Zbirka rijesenih zadataka - PBF - Sveučilište u Zagrebu

Ž. Kurtanjek: PBF Mjerenja i automatizacija 2007/2008 30
Izdvojimo izlaznu veličinu kao nepoznanicu a ulazne veličine kao nezavisne
varijable zadržimo na desnoj strani:
( 1 + WP2
⋅WI
⋅WR
⋅WM
) ⋅Y
= WP1
⋅ X
P1
+ WP2
⋅ X
P2
+ WP2
⋅WI
⋅WR
⋅ X
I
Y
=
WP
( 1+
WP ⋅W
⋅W
⋅W
)
2
I
WP
( 1+
WP ⋅W
⋅W
⋅W
)
2
I
WP ⋅W
I
( 1+
WP ⋅W
⋅W
⋅W
)
2
2
I
1
2
I
R
R
⋅W
R
R
M
M
M
⋅ X
⋅ X
⋅ X
P1
P2
+
+
Pojedine prijenosne funkcije sustava su:
X P1
W 1
X P2
W 2
+
+
Y
+
X I
W 3
Y
= W1
⋅ X
P1
+ W2
⋅ X
P2
+ W3
W
W
2
W
1
3
=
=
=
WP
⋅ X
( 1+
WP ⋅W
⋅W
⋅W
)
( 1+
WP ⋅W
⋅W
⋅W
)
2
I
( 1+
WP ⋅W
⋅W
⋅W
)
I
I
WP
WP ⋅W
2
2
2
2
I
1
R
R
R
⋅W
R
M
M
M
I
b)
Polove regulacijskog sustava odredimo za zadane prijenosne funkcije koje
uvrštavamo u izvedene izraze:
k1
k2
τ
1
⋅ s + 1
τ
2
⋅ s + 1
W1
=
W3
=
k2
k2
1+
⋅ k R
1+
⋅ k R
τ
2
⋅ s + 1
τ
2
⋅ s + 1
Pojednostavnimo dvostruki razlomak: