Cascade control tuning

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FIGURE 2:

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There are several reasons why open loop tuning is seldom used on batch reactor control. One is that it requires the switching of the controller to manual; the other is that it requires the upsetting of the process. If you're not sure if the process is self-regulating or not, you should not try this method due to the risk of causing a run-away reaction or stopping the reaction. To reduce the size of the upset, operators tend to make the step change (?m) small (3% in the example above). But a small step usually results in a small response, which, particularly if the process is noisy, can be hard to read in terms of determining where the 0.63K or the inflection point is and what the slope of the tangent at the inflection point should be.

Closed Loop Tuning of Non-Interacting PID
In this tuning method, the goal is to determine the gain or proportional band that causes sustained, un-dampened oscillation (Ku or PBu) and to measure the corresponding ultimate period of that oscillation (Pu) by measuring the time it takes for one cycle of the sustained oscillation to be completed. 

The tuning test is performed by first setting the dynamics of the PID master to zero (integral time to infinity/repeat, derivative time to zero) and set the proportional at the expected normal value. Or if that is not known, at 100%. Wait for the process to stabilize. When the temperature is constant, introduce an upset by moving the set point up or down (whichever is safer) by 2% for a minute and then return it to its original value. This upset will result in one of the curves shown below. If the response curve resembles A (un-stable, runaway oscillation), the gain is too high (PB too narrow). If it looks like C (stable, damped oscillation), the gain is too low. In either case, the controller gain is adjusted until a state of sustained, undamped, sinusoidal (not limit cycle) oscillation is reached.Once this state is established, one reads the ultimate proportional band that caused it (PBu) and the period of this ultimate oscillation (Pu).

FIGURE 3:

(Click the image to view a larger .pdf version of the figure above.)


The advantages of closed loop tuning are that the controller does not need to be switched to manual, but stays in automatic and therefore all loop components are evaluated during the test and that the PBu and Pu readings are easily made. The disadvantage is that it takes a long time, and when doing it for the first time, one does not know how high the amplitude of the temperature cycle will be. Tuning by this method takes a long time because one needs to wait for several cycles of the oscillation to develop before knowing that the cycling is sustained and undamped. The cycle period is between 3-5 dead times, while the dead time of temperature control loops range from a few seconds to several minutes. Therefore, one might need to wait for three or four cycles that can easily take an hour before finding out that the oscillation was not undamped and that another test is needed. 

Ziegler-Nichols suggests setting the PID at PB = 0.6PBu, I = 0.5Pu (minutes/repeat) and D = 0.125Pu (minutes). Ziegler-Nichols did not consider the Td/T ratio of the process, kept the I and D settings 4:1 apart, and did not differentiate between interacting and non interacting controllers. Over the years we have learned that as the Td/T ratio rises, the PB, I & D settings must drop. We also learned that interacting controllers should be tuned with higher PB & D and lower I settings than non-interacting ones, and that I&D settings should be only 3:1 apart on first order (linear) processes. We have also learned that the correct tuning settings vary as a function of how the upset was introduced (load or set point change) and who’s recommendations are being followed (Z-N, CCC, IAE or Shinskey).

Therefore, while it is better to tune the PID master by the Z-N method then to not tune it at all, I much prefer the damped oscillation, model-based, and other, newer methods that are described in detail in my handbook.

Béla Lipták, Ask the Experts Moderator

THE MANUAL tuning of temperature cascade loops for chemical batch reactions is one of the most interesting control challenges. I devoted some 200 pages in my handbook to the various aspects of it. Here, obviously, I can not cover the topic to that depth, but I will try to give you a brief summary. I should first mention that the tuning I will describe is only for the exothermic (cooling phase) of the batch reaction. As you know, the batch process has several stages. I will not cover the heat-up phase, the switching from heat up to cooling, endpoint detection, or stripping controls.

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