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Ajuda do Scilab >> CACSD > Control Design > Control Loop > feedback

# feedback

feedback operation

### Syntax

`Sl = Sl1 /. Sl2`

### Arguments

Sl1,Sl2

linear systems (`syslin` list) in state-space or transfer form, or ordinary gain matrices.

Sl

linear system (`syslin` list) in state-space or transfer form

### Description

The feedback operation is denoted by `/.` (slashdot). This command returns `Sl=Sl1*(I+Sl2*Sl1)^-1`, i.e the (negative) feedback of `Sl1` and `Sl2`. `Sl` is the transfer `v -> y` for `y = Sl1 u`, `u = v - Sl2 y`.

The result is the same as `Sl=LFT([0,I;I,-Sl2],Sl1)`.

 Caution: do not use with decimal point (e.g. `1/.1` is ambiguous!)

### Examples

```S1=ssrand(2,2,3);S2=ssrand(2,2,2);
W=S1/.S2;
ss2tf(S1/.S2)
//Same operation by LFT:
ss2tf(lft([zeros(2,2),eye(2,2);eye(2,2),-S2],S1))
//Other approach: with constant feedback
BigS=blockdiag(S1,S2); F=[zeros(2,2),eye(2,2);-eye(2,2),zeros(2,2)];
Bigclosed=BigS/.F;
W1=Bigclosed(1:2,1:2);   //W1=W (in state-space).
ss2tf(W1)
//Inverting
ss2tf(S1*inv(eye()+S2*S1))```

### See also

• lft — linear fractional transformation
• blockdiag — Creates a block diagonal matrix from provided arrays. Block diagonal system connection.
• augment — augmented plant
• obscont — observer based controller
 Report an issue << augment Control Loop lft >>

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