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Diagnosis and FTC by Prof. Blanke [pdf] - NTNU

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49<br />

50<br />

Example 5.3: tank system<br />

F = H= A JA H H<br />

D<br />

K J<br />

+ JH <br />

= C HEJD <br />

O J<br />

A L A I A I H<br />

D<br />

6 = <br />

G E J<br />

Single tank system example 5.3<br />

Tank c 1: h(t) = q i(<br />

t) − qo( t)<br />

Input valve c 2 : q() i t = αu()<br />

t<br />

Output pipe c 3 : q o(<br />

t) = k h( t)<br />

Level sensor c 4 : yt ( ) = ht ( )<br />

Control algorithm c 5 : ut ( ) =<br />

⎧1<br />

if y( t) < h0<br />

⎨<br />

⎩0<br />

otherwise<br />

dh() t<br />

differential constraint: c6: h( t)<br />

=<br />

dt<br />

F = H= A JA H H<br />

D<br />

K J<br />

+ JH <br />

= C HEJD <br />

O J<br />

A L A I A I H<br />

G J<br />

D<br />

Mogens <strong>Blanke</strong> – Spring 2006<br />

6 = <br />

G E J<br />

G J<br />

Mogens <strong>Blanke</strong> – Spring 2006<br />

25

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