# Ziegler-Nichols Tuning method

### Ziegler-Nichols open-loop tuning procedure

The first process tuned in simulation was a “generic” process, unspecific in its nature or application. Performing an open-loop test (two 10% output step-changes made in manual mode, both increasing) on this process resulted in the following behavior:

From the trend, we can see that this process is self-regulating, with multiple lags and some dead time. The reaction rate (R) is 20% over 15 minutes, or 1.333 percent per minute. Dead time (L) appears to be approximately 2 minutes. Following the Ziegler-Nichols recommendations for PID tuning based on these process characteristics (also including the 10% step-change magnitude m):

Applying the PID values of 4.5 (gain), 4 minutes per repeat (integral), and 1 minute (derivative) gave the following result in automatic mode:

The process oscillations follow a 10% setpoint change (from 60% to 50%), and take almost an hour to settle. Clearly, this is less-than-robust behavior. The controller is much too aggressive, which is why the process oscillates so much following the setpoint step-change.

Looking closely at the PV and OUT waveforms, we see their phase relationship is nearly 180, consistent with what we would expect for a reverse-acting controller with proportional action dominant. If integral or derivative action were primarily responsible for the oscillation, we would see the influence of an additional 90 phase shift characteristic to those actions (integral naturally produces a -90 phase shift, while derivative naturally produces a +90o phase shift, for any sinusoidal function). Thus, if the oscillations were primarily the result of excessive integral action, we would expect the OUT wave to lead the PV wave by nearly 90 (180 from reverse action − 90 from integral action = 90). If excessive derivative action were primarily responsible for the oscillations, we would expect the OUT wave to lag the PV wave by nearly 90 (180 from reverse action + 90 from derivative action = 270 = −90). Since we see a phase shift of the oscillations between OUT and PV very close to the 180 predicted by proportional action, we can be sure this controller’s response is dominated by proportional action, which would be a good place to start “de-tuning” this over-exuberant controller if we were inclined to modify the Ziegler-Nichols tuning recommendations.

Ziegler-Nichols closed-loop tuning :-

Next, the closed-loop, or “Ultimate” tuning method of Ziegler and Nichols was applied to this process. Eliminating both integral and derivative control actions from the controller, and experimenting with different gain (proportional) values until self-sustaining oscillations of consistent amplitude were obtained, gave a gain value of 11:

From the trend, we can see that the ultimate period (Pu) is approximately 7 minutes in length. Following the Ziegler-Nichols recommendations for PID tuning based on these process characteristics:

It should be immediately apparent that these tuning parameters will yield poor control. While the integral and derivative values are close to those predicted by the open-loop (Reaction Rate) method, the gain value calculated here is even larger than what was calculated before. Since we know proportional action was excessive in the last tuning attempt, and this one recommends an even higher gain value, we can expect our next trial to oscillate even worse. Applying the PID values of 6.6 (gain), 3.5 minutes per repeat (integral), and 0.875 minute (derivative) gave the following result in automatic mode:

The process oscillations follow a 10% setpoint change (from 60% to 50%), and are nowhere near settled after an hour’s worth of time. Once again we see the nearly 180o phase shift between the OUT and the PV waves, indicating proportional-dominant controller response (with reverse action). As expected, this is far too much gain for robust control!

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