This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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# 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:
 Out[1]=

A negative feedback system:
 Out[1]=

A discrete-time positive feedback system:
 Out[1]=

A state-space model with unity negative feedback:
 Out[1]=

Reduce the following system:
 Out[1]=

A negative feedback system in which the first two outputs are fed back to the inputs:
 Out[1]=
Feed back only the first output to the second input:
 Out[2]=
Feed back the first output to the second input, and the second and third outputs to the first input:
 Out[3]=
Specify the feedback from the first output to the second input as positive feedback:
 Out[4]=

A 2-input, 3-output system and a 2-input, 2-output system:
Use negative feedback to connect outputs to inputs :
 Out[2]=
A positive feedback connection between output 3 and input 1:
 Out[3]=
Use negative feedback to connect output 1 to input 2 and positive feedback for output 3 and input 1:
 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:
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:
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