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Comments on the Ziegler-Nichols tuning method

 

The overwhelming majority of control practitioners are familiar with the Ziegler-Nichols tuning methods.  If not from personal experience, then at least from reading or hearing about the tuning rules they developed. Although their tuning rules are widely published and referenced (do a Google search on Ziegler Nichols), I have met only a few control practitioners who have actually read their original paper Optimum Settings for Automatic Controllers published in Transactions of the A.S.M.E., November 1942, and pondered the fundamental premises of their work, and applicability to processes in general.

I think the Ziegler-Nichols tuning rules were indeed ground-breaking and still are elegant, however, there are a few potential problems to consider when applying theses rules.

Issue #1 – Quarter-amplitude damping

Ziegler and Nichols chose quarter-amplitude damping to be “optimum” control loop response.  Although this result lies neatly in the middle between a completely dead controller and an unstable control loop, you should realize that quarter-amplitude damping, by design, causes the process to overshoot its set point and to oscillate around it a few times before eventually settling down.  For many processes, overshoot cannot be tolerated and oscillations are a bad thing.  For these sensitive processes, the Ziegler-Nichols tuning rules cannot be used, unless the controller is detuned from the original settings.

Issue #2 – Low robustness (Close to unstable)

Ziegler and Nichols describe in detail how they designed their tests and how they arrived at the “optimum” tuning settings.  Quite simply, they increased controller gain until they reached the point of instability and then backed the controller gain down by a factor of 0.5 (e.g. if a controller gain of 0.8 makes a loop border-line unstable, they recommend using a gain of 0.4).  This gave them exactly the quarter-amplitude damping they were aiming for, but it makes the margin to loop instability very small.  An equal-percentage control valve’s gain can easily increase by a factor of 10 as the valve position changes between closed and fully open.  The gain of a feed heater temperature loop can quadruple if the process flow through the heater goes from maximum down to 25%.  In both of these examples (and numerous others), a control loop tuned with the Ziegler-Nichols rules can quickly go unstable.

Issue #3 – Poor response on dead-time-dominant processes

Under Ziegler-Nichols tuning, the controller’s integral setting is set proportional to the process dead time: the longer the dead time, the slower the integral will be.  This is acceptable where dead times are short in relation to the process time constant, but not so for dead-time-dominant processes.  For the latter, the integral action becomes too slow, and the loop’s ability to recover from a process upset is diminished.

Issue #4 – Very sensitive to underestimating the dead time

The Ziegler-Nichols open-loop response test (called the “reaction curve” method in their paper) requires graphically measuring the process dead time and time constant on a plot of the process’ response after changing the controller’s output.  If the dead time is significantly smaller than the time constant, its measurement becomes exceptionally difficult – especially due to the effect of process noise and disturbances on the process’ response curve.  Because the Ziegler-Nichols tuning method relies on an accurate measurement of dead time for the calculation of controller gain, integral, and derivative settings, an incorrectly measured dead time will result in a very poorly tuned controller.

Issue #5 – Very sensitive to control valve problems

The ultimate cycling, or ultimate sensitivity, method of Ziegler-Nichols tuning can produce grossly incorrect controller settings if the control loop has a faulty control valve.  This tuning method requires a very linear response between the controller output and process response to obtain the ultimate gain and ultimate period. Control valve dead band and stiction will affect both the ultimate gain and ultimate period, and you will end up with a poorly tuned control loop.

General considerations

In addition to the issues listed above, there are a few additional items to keep in mind when using the Ziegler-Nichols tuning rules:

  • The time units of your process measurements must be the same as your controller’s integral and derivative time units. For example, if your controller’s integral and derivative time units are in minutes, make your process measurements in minutes or convert them to minutes.
  • The rules were developed for the series (interactive) controller algorithm. Controller settings calculated using the Ziegler-Nichols tuning rules must be converted when applied to PID controllers with the ideal (non-interactive) algorithm and PID or PI controllers with the parallel algorithm.
  • The original rules had an integral unit (reset rate as they called it in their paper) of 1/minute, while many controller types also have their integral unit in minutes (or of course, 1/second or seconds). Also, the rules calculate controller gain (called sensitivity in their paper) and not proportional band, which is used by a few controller types.  Be sure to do the proper conversions between calculated controller settings in the units used by Ziegler-Nichols to the units used by your controller.

In Ziegler and Nichols’ defense

In Ziegler and Nichols’ defense, I’ll be quick to point out that many of these issues and most considerations apply to several other tuning rules too.  It is important that you, as a controls practitioner, don’t just blindly apply a tuning rule, but that you understand its objectives and how controllers and tuning rules work.

 

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

 

One Response to “Comments on the Ziegler-Nichols tuning method”

  • Glen:

    The problem is that Ziegler Nichols is based on a faulty premise. One normally does not adjust the controller gains to alter time domain response. Time domain response should be adjusted via a prefilter. One adjusts the controller to obtain desired frequency domain characteristics.

    The other fundamental flaw involved here is that the PID controller is a low order controller. Such a low order controller unnecessarily restricts the ability to realize desired frequency domain characteristics.

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