sensi

Scilab Function
Last update : April 1993

sensi - sensitivity functions

### Calling Sequence

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

### Parameters

- `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)

### See Also

`augment` , `lft` , `h_cl` ,