Problem 1
a) The transfer function of this process can be expressed as the product of three first order
lag transfer functions. The AR and phase angles of a general 1st order lag are:
AR =
K
+1
2
2
and = tan 1 ()
(S1.1)
Thus, applying the principle of su
Problem 1
controller
valve
tank 1
k C (1 + 3 s)
ySP (s)
1
1
0.2s + 0.4s + 1
y(s)
2
Measuring
device
2
Figure 1
The characteristic equation for the closed loop in figure 1 can be written as follows:
1 + G OL (s) = 1 +
2k C (1 + 3 s)
0.2s 2 + 0.4s + 1
(S1.1
Problem 1
ySP (s) +
k = 1.6
5
(s + 1)(2s + 1)
y(s)
The closed loop transfer function can be written as follows:
8
y(s)
8
89
(s + 1)(2s + 1)
G CL (s) =
=
=2
=
2
8
ySP (s) 1 +
2s + 3s + 9 2 9s + 1 3s + 1
(s + 1)(2s + 1)
(S1.1)
Thus, comparing (S1.1) to the
Problem 1
a) For noninteracting capacities with linear resistances subject to a unit-step change in the
input of the first tank, the material balance can be written as follows:
A1R1
dy1
+ y1 = R1u(t)
dt
(S1.1)
A2R 2
dy 2
R
+ y 2 = 2 y1
dt
R1
(S1.2)
subjec
Problem 1
From table 7.1 in the textbook, the Laplace transform of y(t)=te-t is:
L te t = y(s) =
1
(s + 1) 2
(S1.1)
Moreover, the Laplace transform of the unit-impulse (t) is:
L [ (t) ] = u(s) = 1
(S1.2)
Since u(t)=0 all the time but at t=to, assuming tha
Problem 1
Overall Material Balance:
dn d(V) d(Ah)
=
=
= i Fi F
dt
dt
dt
A
dh
d
+ Ah
= i Fi F
dt
dt
(S1.1)
In absence of chemical reactions and at constant temperature and pressure, the density of
the fluid liquid in the tank can be assumed constant. There
Problem 1
Overall Material Balance:
dn d(V)
=
= i Fi F
dt
dt
dV
d
+V
= i Fi F
dt
dt
(S1.1)
Assuming constant density and reactor volume, equation (S1.1) yields:
( Fi F ) = 0
Fi F = 0
(S1.2)
Therefore, the input and output flow rates are equal at each poi
CHBE 470 Process Dynamics and Control Fall 2007
Homework Set 2
Assigned: Wednesday, September 12
Due: Wednesday, September 19
Note: Please staple your papers and include your name in the first page
Use table 7.1 (pages 137-138) from textbook wherever you
Priyanka Chandraker
Dr. Nagrath
CHBE 470
22 September, 2016
Abstract
Anaerobic digestion is a process by which microorganisms break down organic material in the
absence of oxygen. In the context this paper, anaerobic digestion is utilized to treat food wa