sensi — sensitivity functions
[Se,Re,Te]=sensi(G,K) [Si,Ri,Ti]=sensi(G,K,flag)
standard plant (syslin
list)
compensator (syslin
list)
character string 'o'
(default value) or 'i'
output sensitivity function (I+G*K)^-1
K*Se
G*K*Se
(output complementary sensitivity function)
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)];
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)