I have found over and over again that the simplest and best thing you can do for level, pressure, pH, and temperature control on vessels and columns is to simply increase the reset time by a factor of 10. It is truly amazing how many of these loops are in a reset cycle. Current practices for operator interfaces and human nature are big reasons for loops having too much integral action.
Operator screens typically have lots of equipment and piping graphics but show digital values for operating conditions. The PID controller faceplate shows the setpoint (SP), process variable (PV), and output (OUT) as bars besides the digital values. The operator looking at these displays has no sense of direction. Several times I have gotten urgent phone calls that something was wrong with the PID controller. In one instance, the operator was looking at the faceplate for a temperature loop on a reactor, where cooling occurred below and heating occurred above the split range point. The temperature was below setpoint by a degree or two and the operator, who was intently watching the faceplate, said the PID needed to be fixed because the cooling water valve was open instead of the steam valve. I have shown a PID with similar conditions in presentations and asked which valve should be open. I haven’t had one person answer that the cooling water valve should be open. However, if I show a trend chart of the PV trajectory, I get more correct answers.
Integral action will do what a human would do. Integral action just knows the temperature is low and thinks heat should be added. In this case, the contribution from the integral mode is to continually ramp up to add more heat. The contribution from the proportional mode is to decrease to add cooling. People looking at the faceplate naturally decrease the reset time to get what they think is the proper action. People have no sense of deadtime and little sense of trajectory unless the trend chart is set up to display them (for example, per the Checklist in Appendix C. For more on this problem, see the modeling and control blog Are We Misleading Our Operators?
Processes with a slow, gradual response by virtue of a large, back-mixed volume afford the opportunity for a higher PID gain. Vessels have back mixing by virtue of agitation and recirculation. Trays in columns have back mixing from the turbulence of vapor flow going up and reflux flow coming down. The response of each volume is mostly characterized by a process time constant for continuous operations. Vessels can have a process time constant of an hour. Large columns can have a process time constant of five hours. Equipment with large process time constants has a slow, gradual process response. For level and batch operations, volumes have an integrating response that is extremely slow, perhaps 0.0001% per sec. These processes benefit from more proportional action to provide enough muscle to make the process move faster. In most cases, the output should be driven past its final resting value to get the PV to setpoint faster.
Concept: Vessels and columns have a gradual response that requires muscle, with preemptive action based on the approach to setpoint. The controller gain provides this action through the proportional mode. Integral action has no sense of the approach to setpoint and will cause overshoot. Most temperature loops on vessels and columns have a gain that is too low and a reset time that is much too low. Temperature noise is normally negligible due to the slow gradual response of the volume.
Details: Ballpark estimates of useful gain and reset times for temperature loops on large, well-agitated liquid reactors are 25 and 10 minutes, respectively. Ballpark estimates of useful controller gains and reset times for temperature loops on columns are 2.5 and 100 minutes, respectively. Use a near-integrator tuning with Lambda times approaching the deadtime to get these tuning settings. Pressure loops on this equipment may have a controller gain that is about the same as the temperature controller gain. The reset time for pressure control is usually much smaller than the reset time for temperature control, especially for columns, because the vapor response is much faster than the liquid composition response. Noise free level loops on this equipment may have a controller gain five times larger than the temperature controller gain. For horizontal reflux drums, the level controller gain can be even higher. The actual controller gains applied depend upon flow and temperature measurement scale ranges, valve sizes, and process gains. For pH loops on well-mixed vessels, the reset time is comparable to the temperature controller reset time. The controller gain depends heavily upon the slope of the titration curve. The pH controller gain can be as high as 5 for weak acids and weak bases. For strong acids and bases, the controller could be a factor of 100 lower.
Watch-outs: The controller gain is proportional to the time constant time to deadtime ratio but is also inversely proportional to the open loop gain. The open loop gain is the product of the manipulated variable gain, process gain, and measurement gain. Consequently, the controller gain depends upon valve sizes, process relationships, and measurement scales. A reasonable reset time is about four times the deadtime. Runaway reactors may require a reset time that is a factor of ten larger. For temperature loops on vessels, the deadtime depends upon the turnover time from mixing, thermal lags, and sensor lags. For columns, the deadtime depends on the number of stages and the volume per stage. See the Control Talk blog The ABCs of Controller Tuning for the inside story on tuning.
Exceptions: Vessels with poor mixing or narrowed measurement scale ranges have lower controller gains. Column temperature loops that manipulate steam flow will have much smaller reset times.
Insight: Temperature loops on mixed volumes, gas pressure loops, and level loops need much larger than expected controller gains and reset times.
Rule of Thumb: See if increasing the reset time by a factor of 10 for loops on vessels and columns will reduce overshoot and oscillations.