Re: PID tuning

[Fred Proctor <proctor-at-cme.nist.gov>]

EMC PID tuners,

I had a guest researcher here at NIST for a few months, looking into
automatic system identification and PID tuning. I have a few MS Word
pictures showing what he did that I WinZip'ed up and put on the FTP site
in the emc/emcsoft directory, as "pidtuning.zip". They're 8.5x11 posters
that show the theory and some figures for our Bridgeport machine.

It works for systems without a tachometer. We were trying to get the
performance (following error) to be equal to a machine with tachometers,
to reduce cost.

The idea is to hit the axis with a step voltage, and log the resulting
position v. time. The curve rises to some steady state velocity. The
steady state velocity is a function of applied voltage. The time to,
say, 75% of steady state is the same. For several runs, you can get an
average of steady-state velocity per applied voltage, and average rise
time. These can be used to deduce PID gains.

The student, Kees ("Case") Stolk, from the University of Twente in the
Netherlands, wrote a Tcl/Tk script that automates much of the process,
including going into machine-off, opening the log, running the DAC out
command, saving the log, storing multiple runs, and popping up PID
gains. It's pretty slick. I'll put this up on the FTP site once I verify
that it works with the new release.

I ran this on the Bridgeport and the resulting gains outperformed my
manually tuned gains for current mode (no tach), and equalled the
manually tuned gains (with a FF1 feedforward term) in velocity mode
(with a tach).

He used these references:

Modeling of DC Motors:
Kuo, Benjamin C., Automatic Control Systems, Prentice-Hall, Englewood
Cliffs, NJ, 1981. 

Nonlinear Least Squares Model Fitting:
Press, William H. et al, Numerical Recipes in C: the Art of Scientific
Computing, Cambridge University Press, Port Chester, NY, 1992. 

PID controllers:
Åstrom, K., and Haglund, T., PID Controllers: Theory, Design and Tuning,
Instrument Society of America, Research Triangle Park, NC, 1995. 

Internal Model Control:
Rivera, M., Internal Model Control for PID Controller Design, 1986. 

PID tuning:
Lieslehto, J., Tampere University of Technology, Tampere, Finland,
http://www.ae.tut.fi/~juke/java/pidtuning/index.html

This last one is a good web reference for PID tuning, with Java applets.

--Fred