PID controller question

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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.

Re: PID controller question




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

Re: PID controller question



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
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Re: PID controller question




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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.

OT: PID controller question



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=beverly+hillbillies+jed&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

Jerry
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Re: OT: PID controller question




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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.

Re: PID controller question




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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.

[OT] Usenet and links, was: Re: PID controller question




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.

--
Simon Clubley, clubley@remove_me.eisner.decus.org-Earth.UFP
Microsoft: Bringing you 1980's technology to a 21st century world

Re: [OT] Usenet and links, was: Re: PID controller question



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
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Re: [OT] Usenet and links, was: Re: PID controller question




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.

--
Simon Clubley, clubley@remove_me.eisner.decus.org-Earth.UFP
Microsoft: Bringing you 1980's technology to a 21st century world

Re: [OT] Usenet and links, was: Re: PID controller question



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.


--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Re: PID controller question




¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF¯AF

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.

Re: PID controller question



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,
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.

--
Rich Webb     Norfolk, VA

Re: PID controller question




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

Re: PID controller question



On Mon, 01 Feb 2010 07:33:00 -0800, Ray-Rogers wrote:


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.

--
www.wescottdesign.com

Re: PID controller question





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.


--
Regards JCH

 


Re: PID controller question




'real' process identification?  Do you mean on-line/real-time?
In general though I agree; although

Ray



Re: PID controller question





link.http://www.deltamotion.com/peter/Mathcad/Mathcad%20-%20t0p1%20pi%20NG ...

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.


--
Regards JCH

 


Re: PID controller question



On Sun, 31 Jan 2010 16:42:01 -0800, pnachtwey wrote:


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.

--
www.wescottdesign.com

Re: PID controller question



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
--
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

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