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.TH sensi 5 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
sensi - sensitivity functions
.SH CALLING SEQUENCE
.nf
[Se,Re,Te]=sensi(G,K)
[Si,Ri,Ti]=sensi(G,K,flag)
.fi
.SH PARAMETERS
.TP 10
G
: standard plant (\fVsyslin\fR list)
.TP
K
: compensator (\fVsyslin\fR list)
.TP
flag
: character string \fV'o'\fR (default value) or \fV'i'\fR
.TP
Se
: output sensitivity function \fV(I+G*K)^-1\fR
.TP
Re
: \fVK*Se\fR
.TP
Te
: \fVG*K*Se\fR (output complementary sensitivity function)
.SH DESCRIPTION
\fVsensi\fR computes sensitivity functions. If \fVG\fR and \fVK\fR are
given in state-space form, the systems returned are generically minimal.
Calculation is made by \fVlft\fR, e.g.,
\fVSe\fR can be given by the commands
\fV P = augment(G,'S')\fR, \fVSe=lft(P,K)\fR.
If \fVflag\fR = \fV'i'\fR, \fV[Si,Ri,Ti]=sensi(G,K,'i')\fR
returns the input sensitivity functions.
.LP
.nf
[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)];
.fi
.SH EXAMPLE
.nf
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)
.fi
.SH SEE ALSO
augment, lft, h_cl
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