RLC Ladder (Gugercin/Antoulas 2004) - Revision history

Saak at 12:07, 30 April 2026

2026-04-30T12:07:13Z

← Older revision		Revision as of 12:07, 30 April 2026
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]

Schuetz2 at 13:34, 26 January 2026

2026-01-26T13:34:29Z

← Older revision		Revision as of 13:34, 26 January 2026
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	[[Category:SISO]]		[[Category:SISO]]

	{{Infobox		{{Infobox
	\|Title = RCL Circuit Equations		\|Title = RCL Circuit Equations
	\|Benchmark ID =		\|Benchmark ID =

Saak at 09:56, 26 January 2026

2026-01-26T09:56:06Z

← Older revision		Revision as of 09:56, 26 January 2026
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	<figure id="fig1">[[File:Rlc_ladder_segment_GugA04.png\|490px\|thumb\|right\|<caption>One section of the circuit.</caption>]]</figure>		<figure id="fig1">[[File:Rlc_ladder_segment_GugA04.png\|490px\|thumb\|right\|<caption>One section of the circuit.</caption>]]</figure>

	This model represents an electic circuit made of a cascade of interconnected sections. Each section consists of a simple setup as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. The input is the voltage V applied to the first section; the output is the current I of the first section.		This model represents an electic circuit made of a cascade of interconnected sections. Each section consists of a simple setup as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. The input is the voltage <math>V</math> applied to the first section; the output is the current <math>I</math> of the first section.

	:<math>		:<math>
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	==Data==		==Data==
	The following Matlab code assembles the above described <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math>, matrices of requested dimensions. The input parameters R, Rbar, Cap and L represent the two resistances, the capacitance and the inductivity of each section of the circuit, as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. They default to the values from <ref name="morGugA04"/>, when omitted.		The following Matlab code assembles the above described <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math>, matrices of requested dimensions. The input parameters <code>R</code>, <code>Rbar</code>, <code>Cap</code> and <code>L</code> represent the two resistances, the capacitance and the inductivity of each section of the circuit, as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. They default to the values from <ref name="morGugA04"/>, when omitted.

	<div class="thumbinner" style="width:680px;text-align:left;">		<div class="thumbinner" style="width:680px;text-align:left;">

Saak at 09:51, 26 January 2026

2026-01-26T09:51:53Z

← Older revision		Revision as of 09:51, 26 January 2026
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	==Data==		==Data==
	The following Matlab code assembles the above described <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math>, matrices of requested dimensions. The input parameters R, Rbar, Cap and L represent the two resistances, the capacitance and the inductivity of each section of the circuit, as depicted in Figure 1. They default to the values from <ref name="morGugA04"/>, when omitted.		The following Matlab code assembles the above described <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math>, matrices of requested dimensions. The input parameters R, Rbar, Cap and L represent the two resistances, the capacitance and the inductivity of each section of the circuit, as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. They default to the values from <ref name="morGugA04"/>, when omitted.

	<div class="thumbinner" style="width:680px;text-align:left;">		<div class="thumbinner" style="width:680px;text-align:left;">

Saak at 09:51, 26 January 2026

2026-01-26T09:51:04Z

← Older revision		Revision as of 09:51, 26 January 2026
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	==Description==		==Description==
	This model represents an electic circuit made of a cascade of interconnected sections. Each section consists of a simple setup as depicted in Figure 1. The input is the voltage V applied to the first section; the output is the current I of the first section.		<figure id="fig1">[[File:Rlc_ladder_segment_GugA04.png\|490px\|thumb\|right\|<caption>One section of the circuit.</caption>]]</figure>

			This model represents an electic circuit made of a cascade of interconnected sections. Each section consists of a simple setup as depicted in [[RLC_Ladder_(Gugercin/Antoulas_2004)#fig1\|Figure 1]]. The input is the voltage V applied to the first section; the output is the current I of the first section.

	:<math>		:<math>

Saak: Created page with "{{preliminary}} Category:benchmark Category:SISO {{Infobox |Title = RCL Circuit Equations |Benchmark ID = * rlc_ladder_GA_n?m1q1..."

2026-01-23T17:17:20Z

Created page with "{{preliminary}}  Category:benchmark Category:SISO {{Infobox |Title = RCL Circuit Equations |Benchmark ID = * rlc_ladder_GA_n?m1q1..."

New page

{{preliminary}} 

[[Category:benchmark]]
[[Category:SISO]]

{{Infobox
|Title = RCL Circuit Equations
|Benchmark ID =
* rlc_ladder_GA_n?m1q1
|Category = morwiki
|System-Class = LTI-FOS
|nstates =
* arbitrary
|ninputs =
* 1
|noutputs =
* 1
|nparameters = 0
|components = A, B, C, D
|License = MIT
|Creator = [[User:Gugercin]]
|Editor =
* [[User:Saak]]
|Zenodo-link = NA
}}

==Description==
This model represents an electic circuit made of a cascade of interconnected sections. Each section consists of a simple setup as depicted in Figure 1. The input is the voltage V applied to the first section; the output is the current I of the first section.

