Observer design by pole placement
Observer design by pole placement
Observer design by pole placement
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Feedback controller:<br />
σ̂x = (A+LC)̂x +(B + LD)u − Ly,<br />
= (A+LC + BK + LDK)̂x − Ly<br />
u = K̂x<br />
Note: the feedback controller is a dynamical system<br />
Closed-loop system:<br />
[ [ ]<br />
x̂x] A BK<br />
σ =<br />
−LC A+LC + BK][ x̂x<br />
Note: closed-loop system order = plant order + controller order<br />
Error equation:<br />
[ [ ]<br />
x A+BK −BK x<br />
σ =<br />
e]<br />
0 A+LC][<br />
e<br />
ELEC 3035 (Part I, Lecture 7) <strong>Observer</strong> <strong>design</strong> 11 / 12