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)

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

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)

+

+

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')

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)