Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Mathematics and Algorithms > Control Systems > Model Connections and Manipulations > SystemsModelFeedbackConnect >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

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 .
MORE INFORMATION
  • 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 .
EXAMPLESCLOSE ALL
Basic Examples   (7)
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]=
Scope   (11)
A unity negative feedback system:
A positive feedback system:
A negative feedback system:
A positive feedback system:
Applications   (4)
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:
Properties & Relations   (3)
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
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF