If you don’t want to get into the technical jibber-jabber, just skip to the Insight and the Rule of Thumb. Be content without the content. If you don’t want to be distracted by reality, get your kicks in the math. Design new feedback control algorithms, despite the fact that PID has been proven to be time-optimal for unmeasured disturbances since 1976, as detailed in the paper by Alan Bohl and Tomas McAvoy “Linear Feedback vs. Time Optimal Control. II – The Regulator Problems”. Focus on setpoint response and don’t be distracted by the reality that loops on continuous processes rarely have setpoint changes, special logic can be developed because a setpoint change is a quantitatively known event, and batch loops have to correct for disturbances and changes in demand. If you have an upset, put it on the process output instead of the process input so it bypasses the process and is like measurement noise. On the other hand, if you have control loops in your plant that affect product quality, onstream time, or process efficiency, please read this tip.
While working on difficult loops such as incinerator and phosphorus furnace pressure control and compressor surge, where disturbances could cause a trip within a second, and in pH control where disturbances could drive the pH to the limits of the scale and the operators’ patience, I was focused on how the controller could react to minimize peak error. In the literature there is little written on peak error, but in a gem of a book by Peter Harriott, Process Control, I found a simple equation for the peak error.
I moved on to figuring out how to minimize energy use and the amount of off-spec material. Here, I recognized that the integrated error was important, where plus and minus areas of the error on a trend chart cancel out like the errors do in large equipment. I found a simple equation in Greg Shinskey’s books listed in Appendix B that showed that the integrated error (IE) was proportional to the reset time and inversely proportional to the controller gain. However, the control literature was totally focused on integrated absolute error (IAE). I resolved the discrepancy by realizing that if the controller was tuned for a non-oscillatory response, the IE and IAE were identical.
I next sought to minimize the time to reach setpoint in automated start-ups and in batch operations. For bioreactors, I found that pH and temperature overshoot were critical and time was not. Furthermore, the disturbances from changes in cell metabolism were so slow that disturbance rejection was unimportant.
Concept: Loop performance objectives should fundamentally address the need to minimize the process variable (PV) response to disturbances and to maximize the PV response to new setpoints (SP). Disturbance objectives are minimization of peak error and integrated absolute error (IAE). Setpoint objectives are minimization of overshoot, settling time, and rise time (time to reach setpoint). The speed of PID tuning sets the practical limit on loop performance for these objectives. Fast (aggressive) tuning reduces peak error, IAE, and rise time. A PID can be tuned faster if the deadtime and the PV ramp rate for a given change in PID output are decreased. Minimization of overshoot, traditionally achieved by slow PID tuning, can now be achieved by using key PID features without sacrificing other loop performance objectives.
Details: All processes have unmeasured disturbances. Minimize peak error to prevent undesirable reactions, safety instrumented system (SIS) or relief activation, and exceeding environmental limits. Minimize the IAE to reduce the quantity of off-spec produced and the quantity of utilities and raw material used. Minimize both peak error and IAE by maximizing gain and minimizing reset time. Maximizing gain is more important for peak error. Overshoot can cause many of the same problems as peak error. Rise time is important for minimizing cycle time in batch processes and minimizing start-up and grade transition time in continuous processes. Minimize overshoot and rise time by increasing reset time and gain, respectively. Add a setpoint filter time equal to reset time to prevent overshoot in a PID with fast tuning. Minimize settling time by minimizing overshoot and rise time. Add logic for smart sequenced positioning of final control elements and setpoint feedforward to further enhance the setpoint response. In the sequencing of controller outputs, position and hold the output at the appropriate output limit until the rate of change of the PV multiplied by the deadtime is near the setpoint. At this point, position and hold the output at a final resting value for one loop deadtime (see Tip #91 for more details).
Watch-outs: Fast (aggressive) tuning decreases the robustness of the controller (its ability to retain a smooth response for increases in deadtime and PV ramp rate for a given output change). External-reset feedback (dynamic reset limit), described in Appendix E, must be used to prevent a burst of oscillations from fast tuning (high controller gain and/or low reset time), causing the PID output to change faster than a final control element or secondary loop can respond for large disturbances or setpoint changes. The use of a setpoint filter in a secondary loop may degrade the ability of the primary loop to reject disturbances.
Exceptions: For processes with exceptionally slow disturbances (e.g., cell culture changes in bioreactors), the peak error and integrated error are inconsequential, even for slow tuning. For batch operations with long cycle times or continuous processes with long start up times that are sensitive to operating point, minimizing overshoot is more important than minimizing rise time (e.g., bioreactor temperature and pH).
Insight: Loop performance objectives can be achieved by maximizing controller gain and minimizing deadtime, reset time, and ramp rate.
Rule of Thumb: Use disturbance rejection tuning, external-reset feedback, and a setpoint filter in your PID controller to achieve loop performance objectives.
Look for another tip next Friday.