ENG3104
Assignment3
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Assessment: Assignment 3
Due: 2015
Marks: 300
1 (worth 40 marks)
1.1 Introduction
To
assess how useful the wind power could be as an energy
source, use the file ass2data.xls to calculate the total
energy available in the wind for each year of data.
1.2 Requirements
For this assessment item, you must produce
MATLAB code which:
1.
Calculates
the total energy
for each of the years.
2.
Reports to the Command Window the energy for each year.
3.
Briefly discusses
whether there is any trend
in the results
for annual
energy production.
4.
Has appropriate comments throughout.
You must
also calculate
the
total
energy
for the first four
hours of power
data
(i.e.
over the first five data entries)
by hand to verify
your code;
submit
this
working in a pdf
file.
Your
MATLAB code must test (verify)
whether
the computed value of energy is the same as
calculated by hand.
1.3 Assessment Criteria
Your code will be assessed using the following scheme.
Note that you are marked
based on how well you perform for each category, so the correct
answer determined in a basic way will receive half
marks and the correct answer determined using an excellent method/code will receive full marks.
|
Quality of
the code
|
5 marks
|
|
Quality of
header(s) and
comments
|
5 marks
|
|
Quality of
calculation of
the energy for each year
|
15 marks
|
|
Quality of
reporting
|
5 marks
|
|
Quality of
discussion
|
5 marks
|
|
Quality of
verification based on hand
calculations
|
5 marks
|
2 (worth 65 marks)
2.1 Introduction
For the
wind turbines to operate
effectively, they must
turn
to face into
the wind. This could create large stresses in the structure if the wind changes
direction quickly while the wind speed is high.
You are to assess if this is likely to happen
using the data
in ass2data.xls.
2.2 Requirements
For this assessment item, you must produce
MATLAB code which:
1. Calculates the instantaneous rate of change of wind direction
using:
(a) backward
differences
(b) forward differences
(c)
central differences
2.
Plots
the three sets
of derivatives as functions of time.
3.
Produces scatter plots of maximum
wind gust as functions of each of the derivatives.
4.
Displays a message
in the Command Window with a brief discussion
of the scatter plots.
Discuss which of the derivatives should
be used to compare
with the wind gust and why.
Discuss whether you think
the
wind changes direction too quickly while the wind
speed is high and why.
5.
Has appropriate comments throughout.
You must also use a backward
difference, forward difference and central
difference by hand to determine the rate of change of wind direction
for the twelfth
data entry;
submit
this working
in a pdf file. Your
MATLAB code must
test
(verify) whether these values are the same as computed by the code for the three differences.
2.3 Assessment Criteria
Your code will be assessed using the following scheme.
Note that you are marked
based on how well you perform for each category, so the correct
answer determined in a basic way will receive half
marks and the correct answer determined using an excellent method/code will receive full marks.
|
Quality of
the code
|
5 marks
|
|
Quality of
header(s) and
comments
|
5 marks
|
|
Quality of
calculating the
differences
|
30 marks
|
|
Quality of
plotting the
differences as functions of time
|
5 marks
|
|
Quality of
plotting the
wind gust as functions
of the differences
|
10 marks
|
|
Quality of
discussion
|
5 marks
|
|
Quality of
verification based on hand
calculations
|
5 marks
|
3 (worth 70 marks)
3.1 Introduction
A
small non-switching power supply
is being designed and the components must
be selected so
that the voltage
in the
circuit never falls below Vmin .
The voltage
in the
circuit, vc, can be found
using Eq. (1) during
the charging
phase [when Eq. (2) is satisfied]:
C dvc(t)
dt
+ ic =
|vt cos(2πf t)| − 2Vd − vc(t)
2Rd
(1)
vc(t) ≤ |vt cos(2πf t)| − 2Vd
(2)
and using Eq. (3) during
the discharging
phase [when Eq. (4) is satisfied]:
dvc(t)
C dt + ic = 0
(3)
vc(t) > |vt cos(2πf t)| − 2Vd . (4)
The variables in Eqs.
