Newton-Raphson Method in Matlab/simulink

mim

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Dec 29, 2005, 5:43:11 AM12/29/05

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Dear All,

I really need you help especially for those who have already
experienced work with Newton-Raphson Method in Matlab/simulink...

I need to use the method to Non-linear equation of motion
coded in S-functions...and I don't know how to make a start :(

Any sort of help will be much appreciated.

Kindly regards,

Mimi

MImi

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Dec 29, 2005, 6:43:50 AM12/29/05

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Hi,

Just a small detail that I am using it for the full Nonlinear
equations of motion for an Aircraft.

waiting for you r help:)

Meriem

NZTideMan

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Dec 30, 2005, 3:54:28 AM12/30/05

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By "full nonlinear equations of motion", do you mean the Navier Stokes
equations?
And you expect to be able to solve them in Matlab using Newton Raphson?
Wow...............
That's an ambitious project.
I hope you've got a big team, lots of research funds, and lots of time.

I empathise with you. I know how to use Newton Raphson, but I wouldn't
know where to start on such a project either.

Mimi

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Dec 30, 2005, 5:01:32 AM12/30/05

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Dear NZTideMan,

Thanks very much for the reply BUT there is a misunderstanding:

> By "full nonlinear equations of motion", do you mean the Navier
Stokes equations?

Ohh, NO NO, It is just Aircraft Equation of Motions (the known 12
Non-linear equations...)

I am expected to do an inversion numerically using Newton-Raphson
Method ...

But still an ambitious project for me:)

You said:

> I know how to use Newton Raphson....I would be grateful if you
could help as I REALLY DO NOT KNOW HOW to make a start:(

Thanks again, and I look forward to hearing from you.

Regards,
Mimi
which I have to make as soon as Possible.

NZTideMan

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Dec 30, 2005, 5:13:46 PM12/30/05

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OK, so you have 12 eqns of the form (I assume they are functions, not
PDEs?):
f(x1,x2,x3,x4,....,x12)
Now you must differentiate each of these with respect to each of the 12
variables to produce 144 equations (hopefully, most of these will be
zero) and form a 12x12 matrix of equations.

You will need to code each of these 144 equations in Matlab.

Once you've done this, get back to us. Most of the work is done. Now
it's just a matter of setting up the numerical scheme.

Mimi

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Dec 31, 2005, 5:31:27 AM12/31/05

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Dear NZTideMan,

Thanks for the reply:

Yes tehy are not PDEs...

> f(x1,x2,x3,x4,....,x12)
> Now you must differentiate each of these with respect to each of
the 12 variables to produce 144 equations (hopefully, most of these
will be zero) and form a 12x12 matrix of equations.

differentiate them Numerically?...how? sorii I am quite a beginner!

> You will need to code each of these 144 equations in Matlab.

you mean M-file...or S-function...or what exactly?

Hear from you soon,

Mimi

NZTideMan

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Dec 31, 2005, 7:49:12 PM12/31/05

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Differentiate them algebraically, then code them as functions in a .m
file

mimi

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Jan 15, 2006, 6:14:06 AM1/15/06

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Any Extra explanation as I AM STUCK.

NZTideMan

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Jan 15, 2006, 2:17:05 PM1/15/06

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mimi wrote:
> Any Extra explanation as I AM STUCK.

Where are you stuck?
Do you know how to differentiate?
eg if one of the equations is:
f1=1 + ax + bx^2 + cy + dy^2 + exy
then the equations we're looking for are:
df1dx=a + 2bx + ey
df1dy=c + 2dy +ex
and all other 10 equations df1dz, etc, etc are zero.

Now, you must repeat that exercise on all 11 remaining equations, f2 to
f12.

You need to end up with 144 equations.

mimi

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Jan 16, 2006, 8:48:58 AM1/16/06

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Many thanks NZTideMan,

Do u have an example to look at while working...

How can I implement it numerically in a computer...say and M-file for
example...as obviously I would not think I should do 144....

Hear from you sooner.

thx agaian :)

NZTideMan

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Jan 16, 2006, 4:18:54 PM1/16/06

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What is wrong with the example I gave you?
You are the one who wants to use Newton Raphson to solve 12 nonlinear
equations with 12 unknowns.
If you are not prepared to sit down with a pencil and a piece of paper
and write out the 144 equations, as I've suggested, then you cannot
solve the problem. End of story.
You cannot implement it "numerically in a computer" until you have done
the algebra.

Alexandra

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Jan 17, 2006, 4:31:12 AM1/17/06

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Good morning.

Maybe I can Help. Tray look in the help of matlab toolbox symbolic math. There are some codes for differentiate equation symbolically. Try jacobian.

Good luck

mimi

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Jan 23, 2006, 10:25:08 AM1/23/06

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in fact the example u gave me is irrelevant to what I NEEDED:
====================
Hi,

did any one use: optimisation in MAtlab: is fminsearch considered as
optimisation ?

is it the same as Newton raphson?

thx so much

Ken Davis

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Jan 23, 2006, 10:59:42 AM1/23/06

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"mimi" <mer...@hotmail.co.uk> wrote in message
news:ef20d...@webx.raydaftYaTP...

Please read up on Newton's method so you will understand what you are being
told. Finding the Jacobian (matrix of derivatives) of 12 functions of 12
variables is not as hard as it might sound, especially if you have the
Symbolic Toolbox. If you don't have to use Newton's method, there are
probably other approaches, but you said that you had to use Newton's method.