sensi
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
