gfrancis - Francis equations for tracking (original) (raw)
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Scilab help >> CACSD > gfrancis
Francis equations for tracking
Calling Sequence
[L,M,T]=gfrancis(Plant,Model)
Arguments
Plant
syslin list
Model
syslin list
L,M,T
real matrices
Description
Given the the linear plant:
x'= Fx + Gu y = Hx + Ju
and the linear model
xm'= Axm + Bum ym = Cxm + Dum
the goal is for the plant to track the model i.e. e = y - ym ---> 0 while keeping stable the state x(t) of the plant. u is given by feedforward and feedback
u = Lxm + Mum + K*(x-Txm) = [K , L-KT] (x,xm) + Mum
The matrices T,L,M satisfy generalized Francis equations
FT + GL = TA HT + JL = C GM = TB JM = D
The matrix K must be chosen as stabilizing the pair (F,G) See example of use in directory demos/tracking.
Examples
Plant=ssrand(1,3,5); [F,G,H,J]=abcd(Plant); nw=4;nuu=2;A=rand(nw,nw); st=max(real(spec(A)));A=A-st*eye(A); B=rand(nw,nuu);C=2*rand(1,nw);D=0*rand(CB); Model=syslin('c',A,B,C,D); [L,M,T]=gfrancis(Plant,Model); norm(FT+GL-TA,1) norm(HT+JL-C,1) norm(GM-TB,1) norm(J*M-D,1)