(1)–(4)
are the capacitance, C , the current through the circuit,
ic,
the
transformed AC voltage,
vt , the frequency
of the AC power, f , the voltage
across the diode, Vd ,
and the resistance across
the diode, Rd
.
For your assignment,
the
values for these quantities are (note
that all quantities
are in SI
units):
|
Vmin
|
=
|
4.1949 V
|
(5)
|
|
C
|
=
|
8.3052 × 10−5 F
|
(6)
|
|
ic
|
=
|
0.59336 × 10−2 A
|
(7)
|
|
vt
|
=
|
1.0391 × 2 VAC
|
(8)
|
|
f
|
=
|
2.4768 × 10 Hz
|
(9)
|
|
Vd
|
=
|
7.9472 × 10−1 V
|
(10)
|
|
Rd
|
=
|
8.9797 × 10−2 Ω .
|
(11)
|
(Note that these values are indicative of the order
of magnitude that these variables
might take
and are not necessarily within the
limited range
that is used in practice.)
(a) Your task is to simulate
the system
for three cycles
to determine whether
vc
is always larger
than Vmin
, in which
case the components have
been satisfactorily selected. Your initial condition should
be chosen so that the equality
is satisfied in Eq. (2). Use the
following methods
to simulate
the system:
(i) Euler’s method in MATLAB.
You must report
to the Command Window the value
used for ∆t.
(ii) ode45 in MATLAB (iii) ode23 in MATLAB
(b) Your task is to
see how long it
takes for
vc to
charge to Vmin , starting with an initial condition of vc =
0 and assuming that
the system never enters the discharging phase. Use the following methods
to simulate
the system:
(i)
Euler’s method
in Simulink
(ii)
ode45 in Simulink
(iii)
ode23 in Simulink
Note that for part (a),
only moderate accuracy is required for the simulation
(it is not necessary to precisely simulate vc unless its smallest value is very close to Vmin ).
3.2 Requirements
For this assessment item, you must produce
MATLAB code and Simulink modules which:
1.
Simulate Eqs.
(1)–(4) using the three
methods listed
in MATLAB.
2.
Plots the simulated vc(t) for each method, clearly indicating the value of Vmin on
each graph. Non-dimensionalise
the value of time by multiplying
by f ; non-dimensionalise
the
voltage using (vt
− 2Vd
). Non-dimensionalisation allows you to compare cases of different
scale directly because the results are proportional
to the non-dimensionalising parameter.
3.
Displays a message
in the Command Window stating whether vc(t) is always greater
than
Vmin for each of the methods.
4.
Simulates Eq. (1) using Simulink.
5.
Produces a plot using
Simulink showing when vc(t) reaches Vmin .
6.
Displays within
Simulink when vc(t) reaches Vmin .
7. Produces
output to MATLAB
so that MATLAB can report
to
the
Command
Window the simulated times
for vc(t) to reach Vmin
.
8.
Has appropriate comments throughout.
You must also
verify your simulation
using Euler’s
method in MATLAB for the first
two timesteps of part (ai);
submit this
working in a pdf file. Your MATLAB code must test
(verify) whether the value of vc after two timesteps
is the same as computed by the code.
3.3 Assessment Criteria
Your code will be assessed using the following scheme.
Note that you are marked
based on how well you perform for each category, so the correct
answer determined in a basic way will receive half
marks and the correct answer determined using an excellent method/code will receive full marks.
|
Quality of
the code
|
5 marks
|
|
Quality of
header(s) and
comments
|
5 marks
|
|
Quality of
the MATLAB simulations
|
20 marks
|
|
Quality of
the Simulink
simulations
|
20 marks
|
|
Quality of
plots (e.g. axis labels, titles)
|
5 marks
|
|
Quality of
reporting of results
|
10 marks
|
|
Quality of
verification based on hand
calculations
|
5 marks
|
4 (worth 70 marks)
4.1 Introduction
A
smoke alarm sounds at 1 kHz and PL = 75 dB.
You are to determine
whether
these
speci- fications are satisfactory for the chosen application of a corridor of length L. The
propagation of sound is based on the sound
pressure p (the pressure increase from ambient pressure in Pa), where
the appropriate transport equation
is:
∂2p
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