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lft Scilab Group Scilab Function lft
NAME
lft - linear fractional transformation
CALLING SEQUENCE
[P1]=LFT(P,K)
[P1]=LFT(P,r,K)
[P1,r1]=LFT(P,r,P#,r#)
PARAMETERS
P : linear system (syslin list), the ``augmented'' plant, implicitly
partitioned into four blocks (two input ports and two output ports).
K : linear system (syslin list), the controller (possibly an ordinary
gain).
r : 1x2 row vector, dimension of P22
P# : linear system (syslin list), implicitly partitioned into four
blocks (two input ports and two output ports).
r# : 1x2 row vector, dimension of P#22
DESCRIPTION
Linear fractional transform between two standard plants P and P# in state
space form or in transfer form (syslin lists).
r= size(P22) r#=size(P22#)
LFT(P,r, K) is the linear fractional transform between P and a controller
K (K may be a gain or a controller in state space form or in transfer
form);
LFT(P,K) is LFT(P,r,K) with r=size of K transpose;
P1= P11+P12*K* (I-P22*K)^-1 *P21
returns the generalized (2 ports) lft of P and P#.
P1 is the pair two-port interconnected plant and the partition of P1 into
4 blocks in given by r1 which is the dimension of the 22 block of P1.
P and R can be PSSDs i.e. may admit a polynomial D matrix.
EXAMPLE
s=poly(0,'s');
P=[1/s, 1/(s+1); 1/(s+2),2/s]; K= 1/(s-1);
lft(P,K)
lft(P,[1,1],K)
P(1,1)+P(1,2)*K*inv(1-P(2,2)*K)*P(2,1) //Numerically dangerous!
ss2tf(lft(tf2ss(P),tf2ss(K)))
lft(P,-1)
f=[0,0;0,1];w=P/.f; w(1,1)
//Improper plant (PID control)
W=[1,1;1,1/(s^2+0.1*s)];K=1+1/s+s
lft(W,[1,1],K); ss2tf(lft(tf2ss(W),[1,1],tf2ss(K)))
SEE ALSO
sensi, augment, feedback, sysdiag
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