Good question. The goal is to find the transfer function that best estimates plant's response. Normally one captures the process variable, PV, as a function of the control output, CO, and time. In JCH's data the CO is a step jump of one.

If you use AB PLC's then you can save the PV as a function of CO in a trend file.

So why bother? If you know the plant transfer function then one can calculate the PID gains that will provide almost any desired response. Calculating the PID gains is a different issue but the difficult part is finding the plant transfer function. After that calculating the PID gains is easy. See www.controlguru.com for the formulas for calculating the gains.

Andrew, I don't see how you calculated H(t). It doesn't look right, but the transfer function

is pretty good for a two pole solution. See this ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20SysID%20JCH%20Andrew.pdf You can see that your solution is different from mine but that could be because you used a different evaluation function. I basically use the sum of squared errors or divide that by the number of points to get a mean sum of squared error..

You should know that JCH posted actual transfer funciton back on Oct 28. The actual plant is 5 repeated poles with a time constant of 0.123.

Are you familiar with Runge Kutta and optimizing functions? So far we are only at the beginning stages. Issues that haven't been covered yet include offsets in the plant transfer function, using foricing functions other than 1, and dead time.

Peter Nachtwey