Download - Abidin Dinpro Fix
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Tugas Dinamika Proses
Nama: Mochamad Abidin Kurniawan
NIM: 121120149
Ttd:
Tipe soal : Ganjil
Diketahui:
f1, f2 dan f3 bernilai konstan
T1=T2=T3 (tidak ada neraca panas di perhitungan)
Pada saat t=0, maka
c1(t) = c1 ; c2(t)=c2 ; c3(t)=c3
v= 5 m3
f1= 2 m3/menit
f2= 4 m3/menit
c1= 1250 kg/m3
c2= 1500 kg/m3
v
f1,c1(t) f2,c2(t)
f3,c3(t)
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Ditanya:
1. Persamaan diferensial
2. Fungsi transfer
3. AR dan
4. Nyquist plot
Jawab:
Neraca massa
1. 1() + 2. 2() 3. 3() =()
= 3()
1. 1() + 2. 2() 3. 3() = 3()
. . (1)
Saat t = 0 (steady state)
1.c1 + 2.c2 3.c3 = 3
. . . . . (2)
Persamaan (1) persamaan (2)
1 (c1(t) c1) + 2 (c2(t) c2) 3 (c3(t) c3) = (3() 3)
1.C1(t) + 2.C2(t) 3.C3(t) = 3()
. . (3)
Term deviasi
C1 = c1(t) c1 ; 1 = 1
C2 = c2(t) c2 ; 2 = 2
C3 = c3(t) c3 ; 3 = 3
TL persamaan (3)
1.C1(s) + 2.C2(s) 3.C3(s) = S.C3(s)
C3(s).[S + 3] = 1.C1(s) + 2.C2(s)
C3(s) = 1.1()+ 2.2()
+ 3
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Diagram Blok
Mencari AR dan menggunakan metode subtitusi langsung
G(s) = 1+ 2
+ 3
S
G(s) = 1+ 2
(
3
3)
= 1. 1.3+ 2.3
2 32
= 3(1+ 2)
2 32 () +
(1+ 2)
2 32 ()
= arctan (
)
= arctan (
3)
r = 2 + 2
= 1
2 32 3(1 + 2)2 + 2 (1 + 2)2
= 1+ 2
2 32 32 + 2
1/(S+ 3')
2/(S+ 3')
C1(s)
C3(s) C2(s)
+
+
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Nyquist Plot
Perhitungan pada scilab
clc;clear;
v = 5;
f1 = 2; f2 = 4; f3 = f1+f2;
tho1 = f1/v; tho2=f2/v; tho3=f3/v;
w1 = 0; dw=.1; w2=100; w=[w1:dw:w2];
nw = length(w);
for i=1:nw
re(i)=(-tho3*(tho1+tho2))/(-(w(i))^2-tho3^2);
im(i)=(w(i)*(tho1+tho2))/(-(w(i))^2-tho3^2);
end
plot(re,im,'b-')
xlabel('re')
ylabel('im')
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Mengganti nilai w1 menjadi -100 dan w2 menjadi 0.
Maka Nyquist Plot yang didapat adalah
Analisis Nyquist Plot:
Nyquist Plot yang didapat memiliki kondisi stabil karena Nyquist plot tidak mengelilingi titik
(-1,0)