Control Notes

Based on the number of Google searches in 2010, the Cohen-Coon tuning rules are second in popularity only to the Ziegler-Nichols tuning rules. Cohen and Coon published their tuning method in 1953, eleven years after Ziegler and Nichols published theirs.

More Flexible than Ziegler-Nichols

The Cohen-Coon tuning rules are suited to a wider variety of processes than the Ziegler-Nichols tuning rules. The Ziegler-Nichols rules work well only on processes where the dead time is less than half the length of the time constant.

The Cohen-Coon tuning rules work well on processes where the dead time is less than two times the length of the time constant (and you can stretch this even further if required).

Cohen-Coon provides one of the few sets of tuning rules that has rules for PD controllers – should you ever need this.

Quarter-Amplitude Damping

Like the Ziegler-Nichols tuning rules, the Cohen-Coon rules aim for a quarter-amplitude damping response. Although quarter-amplitude damping-type of tuning provides very fast disturbance rejection, it tends to be very oscillatory and frequently interacts with similarly-tuned loops. Quarter-amplitude damping-type tuning also leaves the loop vulnerable to going unstable if the process gain or dead time doubles in value. However, the easy fix for both problems is to reduce the controller gain by half. E.g. if the rule recommends using a controller gain of 1.8, use only 0.9. This will prevent the loop from oscillating around its set point as described above, and will provide an acceptable stability margin.

Target PID Controller Algorithm

There are three types of PID controller algorithms: Interactive, Noninteractive, and Parallel. The Cohen-Coon tuning rules were designed for controllers with the noninteractive controller algorithm. If you are not using the derivative control mode (i.e. using P, PI, of PD control), the rules will also work for the interactive algorithm. However, if you are using derivative (i.e. PID control) on an interactive controller, or if your controller has a parallel algorithm, you should convert the calculated tuning settings to work on your controller.

Noninteractive Controller Structure

A Note on Integral Time

The original Cohen-Coon paper expressed the tuning constant for the integral control mode in terms of reset rate (or integral gain) in repeats per minute. Virtually all the modern texts on process control use integral time, and so do most control systems (DCS & PLC). Also, this blog generically uses integral time and not integral gain. Therefore, the tuning rules below use integral time (the reciprocal of what Cohen-Coon used). If your controller uses integral gain or reset rate, you’ll have to invert the calculated integral time (use 1/Ti).

Also, if your controller’s integral time unit is in minutes, you must make your measurements of dead time and time constant in minutes. Likewise if your controller uses seconds, make your measurements in seconds.

When to use the Cohen-Coon Tuning Rules

The Cohen-Coon tuning rules are suitable for use on self-regulating processes if the control objective is having a fast response, but I recommend you divide the calculated controller gain by two, as described above.

If the control objective is to have a very stable, robust control loop that absorbs disturbances, rather use the Lambda tuning rules.

Tuning Procedure

Assuming the control loop is linear and the final control element is in good working order, you can continue with tuning the controller. The Cohen-Coon tuning rules use three process characteristics: process gain, dead time, and time constant. These are determined by doing a step test and analyzing the results.

Step Test for Tuning – (click to enlarge)

1. Place the controller in manual and wait for the process to settle out.
2. Make a step change of a few percent in the controller output (CO) and wait for the process variable (PV) to settle out at a new value. The size of this step should be large enough that the process variable moves well clear of the process noise/disturbance level. A total movement of five times the noise/disturbances on the process variable should be sufficient.
3. Convert the total change obtained in PV to a percentage of the span of the measuring device.
4. Calculate the process gain (gp) as follows:
   • gp = change in PV [in %] / change in CO [in %]
5. Find the maximum slope on the PV response curve. This will be at the inflection point (where the PV stops curving upward and begins curving downward). Draw a line tangential to the PV response curve through the point of inflection. Extend this line to intersect with the original level of the PV (before the step change in CO). Take note of the time value at this intersection.
6. Measure the dead time (td) as follows:
   • td = time difference between the change in CO and the intersection of the tangential line and the original PV level.
7. Calculate the value of the PV at 63% of its total change. On the PV reaction curve, find the time value at which the PV reaches this level.
8. Measure the time constant (Greek symbol tau) as follows:
   • tau = time difference between intersection at the end of dead time, and the PV reaching 63% of its total change.
9. Convert your measurements of dead time and time constant to the same time-units your controller’s integral mode uses. E.g. if your controller’s integral time is in minutes, use minutes for this measurement.
10. Do two or three more step tests and calculate process gain, dead time, and time constant for each test to obtain a good average of the process characteristics. If you get vastly different numbers every time, do even more step tests until you have a few step tests that produce similar values. Use the average of those values.
11. Calculate new tuning settings using the Cohen-Coon tuning rules below. Note that these rules produce a quarter-amplitude damping response. See the next step.

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      The Cohen-Coon Tuning Rules – click to enlarge

12. Divide the calculated controller gain by two to reduce oscillations and improve loop stability.
13. Compare the newly calculated controller settings with the ones in the controller, and ensure that any large differences in numbers are expected and justifiable.
14. Make note of the previous controller settings, the new settings, and the date and time of change.
15. Implement and test the new controller settings. Ensure the response is in line with the overall control objective of the loop.
16. Leave the previous controller settings with the operator in case he/she wants to revert back to them and cannot find you to do it. If the new settings don’t work, you have probably missed something in one or more of the previous steps.
17. Monitor the controller’s performance periodically for a few days after tuning to verify improved operation under different process conditions.

Stay tuned!
Jacques Smuts – Author of the book Process Control for Practitioners

*G.H. Cohen and G.A. Coon, Theoretical Consideration of Retarded Control, Trans. ASME, 75, pp. 827-834, 1953