Mathematical Modeling of
Chemical Processes
Mathematical Model (Eykhoff, 1974)
a representation of the essential aspects of an existing
system (or a system to be constructed) which
represents knowledge of that system in a usable form
Everything should be
Laplace Transforms
1. Standard notation in dynamics and control
(shorthand notation)
2. Converts mathematics to algebraic operations
3. Advantageous for block diagram analysis
Laplace Transform
L(f (t) = f (t)e -st dt
0
Example 1:
a st
a a
L(a)= ae dt e
PHY 1810
Homework # 6
Current and Resistance
Fall 2013
-1. The current in an electric hair dryer is 10.0 A. How much charge and how many electrons flow
through the hair dryer in 5.0 minutes?
The amount of charge delivered is
60 s
3
Q 10.0 A 5.0 min
3.0
Transfer Functions
Convenient representation of a linear, dynamic model.
A transfer function (TF) relates one input and one output:
u (t )
U (s)
system
y (t )
Y (s)
The following terminology is used:
u
y
input
output
forcing function
response
cause
ef
Dynamic Behavior
In analyzing process dynamic and process control systems, it is
important to know how the process responds to changes in the
process inputs.
A number of standard types of input changes are widely used for
two reasons:
1. They are represen
Dynamic Response Characteristics
of More Complicated Systems
Inverse Response
K(1 + 3 s)
G(s) =
(1 + 1s)(1 + 2 s)
slope (t = 0) 0
If 3 > 0 .fast response
3 < 0 .inverse response
(see Fig. 6.3)
3 : zero of transfer function
Use nonlinear regression for f
Development of Empirical Dynamic
Models from Step Response Data
Black box models
step response easiest to use but may upset
the plant manager (size of input change? move
to new steady-state?)
other methods
impulse - dye injection, tracer
random - PRBS (ps
PHYS 1810
Quiz # 5
Fall 2013
Name: _
-1. What is the equivalent resistance between points a and b in the circuit shown below?
2. A flat iron is marked 120 V and 600W. In normal use, the current in it is:
A) 2 A
B) 4 A
C) 5 A
D) 7.2 A
E) 0.2 A
3. Figure be
Exam
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) Albert uses as his unit of length (for walking to visit his neighbors or plowing his fields)
the albert (A), the distance Albert can throw a s
Prove", 19qu has shod up +0 rapedecl +es+rn3. I? you Howe a piece. oF
"HA a My I 1100de mammd fl'tod you
evidence which clISoSrees (m ;
chat Wed e/vrdence again. Try anomr exp emenf anal see, 76 you. 39
Ma same res M.
Z. a) \Iom drWe 50m 1r 50m + 100m t [
Physics 302 Homework 2 SOlwhons
i. A heavxer obged exPaIences a grower gravfmnomi Force, HAM a 1'3
Objed'l int/1+ H is @160 Aan cfw_0 oLCce/Lerode owm f0 Hs quaer may;
waam W : mg, Quack m @0169, (QQIVVQd +0 accelerqd-e 30m+hrj
VOW some-f'kIra Fans 9mm an
Physics 102 Homework 5 Solutions
1. As the tape moves across the coil, the coil of wire experiences a changing magnetic field. This
changing magnetic field induces a current in the coil, which can be read out as an electrical
signal. A practical applicati
Physics 102 Homework 4 Solutions
1. No, this is not an exception to the entropy principle. The entropy of the water is decreasing
while it freezes. However, the freezer is taking the heat from the inside of the freezer and
transporting it to the outside.
Physics 102 Homework 3 Solutions
1. a. A<E<C<B<D
b. A<E<C<B<D
c. D<B<C<E<A
d. No, the roller coaster car would not be able to reach point F because it loses some of its
kinetic and/or gravitational potential energy to thermal energy, so it will never be a
Preparation for Worksheet 6
Please notice that this file is two pages long.
What Its About
An object moving with a constant speed and in a straight line is said to be in uniform motion.
This worksheet mostly deals with the motion graphs, position versus t
Preparation for Worksheet 7
Please notice that this file is two pages long.
What Its About
Any problem about a moving object in which you do not need to know what is causing the
motion is called a kinematics problem. This worksheet is about the basic quan
Preparation for Worksheets 11 and 12
Please notice that this file is two pages long.
What Its About
Still about problem solving using the equations for constant acceleration, but now also
including the problem of free fall.
A object whose motion is solely
Preparation for Worksheet 8
Please notice that this file is two pages long.
What Its About
How the position-versus-time and velocity-versus-time graphs are related when an object is
accelerating. These topics are covered fairly well in the Young and Freed
Preparation for Worksheet 4
Please notice that this file is two pages long.
What Its About
Using proportionalities. Two quantities, x and y are said to be proportional if they obey the
equation y = cx where c is a constant. (In this worksheet, well always