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SystemsModelParallelConnect
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SystemsModelParallelConnect

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connects the systems models sys1 and sys2 in parallel.

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SystemsModelParallelConnect[sys1,sys2,{{in11,in21},…},{{out11,out21},…}]

connects the inputs in1i to inputs in2i and sums the outputs out1k and outputs out2k.

Details

Examples

open allclose all

Basic Examples  (4)Summary of the most common use cases

Connect two continuous-time systems in parallel:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-j4bnlb
Out[1]=1

Connect two discrete-time systems in parallel:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-bpcetx
Out[1]=1

Connect state-space systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-e2pb9c
Out[1]=1

Parallel connect a two-output, one-input system and a one-input, one-output system:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-fyoteg

Merge no inputs and sum no outputs:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-j1cnhm
Out[2]=2

Merge inputs and sum no outputs:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-zx1un
Out[3]=3

Merge no inputs and sum output 2 from sys1 with output 1 from sys2:

In[4]:=4
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-g5k16
Out[4]=4

Merge inputs and sum output 2 from sys1 with output 1 from sys2:

In[5]:=5
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-fxqcam
Out[5]=5

Scope  (14)Survey of the scope of standard use cases

Basic Uses  (7)

Connect a two-input, one-output system in parallel with a one-input, one-output system:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-8sd1f

Use the first input of the two-input system:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-e8ooeh
Out[2]=2

Use the second input:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-cwbgo7
Out[3]=3

Parallel connect a two-output system with a single-output system:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-bo6nmf

Use the first output of the two-input system:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-jejqyt
Out[2]=2

Use the second output:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-c80mo
Out[3]=3

Connect scalar systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-d3i6bx
Out[1]=1

Connect multivariable systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-e9tzx8
Out[1]=1

Merge the second input and sum the first output of each system:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-cjmtpx
Out[1]=1

Connect discrete-time systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-c75cik
Out[1]=1

Connect a StateSpaceModel to a TransferFunctionModel:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-g6eoec
Out[1]=1

System Types  (7)

Connect two TransferFunctionModel systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-omtvq3
Out[1]=1

With delays:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-blx1qv
Out[2]=2

Using improper transfer functions:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-bunng0
Out[3]=3

Connect two StateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-8062pm
Out[1]=1

With delays:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-jsvinl
Out[2]=2

Using descriptor state-space models:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ddom91
Out[3]=3

Input linear AffineStateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-wymneu
Out[1]=1

General nonlinear NonlinearStateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-lj0qwy
Out[1]=1

Connecting a transfer function and state-space model will give a state-space model:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-s27jj
Out[1]=1

Reversing the order gives an equivalent state-space model:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-w8e3yc
Out[2]=2

They give the same transfer functions:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-2t3bp6
Out[3]=3

Connection with delays:

In[4]:=4
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-bxf1xe
Out[4]=4

Connecting a standard linear system and an input linear system will give an affine model:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ojg65x
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-b2n1y9
Out[2]=2

Connecting a standard linear or affine system with a nonlinear system gives a nonlinear model:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-dzd7s
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-1v79d
Out[2]=2

Generalizations & Extensions  (3)Generalized and extended use cases

Merge two systems:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-n9x9e2
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-x5qolj
Out[2]=2

Connect the corresponding inputs:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-s98l8o
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-2jyjnq
Out[2]=2

Sum the corresponding outputs:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-hitvus
In[2]:=2
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-wfnofz
Out[2]=2

Applications  (3)Sample problems that can be solved with this function

A function that connects any number of matching systems in parallel:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-haxqa

Connect a family of first-order systems in parallel:

In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ehtleq
Out[2]=2

Connect several multiple-input, multiple-output systems:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-bdswv
Out[3]=3

Construct a parallel RLC circuit:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-iux1za
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-125730
Out[2]=2

Add a disturbance model to the output of a system:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-jbab3v
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ytbu96
Out[2]=2

Properties & Relations  (3)Properties of the function, and connections to other functions

SystemsModelParallelConnect is essentially a summation operation:

In[1]:=1
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-hgoi7
Out[1]=1

SystemsModelParallelConnect is a special case of SystemsConnectionsModel:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-eeqe9h
In[2]:=2
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-vpvhs
Out[2]=2

The common input and summer blocks:

In[3]:=3
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-yyhu1l
In[4]:=4
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-o2856x

Use SystemsConnectionsModel to specify the connections:

In[5]:=5
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-vfii
Out[5]=5

Merge the connections:

In[6]:=6
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ylii0u
Out[6]=6

A parallel connection leaves the states of the subsystems unchanged:

In[1]:=1
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-e3fzor
In[2]:=2
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-ccfdmd
Out[2]=2

The resulting system has at least as many inputs as each subsystem:

In[3]:=3
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https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-8g8xig
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-k15kjs
Out[4]=4

A similar result holds for the minimum number of outputs:

In[5]:=5
✖
https://wolfram.com/xid/0bsvxxf3scb9kvxiwq-7814up
Out[5]=5
Wolfram Research (2010), SystemsModelParallelConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html (updated 2014).
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Wolfram Research (2010), SystemsModelParallelConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html (updated 2014).

Text

Wolfram Research (2010), SystemsModelParallelConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html (updated 2014).

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Wolfram Research (2010), SystemsModelParallelConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html (updated 2014).

CMS

Wolfram Language. 2010. "SystemsModelParallelConnect." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html.

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Wolfram Language. 2010. "SystemsModelParallelConnect." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html.

APA

Wolfram Language. (2010). SystemsModelParallelConnect. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html

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Wolfram Language. (2010). SystemsModelParallelConnect. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html

BibTeX

@misc{reference.wolfram_2025_systemsmodelparallelconnect, author="Wolfram Research", title="{SystemsModelParallelConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html}", note=[Accessed: 24-March-2025 ]}

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@misc{reference.wolfram_2025_systemsmodelparallelconnect, author="Wolfram Research", title="{SystemsModelParallelConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html}", note=[Accessed: 24-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_systemsmodelparallelconnect, organization={Wolfram Research}, title={SystemsModelParallelConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html}, note=[Accessed: 24-March-2025 ]}

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@online{reference.wolfram_2025_systemsmodelparallelconnect, organization={Wolfram Research}, title={SystemsModelParallelConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelParallelConnect.html}, note=[Accessed: 24-March-2025 ]}