion of how to minimize the oscillation from analyzer sample time delay. So many minimums and so little time.

Composition measurements with sample systems and cycle times termed “at-line analyzers” offer incredible opportunities for understanding and controlling what affects what you ultimately want to know for a process output stream – the composition. The sample time delay from the cyclic results from an at-line analyzer is more problematic than the transportation delay for a continuous measurement via a probe in a sample line termed “in-line analyzers”. The “at-line analyzer” has a stepped response and sometimes spikes from bad readings with no intermediate values. The result is a propensity for oscillations when used for feedback control.

One might think a deadtime compensator would help the traditional PID deal with the deadtime from a cyclic time delay. However, these deadtime compensators are notoriously sensitive to a mismatch between the actual process deadtime and the estimated deadtime used in the compensator. The loop deadtime from unsynchronized digital devices and at-line analyzers is extremely variable and can at best be estimated after the fact.

It is interesting that the solution for suppressing oscillations from at-line analyzers resulted from improvements to the PID developed for variable updates from wireless devices (see February 9, entry on “Unexpected Wireless Benefits”). The control solution for WirelessHART requires no estimate of deadtime and is more robust than a traditional PID. The PID execution is kept relatively fast (once per second). The contribution of the proportional mode is computed every execution. The proportional action every scan provides a good set point response for a PID structure with proportional action on error. The contribution of the integral and derivative mode is only computed when the measurement has changed per the resolution setting of wireless device. Furthermore, the time used in the integral and derivative mode calculations is not the scan time but the elapsed time from the last measurement update.

The use of the elapsed time in the integral calculation and a reset time the same as the process time constant provides an integral correction that is equal to and opposite to the process response in the elapsed time. Even if the process time constant changes, making an integral correction only when there is update eliminates the extraneous ramp of the integral mode in the traditional PID acting on old information. The suspension of integral action until there is new information also helps the PID deal with a valve that is momentarily stuck provided position read back is used for dynamic reset limiting.

The use of elapsed time instead of PID execution time in the derivative calculation spreads the change in the process over the elapsed time rather than taking it to all occur in the single execution time. This more intelligent rate action eliminates spikes in the controller output that would occur in a traditional PID when there is an update.

The wireless PID greatly stabilized the glucose control of a bioreactor which had at-line analyzer sample time delays that varied from 6 to 12 hours. The improvement is greatest for self-regulating processes and controllers tuned for maximum performance. The suppression of oscillations can be seen on slides 29 – 33 of the Interphex 2009 Presentation “Advances in Bioreactor Modeling and Control.”