how to use limit cycle to tune PID


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I want to tune a PID controller for a heater with limit cycle. Supposed transfer function of the controlled object is not known. As it is
known, the describing function of the limit cycle is N=4h/¦Ð*a, where h is the height of limit cycle, and a is the swing of first order harmonic wave of the input of limit cycle. How to get the ¡®a¡¯? How to calculate the output of controller? How could I do the auto tuning experiment? Could you give me the experiment detail?
We have developed the Z-N method further and eliminated the biggest obstacle: The need for a stable oscillation.

It just requires a setpoint change such that the response shows 2 peaks. The test can stop after the second peak, there is no need to wait
for line-out. From 5 values we can calculate both the process parameters and the PID tuning - with the help of a suitable tool like TOPAS.

Further info is on our Web site under FAQ^Òs and under TOOLS.

Hans H. Eder
[email protected] and [email protected]
The reaction curve is very close to the Xfr function. But it is not the sme. Z_N use reaction curve. All material tell you to perturb the loop. This is not required. You can closely evaluate the two dominant time constants. From there you can plot and evaluate all the
parameters used by Z_N. This method is not published to my knowledge it's mine personal. In years experience it proved valuable tools. I
will not give away, but with some patience and expertise in approximation of function, you can make your own. My method does not open the loop. And for your Xfr function you need to know the differential equation of your system , therefore the governing parameters which is what I'm doing but directly w/o opening the loop.
What you are referring to is Astrom's and Hagglund's method (not Ziegler-Nichols's one) although it used Ziegler-Nichols's tuning rules. You can find its description on US Patent Ofice site (use "Astrom" as a keyword for your search).
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