:<math>
\begin{align}
\dot x(t) &= A x(t) + B u(t), \\
y(t) &= C x(t) + D u(t), \\
x(0) &= x_0,
\end{align}
</math>

with <math>t>0</math>.

==Origin==
This model was used in the numerical experiments section of <ref name="morGugA04"/>.

==Data==
The following Matlab code assembles the above described <math>A</math>, <math>B</math>, <math>C</math>, and <math>D</math>, matrices of requested dimensions. The input parameters R, Rbar, Cap and L represent the two resistances, the capacitance and the inductivity of each section of the circuit, as depicted in Figure 1. They default to the values from <ref name="morGugA04"/>, when omitted.

<div class="thumbinner" style="width:680px;text-align:left;">
<syntaxhighlight lang="matlab">
function [A, B, C, D, sys_rlc] = circuit_sparse(N, R , Rbar, Cap, L)
% circuit_sparse generates a SISO RLC ladder model of prescribed dimensions
%
% The model follows the descriptioin in DOI:10.1080/00207170410001713448
% and the input parameters R, Rbar, Cap and L default to the values given
% there, when omitted. If also N is omitted the original 100 dimensional
% realization is created.
%
% The code is a sparse adaption of the original dense generator function by
% Serkan Gugercin.
%

%
% MIT License
%
% Copyright (c) 2026 The MORwiki Community
%
% Permission is hereby granted, free of charge, to any person
% obtaining a copy of this software and associated documentation files
% (the "Software"), to deal in the Software without restriction,
% including without limitation the rights to use, copy, modify, merge,
% publish, distribute, sublicense, and/or sell copies of the Software,
% and to permit persons to whom the Software is furnished to do so,
% subject to the following conditions:
%
% The above copyright notice and this permission notice shall be
% included in all copies or substantial portions of the Software.
%
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
% EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
% MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
% NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
% BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
% ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
% CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
% SOFTWARE.
%

if nargin < 1
N = 100;
end

if nargin < 2
% parameter values from DOI:10.1080/00207170410001713448
R = 0.1;
Rbar = 1;
Cap = 0.1;
L = 0.1;
end

z1 = 1 / L * ones(N, 1);
z2 = -1 / L * Rbar * R / (Rbar + R) * ones(N, 1);
z3 = -1 / L * Rbar / (Rbar + R) * ones(N, 1);

% Every second row needs to be adapted for the second ladder step
z3(2:2:N) = -1 / Cap;
z2(1:2:N) = -1 / Cap / (Rbar + R);
z1(2:2:N) = 1 / Cap * Rbar / (Rbar + R);

% start end end are exceptional
z2(1) = -1 / R / Cap; % sets A(1, 1)
z3(1) = -1 / Cap; % sets A(1, 2)
z2(N) = -Rbar / L; % sets A(N, N)
z1(N - 1) = 1 / L; % sets A(N, N-1)

A = spdiags([z1 z2 z3], -1:1, N, N);
B = [(1 / R / Cap); sparse(N - 1, 1)];
C = [(-1 / R) sparse(1, N - 1)];
D = 1 / R;

if exist('sparss', 'file')
sys_rlc = sparss(A, B, C, D);
else
sys_rlc = [];
end
</syntaxhighlight>
</div>

==Citation==
To cite this benchmark, use the following references:

* For the benchmark itself and its data:
:: '''RLC Ladder (Gugercin/Antoulas 2004)'''. hosted at MORwiki - Model Order Reduction Wiki, 2026. http://modelreduction.org/index.php/RLC_Ladder_(Gugercin/Antoulas_2004)

@MISC{morwiki_steel,
author = <nowiki>{{The MORWiki Community}}</nowiki>,
title = {RLC Ladder (Gugercin/Antoulas 2004)}
howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
url = <nowiki>{https://modelreduction.org/morwiki/RLC_Ladder_(Gugercin/Antoulas_2004)}</nowiki>,
year = 2026
}

* For the background on the benchmark:

@Article{morGugA04,
author = {Gugercin, S. and Antoulas, A.~C.},
title = {A survey of model reduction by balanced truncation and some
new results},
journal = IntControl,
year = 2004,
volume = 77,
number = 8,
pages = {748--766},
doi = {10.1080/00207170410001713448}
}

==References==

<references>

<ref name="morGugA04"> S. Gugercin and A.C. Antoulas, <span class="plainlinks">[https://doi.org/10.1080/00207170410001713448 A survey of model reduction by balanced truncation and some new results]</span>, International Journal of Control,
77:8, 748-766, 2004.</ref>

</references>