This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

SystemsModelFeedbackConnect

SystemsModelFeedbackConnect[sys]
gives the closed-loop system for the StateSpaceModel or TransferFunctionModel object sys with unity negative feedback.
SystemsModelFeedbackConnect
creates negative or positive feedback depending on type.
SystemsModelFeedbackConnect
creates a negative feedback of only output y to input u.
SystemsModelFeedbackConnect
creates feedback of the specified type.
SystemsModelFeedbackConnect
feeds output back to input .
SystemsModelFeedbackConnect
specifies connection types.
SystemsModelFeedbackConnect
closes the negative feedback loop for system via system .
SystemsModelFeedbackConnect
creates feedback of the specified type.
SystemsModelFeedbackConnect
connects only outputs of to sequentially numbered inputs of and feeds sequentially numbered outputs of back to inputs of to form a closed-loop system with negative feedback.
SystemsModelFeedbackConnect
uses when connecting to input .
  • By default, is a unity gain system.
  • The arguments u, y, , and are integers specifying the positions of the input or output channels.
  • If or is in state-space form, the result is given in state-space form.
  • The type can be specified as or for negative feedback, and or for positive feedback. The default type is .
A negative unity feedback system:
A negative feedback system:
A discrete-time positive feedback system:
A state-space model with unity negative feedback:
Reduce the following system:
A negative feedback system in which the first two outputs are fed back to the inputs:
Feed back only the first output to the second input:
Feed back the first output to the second input, and the second and third outputs to the first input:
Specify the feedback from the first output to the second input as positive feedback:
A 2-input, 3-output system and a 2-input, 2-output system:
Use negative feedback to connect outputs to inputs :
A positive feedback connection between output 3 and input 1:
Use negative feedback to connect output 1 to input 2 and positive feedback for output 3 and input 1:
A negative unity feedback system:
In[1]:=
Click for copyable input
Out[1]=
 
A negative feedback system:
In[1]:=
Click for copyable input
Out[1]=
 
A discrete-time positive feedback system:
In[1]:=
Click for copyable input
Out[1]=
 
A state-space model with unity negative feedback:
In[1]:=
Click for copyable input
Out[1]=
 
Reduce the following system:
In[1]:=
Click for copyable input
Out[1]=
 
A negative feedback system in which the first two outputs are fed back to the inputs:
In[1]:=
Click for copyable input
Out[1]=
Feed back only the first output to the second input:
In[2]:=
Click for copyable input
Out[2]=
Feed back the first output to the second input, and the second and third outputs to the first input:
In[3]:=
Click for copyable input
Out[3]=
Specify the feedback from the first output to the second input as positive feedback:
In[4]:=
Click for copyable input
Out[4]=
 
A 2-input, 3-output system and a 2-input, 2-output system:
In[1]:=
Click for copyable input
Use negative feedback to connect outputs to inputs :
In[2]:=
Click for copyable input
Out[2]=
A positive feedback connection between output 3 and input 1:
In[3]:=
Click for copyable input
Out[3]=
Use negative feedback to connect output 1 to input 2 and positive feedback for output 3 and input 1:
In[4]:=
Click for copyable input
Out[4]=
A unity negative feedback system:
A positive feedback system:
A negative feedback system:
A positive feedback system:
Obtain the closed-loop transfer function of a discrete-time system with an integral controller and feedback sensor:
A motor-load servo system with position and velocity feedback:
With only position feedback the system is unstable:
The closed-loop system with rate feedback in the inner loop and position feedback in the outer loop:
The response to a unit step:
Use SystemsModelFeedbackConnect in multi-loop reduction:
Compute the complementary sensitivity function from the loop transfer function:
SystemsModelFeedbackConnect yields a system that has the inputs and outputs of the first system:
SystemsModelFeedbackConnect is essentially equivalent to
TransferFunctionModel[Inverse[IdentityMatrix+tf1[s].tf2[s]].tf1[s], s] without any pole-zero cancellations:
If any one of the subsystems is a StateSpaceModel object, so is the result:
New in 8