Re: Iterative Technique for PID Controller Tuning

Peter Nachtwey wrote:
JCH wrote:

I also looked again at the output using the second derivative. There is no difference.


???. How can we tell?


What about the example in
http://home.arcor.de/janch/janch/_control/20070407-control-e/

This link doesn't show a step from 0 to 1. I see a sine wave.


I don't see the examples. In fact it isn't clear what you are doing.
It looks like you are just inverting system constants and calling that a controller.
What is F(s)?

Meanwhile I do understand what Pieter and Tim are doing. Here are some comparisons.
ftp://ftp.deltacompsys.com/public/PDF/Mathcad%20-%20T1C1%20PD2D.pdf
Pages 3-4 just show how I did the simulation. Students might like this.
Page 5 The point to point response for my 3 poles at -2*PI*10 is plotted. The response is a critically damped response except for when the output is saturate. Then the under damped system shows its true self. Actually, if I were tuning this I would use an integrator too.
Page 6 Open loop bode plot. I don't usually find these that interesting.
Page 7 Zeros and Poles. Notice that poles are were I put them but as I said before, the zeros can go anywhere. In this case they cause the bobble. In the otherwise smooth response. One can use different gains in the forward path than the feed back path to smooth the response out.
Page 8 The closed loop Bode plot. Pretty mellow compared to what is to come.
Page 9 Pieter's tuning with the Kp at 2.8 and a low pass filter added. Actually it works well for only using the proportional gain but my customers wouldn't like it.
Page 10 A closed loop Bode plot. It looks OK. A least it is safe you can see the resonance peak though.
Page 11 Tim's open loop Bode plot. Weird looking but it works.
Page 12 Tim closed loop Bode plot. Wow! That response is flat but as Tim hinted at above we can make the response as flat as we want on paper. Tim's response is not very realistic UNLESS one uses a Kalman filter or observer to provide smooth acceleration data. but since Tim does custom systems he can do that.

Over the years I have noticed that Tim must start with the zeros. His zeros are always real. The poles seem to be added to filter out the zeros. PID controllers always have two zeros and they are often not real.
Page 14. The closed loop zero and pole locations. Tim, did you intend the zero and pole at about -1 to be there?

Let me know about any errors in the .pdf.

In as much as I can tell by a quick read, the pdf looks correct.

I think my zeros are always real because when they aren't they stick out like a sore thumb in a Bode plot -- when I see the dip in a complex pair, I say "oops" and adjust things, unless I'm intentionally notching out a resonance such as I did in my second example controller.

And no, I didn't _intend_ for the zero and pole at about -1, but I did notice the dip in the Bode plot, which implies their existence.

--
Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
.

Relevant Pages

  • Re: Iterative Technique for PID Controller Tuning
    ... Page 5 The point to point response for my 3 poles at -2*PI*10 is plotted. ... The response is a critically damped response except for when the output is saturate. ... Notice that poles are were I put them but as I said before, the zeros can go anywhere. ... Page 8 The closed loop Bode plot. ...
    (sci.engr.control)
  • Re: Bandpass system identification using IIRs (audio)
    ... You've specified the response relatively very far away from the ... location of the poles and zeros, and with only 6 digit precision, ... like it requires many more bits of precision to specify the ...
    (comp.dsp)
  • Re: IIR and FIR filters
    ... This was wrong - too quick of a response. ... An IIR has non-trivial poles (it could have non-trivial zeros as well). ...
    (comp.dsp)
  • allpass filter
    ... response is known, but not the poles or zeros. ... Can the function 'invfreqz' be used or is there some other ...
    (comp.soft-sys.matlab)
  • Re: filter with arbitrary and variable rolloff
    ... realized by alternating real poles with real zeros. ... If you plot R.B-J's poles and zeros on log paper, ... if i recall correctly there was some manual adjustment ...
    (comp.dsp)
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