Angewandte Regelung und Optimierung in der ... - uni-stuttgart
Angewandte Regelung und Optimierung in der ... - uni-stuttgart
Angewandte Regelung und Optimierung in der ... - uni-stuttgart
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Gauss-Jordan Simplification<br />
Setup of l<strong>in</strong>earized equations system<br />
• Once all nodes selected have been elim<strong>in</strong>ated, the equation system<br />
can be reconverted to a nonl<strong>in</strong>ear one us<strong>in</strong>g follow<strong>in</strong>g assumptions<br />
• R n,m = 100 (Roughness)<br />
• D=L (D)iameter and (L)ength of pipe<br />
⎛ ⎛<br />
⎜<br />
⎜<br />
⎜ g~<br />
⎝<br />
⎜<br />
⎜⎛<br />
⎜<br />
⎜<br />
⎜−<br />
g~<br />
⎝⎝<br />
22<br />
N ,2<br />
g~<br />
2,1<br />
− g~<br />
g~<br />
1,2<br />
11<br />
...<br />
g~<br />
N ,1<br />
− g~<br />
g~<br />
11<br />
⎞<br />
⎟<br />
⎠<br />
1,2<br />
⎞<br />
⎟<br />
⎠<br />
...<br />
...<br />
...<br />
⎛<br />
⎜−<br />
g~<br />
⎝<br />
⎛<br />
⎜ g~<br />
⎝<br />
2, N<br />
0.54g g~<br />
−0.46<br />
n, m<br />
| hn<br />
− hm<br />
| =<br />
N<br />
g~<br />
−<br />
g~<br />
...<br />
g~<br />
−<br />
g~<br />
N ,1<br />
11<br />
2,1<br />
11<br />
g~<br />
nm<br />
g~<br />
1, N<br />
1, N<br />
⎞⎞<br />
⎟<br />
⎟<br />
⎟⎛<br />
δh<br />
⎠ ⎜<br />
⎟<br />
⎜ ...<br />
⎞ ⎟<br />
⎜<br />
⎟<br />
⎟ ⎝δh<br />
⎠ ⎟<br />
⎠<br />
2<br />
N<br />
⎛<br />
⎜ δq<br />
⎞<br />
⎟ ⎜<br />
⎟ = ⎜<br />
⎟ ⎜<br />
⎠<br />
⎜δq<br />
⎝<br />
nod<br />
2<br />
nod<br />
N<br />
+<br />
+<br />
g~<br />
g~<br />
...<br />
g~<br />
g~<br />
2,1<br />
1<br />
N ,1<br />
1<br />
δq<br />
δq<br />
nod<br />
1<br />
nod<br />
1<br />
⎞<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎟<br />
⎠<br />
D<br />
n,<br />
m<br />
⎛ g<br />
⎜<br />
⎝ 3.58821⋅10<br />
n,<br />
m<br />
= Ln,<br />
m<br />
=<br />
−4<br />
⎞<br />
⎟<br />
⎠<br />
1<br />
2.09<br />
© ABB Group<br />
June 28, 2010 | Slide 63