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SystemsModelFeedbackConnect
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SystemsModelFeedbackConnect

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connects the outputs from sys to the inputs with negative feedback.

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SystemsModelFeedbackConnect[sys,{con1,…}]

only feedback connect the outputs and inputs in coni.

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connects the outputs of sys1 to sys2 and the outputs of sys2 to the inputs of sys1 in feedback.

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SystemsModelFeedbackConnect[sys1,sys2,{out1,…},{{in1,ftype1},…}]

connects output outi of sys1 to the i^(th) input of sys2 and the j^(th) output of sys2 to input inj of sys1 with feedback type ftypej.

Details

  • The systems model sysi can be a TransferFunctionModel, StateSpaceModel, AffineStateSpaceModel, or NonlinearStateSpaceModel.
  • Connections coni can be given as:
  • {out,in}connect output out to input in in negative feedback
    {out,in,ftype}use positive or negative feedback type ftype
  • By default, sys2 is a unity gain system.
  • The arguments in, out, ini, and outi are integers specifying the positions of the input or output channels.
  • The ftype can be specified as "Negative" or -1 for negative feedback, and "Positive" or 1 for positive feedback. The default type is "Negative".

Examples

open allclose all

Basic Examples  (6)Summary of the most common use cases

A transfer function with negative unity feedback:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-dk1x8j
Out[1]=1

Connect two continuous-time systems in negative feedback:

In[1]:=1
✖
https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-j4bnlb
Out[1]=1

Connect two discrete-time systems in negative feedback:

In[1]:=1
✖
https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-bpcetx
Out[1]=1

A state-space system with negative feedback:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-bdvwjq
Out[1]=1

Connect two state-space systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-e2pb9c
Out[1]=1

Feedback the second output to the first input:

In[1]:=1
✖
https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-tn473p
Out[1]=1

Scope  (18)Survey of the scope of standard use cases

Basic Uses  (10)

A unity negative feedback system:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-3gfa3b
Out[1]=1

A positive feedback system:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-r5p0wo
Out[1]=1

Connect two scalar systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-d3i6bx
Out[1]=1

Connect multivariable systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-e9tzx8
Out[1]=1

Connect the second output to the first input:

In[1]:=1
✖
https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-h9p2tg
Out[1]=1

Connect the second output to the first input through a feedback system:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-cjmtpx
Out[1]=1

Connect discrete-time systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-c75cik
Out[1]=1

Connect two systems in positive feedback:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-1d3m3
Out[1]=1

Connect two state-space models as shown in the diagram:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-kd2h0m
Out[1]=1

Connect a StateSpaceModel to a TransferFunctionModel:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-g6eoec
Out[1]=1

System Types  (8)

Connect two TransferFunctionModel systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-omtvq3
Out[1]=1

With delays:

In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-blx1qv
Out[2]=2

Using improper transfer functions:

In[3]:=3
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-bunng0
Out[3]=3

Connect two StateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-8062pm
Out[1]=1

With delays:

In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-jsvinl
Out[2]=2

Using descriptor state-space models:

In[3]:=3
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-ddom91
Out[3]=3

Input linear AffineStateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-wymneu
Out[1]=1

General nonlinear NonlinearStateSpaceModel systems:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-lj0qwy
Out[1]=1

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

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-s27jj
Out[1]=1

Connection with delays:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-bxf1xe
Out[1]=1

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/0d2mvu1rmdtqdy0ojeox52-ojg65x
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-b2n1y9
Out[2]=2

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

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-dzd7s
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-1v79d
Out[2]=2

Generalizations & Extensions  (2)Generalized and extended use cases

Use one feedback type for all connections:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-n5fbq
Out[1]=1

Connect two systems with positive feedback:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-crk3nf
Out[1]=1

Applications  (5)Sample problems that can be solved with this function

Obtain the closed-loop transfer function of a discrete-time system with an integral controller and feedback sensor:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-yapwf9
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-r2mxxw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-io76ja
Out[3]=3

A motor-load servo system with position and velocity feedback:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-rzd4yi

With only position feedback, the system is unstable:

In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-kkcj1u
Out[2]=2

The closed-loop system, with rate feedback in the inner loop and position feedback in the outer loop:

In[3]:=3
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-y5fr1k
Out[3]=3

The response to a unit step:

In[4]:=4
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-jmtydb
Out[4]=4

Use SystemsModelFeedbackConnect in multi-loop reduction:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-dl7fqn
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-gw90bs
Out[2]=2

Compute the complementary sensitivity function from the loop transfer function:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-z0xpqo
Out[1]=1

A crankshaft receives a delayed input signal from the engine controller:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-kjh71h
Out[1]=1

Including a simple controller shows the delay is internal to the closed-loop system:

In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-h38gcs
Out[2]=2

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

The resulting system has the inputs and outputs of the first system:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-bhv5ob
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-be6ds8
Out[2]=2

SystemsModelFeedbackConnect is a special case of SystemsConnectionsModel:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-m5dy8e
In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-qsi6qw
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-uky7hy
Out[3]=3

Connect two transfer functions tfm1 and tfm2:

In[1]:=1
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-vw1kd6
Out[1]=1

This is equivalent to (IdentityMatrix[n]+tfm1.tfm2)-1.tfm1:

In[2]:=2
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https://wolfram.com/xid/0d2mvu1rmdtqdy0ojeox52-qg38u1
Out[2]=2
Wolfram Research (2010), SystemsModelFeedbackConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html (updated 2014).
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Wolfram Research (2010), SystemsModelFeedbackConnect, Wolfram Language function, https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html (updated 2014).

Text

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

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

CMS

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

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

APA

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

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

BibTeX

@misc{reference.wolfram_2025_systemsmodelfeedbackconnect, author="Wolfram Research", title="{SystemsModelFeedbackConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html}", note=[Accessed: 29-March-2025 ]}

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@misc{reference.wolfram_2025_systemsmodelfeedbackconnect, author="Wolfram Research", title="{SystemsModelFeedbackConnect}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html}", note=[Accessed: 29-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_systemsmodelfeedbackconnect, organization={Wolfram Research}, title={SystemsModelFeedbackConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html}, note=[Accessed: 29-March-2025 ]}

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@online{reference.wolfram_2025_systemsmodelfeedbackconnect, organization={Wolfram Research}, title={SystemsModelFeedbackConnect}, year={2014}, url={https://reference.wolfram.com/language/ref/SystemsModelFeedbackConnect.html}, note=[Accessed: 29-March-2025 ]}