sensi

sensitivity functions

Calling Sequence

[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)

See Also

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