| Control System Toolbox™ | |
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You can use the Control System Toolbox model interconnection functions to help you build models. With these functions, you can perform I/O concatenation ([,], [;], and append), general parallel and series connections (parallel and series), and feedback connections (feedback and lft). These functions are useful to model open- and closed-loop systems.
Interconnection Operator | Description |
|---|---|
| [,] | Concatenates horizontally |
| [;] | Concatenates vertically |
| append | Appends models in a block diagonal configuration |
| augstate | Augments the output by appending states |
| connect | Forms an SS model from a block diagonal LTI object for an arbitrary interconnection matrix |
Forms the feedback interconnection of two models | |
Produces the LFT interconnection (Redheffer Star product) of two models | |
| parallel | Forms the generalized parallel connection of two models |
| series | Forms the generalized series connection of two models |
LTI model concatenation is done in a manner similar to the way you concatenate matrices in the MATLAB technical computing environment, using
sys = [sys1 , sys2] % horizontal concatenation sys = [sys1 ; sys2] % vertical concatenation sys = append(sys1,sys2) % block diagonal appending
In I/O terms, horizontal and vertical concatenation have the
following block-diagram interpretations (with
and
denoting
the transfer matrices of sys1 and sys2).
You can use concatenation as an easy way to create MIMO transfer functions or zero-pole-gain models. For example,
H = [ tf(1,[1 0]) 1 ; 0 tf([1 -1],[1 1]) ]
specifies
Use
append(sys1,sys2)
to specify the block-decoupled LTI model interconnection.
See append for more information on this function.
The following LTI model interconnection functions are useful for specifying closed- and open-loop model configurations:
feedback puts two LTI models with compatible dimensions in a feedback configuration.
series connects two LTI models in series.
parallel connects two LTI models in parallel.
lft performs the Redheffer star product on two LTI models.
connect works with append to apply an arbitrary interconnection scheme to a set of LTI models.
For example, if sys1 has m inputs and p outputs, while sys2 has p inputs and m outputs, then the negative feedback configuration of these two LTI models
is realized with
feedback(sys1,sys2)
This specifies the LTI model with m inputs and p outputs whose I/O map is
See the reference pages online for more information on feedback, series, parallel, lft, and connect.
| Arithmetic Operations on LTI Models | Continuous/Discrete Conversions of LTI Models | |
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