PID controller question

I have two questions regarding solving the problem (http:// i50.tinypic.com/33usrqs.png) and comparing with the textbook's
solution manual's approach (
http://i45.tinypic.com/wtxahe.png )
1. I have noticed that the PID controller shown in equation 6.6.16 is used to cancel out the plant's poles. Do you happen to know why the controller is used to cancel the plant's poles?
2. For second order systems, I recall the characteristic equation is (http://latex.codecogs.com/gif.latex?s^2%20+%202 \zeta\omega_%20+ %20\omega_^2=%200). However, as the problem provides the specification that the bandwidth is 2 rad/s, I was under the impression of making the middle term in that equation to be 2. However, the solutions made it to be 2.08, and the third term to be 2.56. Do you think these two terms can be anything that would work in terms of making the controller?
Thanks in advance for your comments.
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It looks interesting but we can't see what you are talking about. Always post links on a separate line.
Canceling poles is done by placing zeros at the same point as the poles. Reducing a pole reduces the phase lag. If one can cancel all the poles but one then the closed loop transfer function, CLTF, will have a response like a single pole low pass filter and will not over shoot or oscillate. At least that is how it works in the text books. The internal model control, IMC, PID gain methods basically cancel poles. I am not a fan of canceling poles because you must know exactly where they are and sometime they move around as the system warms up or loads change. I prefer to place them in safe places like on the negative real axis. Then if they move a bit they cause no harm.
An extremely simple example of pole placement and how to post a link. http://www.deltamotion.com/peter/Mathcad/Mathcad%20-%20t0p1%20pi%20NG.pdf Notice that the link is on a separate line.
Peter Nachtwey
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pnachtwey wrote:

It's easy to see that the link is broken. IOt's easy to fix the broken link. Why is anybody crabbing? Here:
http://i50.tinypic.com/33usrqs.png
Jerry
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Thanks for your explanation. I have no idea that including links in the same line as my description would cause such havoc. I will keep that in mind in the future.
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ssylee wrote:

That depends on the program you use to send email and use newsgroups. Thunderbird won't break any block of letters that doesn't include a space. for example: http://www.google.com/search?q verly+hillbillies+jed&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
Jerry
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I don't know how to use Thunderbird to post newsgroup messages to this group. I'm using Google Groups to get this done.
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Thanks for your explanation. I have no idea that including links in the same line as my description would cause such havoc. I will keep that in mind in the future.
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It's not so much that the link is on the same line as text, but that the link has been wrapped onto another line by your news client.
This is how I see part of your post when I look at it using slrn:

Notice how the first link has been wrapped between two lines.
Simon.
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Simon Clubley wrote:

I notice. Now see how Thunderbird treats the same original text:
I have two questions regarding solving the problem (
http://i50.tinypic.com/33usrqs.png ) and comparing with the textbook's solution manual's approach (
http://i45.tinypic.com/wtxahe.png )
Jerry
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Interesting, thanks; I wasn't aware that Thunderbird does processing of the original text.
The Thunderbird approach is better in this case; unfortunately I read news over a SSH connection. :-)
Simon.
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Simon Clubley wrote:

They don't actually process the text beyond finding suitable break points. If there are none, they don't break the line.

Jerry
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Thanks for your explanation. I have no idea that including links in the same line as my description would cause such havoc. I will keep that in mind in the future.
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On Sun, 31 Jan 2010 16:42:01 -0800 (PST), pnachtwey

It's also *usually* possible in most readers to force a single line by enclosing a long link in angle brackets, although even so, <(http://latex.codecogs.com/gif.latex?s^2%20+%202 \zeta\omega_%20+%20\omega_^2=%200)> still seems to fargle on the ^ character in Agent.
Interesting paper in your link. Which version of Mathcad is that? I stopped upgrading with 2001i, when they went with the crappy new licensing scheme -- although I had followed practically every upgrade since my original 5 1/4" Hercules graphics version.
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As Peter said. If you ever try this, direct pole cancellation, then also run simulations where the poles have moved because of age, manufacturing error, environmental changes, and with physical limits on the driver. Your trying to paper over a pothole instead of moving it; that might hurt. I've done it when I couldn't get the mechanical designers to modify the design and had to get the performance; I did complain and explain. It worked really great: for about six months, then they had to do the redesign. The point is, do the simulations with reasonable (or worst case) conditions early before effort is wasted on the wrong track. Also keep and structure the simulation process so you can redo it when the mechanical part of the design changes.
Ray
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On Mon, 01 Feb 2010 07:33:00 -0800, Ray-Rogers wrote:

20NG...
I found myself doing this a lot at one point in my career. I took to getting my work done, then summing up my final status report with a statement of the real problem, and a prediction of how long it would be before I was tinkering with the design again.
After a while, they started letting me in to the mechanical design reviews.
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wrote:

What you basically need is a 'real' process identification. Let's think you have found a nasty one of
1,319279E-04 v1'' + 0 + 0 = v2 (non-self regulating)
Then you must compensate the disturbances z appropriately.
See this example:
* http://home.arcor.de/janch/janch/_control/20100201-difficult-process-control /
The optimization routine would have tuned the PID controller more sensitive. Therefore I stopped optimization to have robust controlling.
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'real' process identification? Do you mean on-line/real-time? In general though I agree; although
Ray
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wrote:

Yes, using 'real measured process data'. See therefore example:
* http://home.arcor.de/janch/janch/_control/20100202-process-identification /
That changes data sets to differential equations. Then I have the process 'as-is' on my computer. This can be connected to
- PID Controller - Feed Forward - Compensations
and gives you 'real' results.
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On Sun, 31 Jan 2010 16:42:01 -0800, pnachtwey wrote:

20NG.pdf
I kind of agree, but:
Pole placement can lead you to designing a system that's not very robust, unless you know from the get-go what sort of pole locations will work well with your system. Peter can do this because he's very familiar with the systems he designs for. The rest of us may want to do some checking of our design.
Pole-zero cancellation is _not_ a panacea -- in fact, it can easily be a garden path down which you can lead yourself. It _can_ be used to good effect _if_ the poles being canceled are within the loop closure frequency, and _if_ you take the expected real-world range of the plant's poles into account when you do your design. Even there, however, it's almost always better to feed the command forward, around the feedback controller, rather than use 'real' pole-zero cancellation. This complicates your design because you now have a two-input controller, but it allows the controller to 'goose' the plant on sudden command changes without putting too much gain in the feedback path.
Controlling a plant with a pole at +10 rad/sec with a controller that has a zero in the same place is right out, of course.
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Tim Wescott wrote:

I learned a bit about pole-zero cancellation pushing op-amp circuits to peak performance. It can do great things for phase margin, but it can have a strange effect even with no component aging. The phase margin isn't much affected by a slight failure of exact cancellation, but the last bit of settling to final value is greatly extended. I won't go into the math, but the system "sees" another time constant about equal to the *difference" between the exact zero and the actual one. That's long!
Jerry
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