Can Ziegler-Nichols Equations Be Used to Tune Non-Interactive Controllers?

Our Experts Chime In and Talk about How Tuning Has Changed Since We Entered the Digital Age

By Bela Liptak

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Q: Thank you for your contributions to our industry. I have learned much from reading your articles and columns. I have a simple question to which I have not found a definite answer.

In general, using the Ziegler-Nichols (Z-N) equations, we can calculate a starting set of tuning constants. My question is, are the calculations based on interacting controllers? Can they be used for non-interacting controllers? If they have been developed on non-interacting controllers, can they be converted for tuning interacting ones?

Some references and text books state that the Z-N equations are for non-interacting controllers, but I have read that the interactive controller was used, and that you can use conversion tools. What do I tell students? I'm tending to say that Z-N was developed using an interactive controller, and they would need to convert to a non-interacting form.

Don Lovell

A: Your question concerning the Ziegler-Nichols controller is fully answered by a dozen excellent comments given below by my expert colleagues. Therefore, I will not focus on this narrow topic, but will say a few words about tuning itself and about what has changed since we entered the digital age.

Tuning a controller is like teaching a pilot how to keep his/her vehicle on course. This requires that the "personality" of the controlled process (the vehicle) be fully understood by the pilot (the controller). The dynamic response of a self-regulating process to an upset (a step change in load or setpoint) can be described by its reaction curve (Figure 1). When a programmer at a DCS supplier of, say, Foundation fieldbus, or at a PLC supplier is preparing a tuning algorithm, he or she assumes that all that is needed is the data I show on Figure 1 (A/B, Td and R) to calculate the required settings for the controller's gain ("P," which responds to the present error), for integral ("I", which considers the error accumulated in the past), and for derivative ("D", which predicts what the error would be in the future if not corrected). When done, programmers think that the job is done. In a way, they are correct, because that is all that a programmer is qualified to do.

This is the point where the role of the process control engineer starts. Why? Because most processes are not that simple. When we are controlling a nuclear reactor or a fracking process, etc., the values of B/A, Td and R are not constants, but variables for many reasons: Because PID loops interact and each has its own safety limit; because some of these loops are not self-regulating; because the continuous measurements of B/A, Td and R are difficult, if not impossible, to obtain; because noise prevents accurate measurements, etc., etc. Therefore, the duty of our profession is to understand this.  If automatic control does not work, the system will be switched to manual and will not only operate at low efficiency and produce low quality products, but in critical processes, safety will be lost.

Therefore, we must understand that the process must be fully understood before it can be controlled (and a programmer is not qualified to do that), and that the respect for and recognition of our profession will not grow, unless we, the process control engineers, take on the responsibility to check and modifying the programmer's algorithms as needed.

Béla Lipták

Also Read "Reader Feedback: Basic PID and Control Issues"

A: The Z-N tuning rules were developed on a Taylor Fulscope controller, which was interacting with parallel feedback of the output to the integral (I) and derivative (D) restrictors. This compares to the Foxboro Model 40 controller which had a serial feedback connection through the two restrictors. (Foxboro patented the serial configuration.)

For both controllers, the effective value of integral time was the sum of the two time constants: D + I, and the effective value of the derivative time was 1/(1/D + 1/I). For the Foxboro controller, the effective proportional gain was K(1 + D/I), but for the Fulscope controller it was K(1 + D/I)/(1 - D/I).

The last term had a powerful effect as D approached I, and if D > I, the controller would work backwards. Hence, Z-N settings fixed the D/I ratio at 1/4, whereas more like a ratio of 1/2.5 was optimum with a Foxboro controller; the M-40 had a mechanical stop that prevented D from exceeding I.

This is covered in some detail on pp. 71-73 of my book, Feedback Controllers for the Process Industries, McGraw-Hill, 1994, under the heading of "Single-Stage Interacting Controllers."

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  • <p>Interactive and non-interactive forms have equivalent values for P, I, D with quick conversions. In Z-N I and D depend on dead-time using the interactive form. Tuning is then reduced to setting P/Gain from computed values or closed loop response and P further adjusted based on closed loop response. In the interactive form D/I is 0 to .5, and is not altered by P changes. Thus in the field the interactive form is considerably easier to adjust usually only changing P.</p>


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