Dear Mr. Stechenko,
the model order reduction algorithms doing exactly what you are looking for.
And you are right, that you only have to provide the data in the linear matrix representation
H(z) = N(z)/M(z) = C*(s*E - A)^-1*B + D
or in the time domain representation
Ex'(t) = Ax(t) + Bu(t),
y(t) = Cx(t) + Du(t).
As a result, smaller matrices are computed, which lead to polynomials in the transfer function of smaller order.
You can also look this up in the documentation of the different model reduction algorithms in the toolbox by using the "help" command.
Best regards,
Steffen W. R. Werner
----- Am 3. Okt 2017 um 13:21 schrieb Julien Bect <address@hidden>:
Le 27/09/2017 à 23:06, Sergei Steshenko a écrit :
> From: Julien Bect <address@hidden>
> To: help-octave Octave <address@hidden>
> Sent: Tuesday, September 26, 2017 10:54 AM
> Subject: MORLAB (Model Order Reduction LABoratory) v3.0
>
> Seen on the "NA Digest" list :
>
> -------- Message transféré --------
> Sujet : [NADIGEST] NA Digest, V. 17, # 26
> Date : Mon, 25 Sep 2017 23:28:25 -0400
> De : NA Digest Editor <address@hidden>
> Répondre à : NA-Digest <address@hidden>
> Pour : address@hidden
>
> From: Steffen W. R. Werner address@hidden Date: September 20, 2017
> Subject: Software Release: MORLAB 3.0 Version 3.0 of the MORLAB (Model Order Reduction LABoratory) toolbox
> has been released. The toolbox is a collection of MATLAB/OCTAVE
> routines for model order reduction of linear dynamical systems based
> on the solution of matrix equations. The implementation is based on
> spectral projection methods, e.g., methods based on the matrix sign
> function and the matrix disk function. The toolbox contains implementations for standard and descriptor
> systems:
> - Modal truncation
> - Balanced truncation
> - Bounded-real balanced truncation
> - Positive-real balanced truncation
> - Balanced stochastic truncation
> - Linear-quadratic-Gaussian balanced truncation
> - H-infinity balanced truncation
> - Hankel-norm approximation
> Also, matrix equation solvers based on the matrix sign function as
> well as further subroutines for linear dynamical systems can be found
> in the MORLAB toolbox. For more details on this software, see: http://www.mpi-magdeburg.mpg.de/projects/morlab_______________________________________________
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> https://lists.gnu.org/mailman/listinfo/help-octave
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>
> I am not familiar with this stuff, but the "model reduction" suggests the SW might realize what I need - the description of what I need is right below.
>
> Suppose I have an IIR filter expressed in its standard form in, say, Z-domain: H(z) = B(z)/A(z) where B(z) and A(z) are polynomials in my case of the same order. The way I obtain the polynomials is through fitting experimental frequency response, and by the very construction of the method I use the order of the polynomials is definitely higher than needed to fit the curve.
>
> So, I need to reduce the order of the polynomials - are these Model Order Reduction algorithms capable of doing what I need provided I change the representation of the IIR into a matrix form demanded by the algorithms ?
Hi Sergei,
I can't help you, but perhaps the author of MORLAB (in CC) can ?
@++
Julien
--
Steffen W. R. Werner, M.Sc.
Max Planck Institute for Dynamics of Complex Technical Systems
Department of Computational Methods in Systems and Control Theory
Sandtorstr. 1
D-39106 Magdeburg (Germany)
Phone: +49 391 6110 484
Email: address@hidden