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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

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