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MATLAB Review + Simulation
CHE 361
A vertical cylindrical tank is constructed with holes in its side such that the flow rate of liquid out
of the tank is proportional to the height of liqu
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MATLAB Review + Simulation
CHE 361
A vertical cylindrical tank is constructed with holes in its side such that the flow rate of liquid
out of the tank is proportional to the height of liqu
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Inclass Heat Loss
CHE 361
Done Thur Week 2
Exercise 4.10 pg. 71 - Physical example of input/output relationship and transfer
function. Review Section 2.4 = Dynamic Models of Representa
Bode_fit 1/8
Identifying G(s) from a Bode Plot
CHE 361
Bode plots contain the frequency response of a transfer function model G(s) (for example generated by
using freqg) or obtained from an analysis o
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Computer Shortcut: freqg.p
CHE 361
Task: Use the MATLAB "program" file freqg.p to determine the frequency response of:
G( s) =
2e 0.2 s
for the freqency range of from 0.01 to 10 rad/min
10
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% BodeCHE361.m
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A simple program to make a Bode plot for first-order process
using MATLAB bode function and using "short-cut" method
for first-order with time delay process.
Dr. K
Fig 14 Bode
Fig 14.2 Bode
diagram for a
first-order process
(no time delay)
time delay)
Slope = -1
All G(s) have the
same plot of normalized
ARN vs (omega*tau) !
Assymptotes at lower & higher frequenc
freq_resp 1/2
Frequency Responses: t "domain"
1
1/(2*3.14159)s+1
Sine Wave1
Transfer Fcn1
CHE 361
+
7
+
Constant1 Sum1
+
9
+
Constant2 Sum2
1
1/(2*3.14159)s+1
Sine Wave2
Transfer Fcn2
+
1
+
Constant3
u '(t ) = A sin ωt sinusoidal input to 1st-order G ( s )
ω
K
Y '( s ) =
= G ( s )U '( s )
A 2
2
KA
τ s + 1 s + ω
=
y '(t )
ωτ e − t /τ − ωτ cos ωt + sin ωt )
(
freqresp2.mdl =
ω 2τ 2 + 1
Frequ
pulse_test 1/5
Pulse Testing Experiments
CHE 361
Read pgs 344-348 of SEM1 text attached - note the input is called x(t).
The analysis of a pulse test allows the calculation of the frequency response o
Bioreactor Pulse Testing = 3 Hints
CHE 361
Hint #1. When doing a pulse test, the analysis is easiest to interpret when the the transfer
function has a positive gain. In order to simplify the Bode plot
Chap 14 = Frequency Response Analysis of Process Dynamics
CHE 361
SEMD3 = EXERCISE 14.3 pg. 268. (In-class)
A data acquisition system for environmental monitoring is used to record the temperature of
EXAM 2 preview/review
CHE 361
Winter 2012
Remember. Midterm # 2 is 10 - 11:50 am Thur. Mar. 1, 2012 in Kearney 212.
Bring your own (Textbook+), paper, pencils, calculator with charged batteries, etc.
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Base Case G(s) = Bio2x2Glocal.p Numerical Linearization CHE 361
> Bio2x2Glocal
(after modifying and saving bioreac2x2.mdl
Enter flow rate F = (1 for nominal ss) = 1
Enter feed nutrient co
G (s) =
CHE 361 - Bioreactor Project
output =
input =
"BUGS" FOR : _ / # _ (TEAM Name / # )
Student signed initials: _
A. Your BUG Kinetic Constants:
_
_
base metabolic rate
M = _
(0.001 - 0.2 g food/
Speed-up Effect of Zero (Overdamped 2nd-order) Step Response
So … a zero “speeds-up” the response of a process = but Why? and How?
Simple example: poles at -0.2 and -1 with a zero at -0.5, thus
= 5, τ
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Numerical Method to Solve Initial Value Problems (IVPs) CHE 361
Both Euler and RK4 use fixed step size in time.
(Can be used with nonlinear as well as linear ordinary differential Equ
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CHE 361: Least-squares Fit of Step Responses: step2g
First copy the Simulink example file "HW5_1sim.mdl" from the class web site into your
directory folder where all your other MATLAB file
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SCHOOL OF CHEMICAL, BIOLOGICAL, and ENVIRONMENTAL ENGINEERING
OREGON STATE UNIVERSITY
CHE 361 - TEAM BIOREACTOR PROJECT
WINTER Quarter 2012
I. OUTLINE OF PROJECT STEPS
This special project
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Complex Conjugate Pair of Roots
CHE 361
It sometimes happens in process dynamics problems that we obtain part of Y(s) that looks like:
A
A
Y ( s) = + + + +
s r+ s r
After evaluation of
+
2nd
1. Step Input
order G(s)
A sudden change in a process variable can be approximated by
a step change of magnitude, M:
In analyzing process dynamic and process control systems, it is
important to
Transfer Functions
Definition of the transfer function:
of the transfer function:
Convenient representation of a linear, dynamic model.
Let G(s) denote the transfer function between an input, x, and
1. Standard notation in dynamics and control
(shorthand notation) = how you communicate
with other engineers.
other engineers
2. Converts differential calculus mathematics to
algebraic operations, ver
CHE 361: PREVIEW
MODELING EQUATIONS - Ordinary Differential Equation Models from Mass and Energy Balances
A.
Develop equations: rate of accumulation and other rates
B.
Operating point: steady-state an
Rev: 6-14-11
Corrections for the 2nd Printing of SEMD, 3/e
Page Column
Location
Correction
6
37
50
60
both
right
left
left
Fig. 1.6
Fig. E2.13
One line below (3-91)
Eq. (4.13)
Move x1 down so it is al
Rev: 10-3-10
Corrections for the First Printing of SEMD, 3/e
Page Column
Location
vii
vii
ix
13
42
50
Right
Right
Left
Left
Left
Right
1st line
2ndt line
7 lines from bottom
Fig. 1.12
Entry 6 in Table