Transfer function: s^2+196/(s^2+100)
Design a PID controller such that the first spike in the frequency
response plot(bode diagram)is smoothed out.
The step response is oscillatory, but the Z-N tuning rules require it
to be monotonic.
The nyquist plot is singular due to poles on im axis, but Z-N rules
require it to intersect the negative real axis.
Can a PID controller be designed using Z-N rules?
Thanks

snovite wrote in news:48add45d-2fcc-456e-bce5-
snipped-for-privacy@m77g2000hsc.googlegroups.com:
Depends on whether you're talking about tuning on paper or tuning a real
system.

This looks strange to me.
This sounds like home work to me.
Yep, one can see the damping factor is 0.
Yes, but I don't think they will work well for this.
Yes, this is obviously a homework problem. How do you get a transfer
function where the order of the numerator is the same as then
denominator?
I didn't have time to look at this in detail and take into account the
zeros. I can place the three closed loop poles at -10 with the gains
of
Ki=3D5.012 Kp=3D1.02 and Kd=3D0.153.
I used pole placement. If this is a student problem then the answer
will not do you much good without knowing how to place the poles.
One word of warning. I ignored the s^2 in the numerator. The best
solution may require separate gains for the forward path so the result
is a two degrees of freedom PID.
Look up pole placement or look for some of my threads where a mention
Ackermanns method.
Peter Nachtwey
Peter Nachtwey

pnachtwey wrote in news:8b069fe0-8f26-4a70-908d-
snipped-for-privacy@e6g2000prf.googlegroups.com:
What about dividing through by the denominator, and getting something along
the lines of 1 + [As+B]/[s^2 + 100] instead of the transfer function given.
It looks like it either turn into a mess, or turn into a nifty
superposition problem.

Would you like us to CC your professor with our responses?
Z-N rules are for tuning a system when you don't know, and never want to
find out, the transfer function. If you have the transfer function
already, then you can come up with a controller using pole placement.
Like Peter, I see some practical trouble involved with the improper
fraction -- you're specifying a system that responds immediately, which
simply doesn't happen in real life. Even if the above is an accurate
model in that the real thing responded much faster than any controller
you could devise, you'd probably be smart to intentionally add some lag
to your controller, to prevent the controller's unmodeled dynamics from
causing oscillation.

Divide it's length by the speed of light -- at best you'll see frequency
dependent effects starting at around 1/10 the resulting frequency,
depending on the physical design you may see them at much lower
frequencies.
A better example for my purposes would be the op-amp. You can design
circuits with it _assuming_ infinite gain, and do things like using
resistive dividers for feedback. Many people do, in fact, and you can
run into serious trouble with stability if you get too clever. This
happens because while most op-amps these days have been carefully
designed to be stable in a wide variety of circuits they cannot be stable
in all; their propensity toward stability leads designers who aren't
obsessive about it to fail to check, and they find those cases where the
regular op-amp _isn't_ stable.

Pole placement doesn't work because the numerator is the same order as
the denominator so ignore my previous answer. I used by last ditch
tecnique which is to find the gains that minimize the sum of
squarederror,SSE, between a desired closed loop transfer function's
frequency response and the actual closed loop transfer function's
frequency response.
The first .pdf shows how to smooth out the spike caused by the
imaginary poles. It doesn't do anything about the imaginary zeros
which cause the dip in the response..
The first .pdf calculates the gains and generates a Bode plot.
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1-Min%20Bode%20snovite=
.pdf
The next .pdf plots the poles and zeros. Notice the poles are in a
safe location and clustered relatively close to the desired location
ot -2PI. This removes the spike caused by the imaginary poles.
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20T0C1-Min%20Bode%20snovite=
%20B.pdf
Notice that the proportional gain is negative. The proportional gain
can be negative IF it is only used in the feed back path. This means
the controller needs to be a I-PD controller.
This problem is not a good one for learning PID tuning, gain
calculations or anything but frustration. It is a flawed problem so
the answers aren't that good either.
Peter Nachtwey

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