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See the recommended documentation of this function

sensi

sensitivity functions

Syntax

```[Se,Re,Te]=sensi(G,K)
[Si,Ri,Ti]=sensi(G,K,flag)```

Arguments

G

standard plant (`syslin` list)

K

compensator (`syslin` list)

flag

character string `'o'` (default value) or `'i'`

Se

output sensitivity function `(I+G*K)^-1`

Re

`K*Se`

Te

`G*K*Se` (output complementary sensitivity function)

Description

`sensi` computes sensitivity functions. If `G` and `K` are given in state-space form, the systems returned are generically minimal. Calculation is made by `lft`, e.g., `Se` can be given by the commands `P = augment(G,'S')`, `Se=lft(P,K)`. If `flag` = `'i'`, `[Si,Ri,Ti]=sensi(G,K,'i')` returns the input sensitivity functions.

```[Se;Re;Te]= [inv(eye()+G*K);K*inv(eye()+G*K);G*K*inv(eye()+G*K)];
[Si;Ri;Ti]= [inv(eye()+K*G);G*inv(eye()+K*G);K*G*inv(eye()+K*G)];```

Examples

```G=ssrand(1,1,3);
K=ssrand(1,1,3);
[Se,Re,Te]=sensi(G,K);
Se1=inv(eye()+G*K);  //Other way to compute
ss2tf(Se)    //Se seen in transfer form
ss2tf(Se1)
ss2tf(Te)
ss2tf(G*K*Se1)
[Si,Ri,Ti]=sensi(G,K,'i');
w1=[ss2tf(Si);ss2tf(Ri);ss2tf(Ti)]
w2=[ss2tf(inv(eye()+K*G));ss2tf(G*inv(eye()+K*G));ss2tf(K*G*inv(eye()+K*G))];
clean(w1-w2)```

• augment — augmented plant
• lft — linear fractional transformation
• h_cl — closed loop matrix