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

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73<br />

74<br />

Constraints – forces from actuators<br />

c<br />

N =− l c ( θ ) + l c ( θ ) + l c ( n ) torque from actuators<br />

<strong>and</strong> wind<br />

c : T c ( n ) g ( ) total sway force<br />

c : T c ( ) c ( ) g ( ) total surge force<br />

1 :<br />

z y T 1 y T<br />

N<br />

+ gw<br />

( vw)<br />

2 x b 3<br />

2 y = b 3 +<br />

Y<br />

w vw<br />

3 x = T θ1 + T θ2 +<br />

X<br />

w vw<br />

Constraints – dynamics <strong>and</strong> kinematics<br />

c4: −1⎡Tx⎤ −1<br />

v= M ⎢ ⎥−A<br />

( ψ ) vc<br />

⎣Ty⎦ linear acc. of body<br />

c5<br />

: p= A( ψ ) v+ vc<br />

geographical position<br />

c6: −1<br />

ψ = I N angular acc. of body<br />

d1<br />

:<br />

d<br />

v= v<br />

dt<br />

differential<br />

d2<br />

:<br />

d<br />

p= p<br />

dt<br />

differential<br />

d3<br />

:<br />

d d<br />

ψ = ( ψ)<br />

dt dt<br />

double differention<br />

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

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

37

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