sensi

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)

See also

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