feedback

feedback operation

Calling Sequence

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=`sysdiag`_(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
• sysdiag block diagonal system connection
• augment augmented plant
• obscont observer based controller