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
Solutions - CHBE 470, Fall 2016 Exam #2 (closed-book)
Problem 1
1) Match the transfer functions with the responses to a unit step function shown
in the figure. Please justify your answers. [Hint: You can use IVT cfw_lim! ()
and FVT cfw_lim! ()]
Solutions HW #1 (Due: Sep. 9th 2016)
a)
a)
Problem 1 (1.6)
Feedback Control : Measured variable: y
Manipulated variable: D,R, or B(schematic shows D)
Feedback Control :
Feedback Control : Measured variable: y
Manipulated variable: D,R, or
B(schematic
CHBE 470 Homework # 3
Due: Friday, Sep. 30th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
Grades on late homework will be reduced 10% per day (including weekends).
Illness and family emergenc
CHBE 470 Homework # 5
Due: Friday, Oct 28th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
Grades on late homework will be reduced 10% per day (including weekends).
Illness and family emergenci
CHBE 470 Homework # 2
Due: Friday, Sep. 20th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
Grades on late homework will be reduced 10% per day (including weekends).
Illness and family emergenc
CHBE 470 Homework # 4
Due: Thursday, Oct. 20th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework: Grades on late homework will be reduced 10% per day (including
weekends). Illness and family emergencies
CHBE 470 Homework # 1
Due: Friday, Sep. 9th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
Grades on late homework will be reduced 10% per day (including weekends).
Illness and family emergenci
ChBE 470, Fall 2016 Exam #1 (closed-book)
October 6, 2016, 9:25 am-10:40 am, In class
Total points: 100
Do not forget to write and sign your Honor Code pledge.
No calculators needed or allowed.
1) Which of the following statements are true?
(15 point
CHBE 470 Homework # 7
Due: Friday, Dec. 2", 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
GIades on late homework will be reduced 10% per dag.r (including weekends). lness and famin
emergencies will be d
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
Chemical Engineering Design
ChBE 404 Spring 2017
Homework 1
Due: Thursday, January 19 (10:50 am)
ChBE 404 Homework Honor Code Policy: Students are encouraged to talk to each other, the
teaching assistants, the instructor, or anyone else about any homework
Solutions - HW #7 (Due Dec. 2nd 2016)
Problem 1 (12.1)
Problem 2
Problem 3 (18.6)
Problem 4 (18.21)
Problem 5
a)
Problem 6
OPTION A: Controlled variable: Y1, Y2
Manipulated variables: U1, U2
The steady-state gain matrix is
]
[
18
Using the formula in Eq
CHBE 470 Homework # 6
Due: Friday, Nov. 18th, 5 pm in CHBE 470 Mailbox,
Chemical and Biomolecular Engineering Department,
Abercrombie
Homework:
Grades on late homework will be reduced 10% per day (including weekends).
Illness and family emergenc