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Master of Engineering, Energy Automation Sustainable Engineering
Åland University of Applied Sciences, Mariehamn
Pre-Assignment
Energy Automation Sustainable Engineering
Pre-assignment: This pre-assignment is a mandatory part in the application for the program in Master
of Engineering in Energy Automation Sustainable Engineering oered by Åland University of Applied
Sciences in Mariehamn. A score of at least 50 points on the assignment, of a maximum of 100 points, is
required for being eligible for admission. The pre-assignment should be submitted no later than March
5
th, 2025, at 15:00 EEST, UTC+03:00.
If you have questions related to accessibility, please contact Degree Program Director Florian Haug:
orian.haug@ha.ax.
The intention of the assignment is to map the basic skills and interest needed for developing abilities
to use and creatively explore modern tools for modeling and data analysis, read and analyze scientic
writing within the eld, and eectively communicate results.
1 Task 1: Letter of Motivation
Submit a letter of motivation of a maximum of 700 words outlining why you consider yourself a good
candidate for the program. In addition to the topics you might choose to emphasize, e.g., suitable
experience, visions for future roles and possibilities, possible thesis topics, etc., the letter should reect
your formal language skills. The letter of motivation can give a maximum of 40 points.
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2 Task 2: Simulations
In the book Thinking Fast and Slow1
, the Nobel Prize laureate Daniel Kahneman dierentiates between
two modes of thought: System 1 described as automatic and fast, and System 2 as controlled and
slow. To illustrate the dierences with an example, assume that you are told that you pay one euro and
20 cents for a pen and an eraser and that the eraser costs one euro more than the pen. If you are asked
how much you pay for the eraser and only consult System 1, you could give the erroneous answer that
you pay one euro for the eraser. Your System 2 would instead solve the linear equation and give the
correct answer that you pay one euro and 10 cents for the eraser.
In the article, Evolutionary game dynamics of controlled and automatic decision-making2
, the authors
study under what circumstances agents with an either-or mode of thinking can co-exist, dominate, or
periodically dominate alternatingly over time. For this purpose, they, among other things, explore the
system of dierential equations
x ̇ = (x − 1) x
a
a − βρ + ρ + βρx +
ρ + βρx
a + 1
− 1
β ̇ =
x − β
τb
(1)
In the equation, x(t) is the fraction of controlled agents, 1 − x(t) the fraction of automatic agents, ρ
the probability of nding a good, β(t) the competitive advantage automatic agents have over controlled
agents in acquiring goods (where β = 0 means that both types of agents have an equal probability of
acquiring goods), a determines the extent of diminishing marginal returns [on consumption of goods],
with lower a leading to more steeply diminishing returns, and a lag τb capturing the fact that an increase
in x at time t does not always have an immediate impact on x.
For a = 0.8, τb > 200 and 0.2 < ρ < 0.3 the fraction of controlled agents x and automatic agents 1 − x
will, according to the article, alternate periodically over time. The assignment is to verify this result
by solving Eq. (1) for your own choice of parameters τb > 200 and 0.2 < ρ < 0.3. In your simulations,
what is the period for x(t)? For how long will x(t) dominate over 1−x(t) within one period? In your
submission, include a gure illustrating x(t) and 1 − x(t) over time. This task can give a maximum
of 30 points.
1Highly recommended not only for its contents but also for the enjoyable and enlightening introduction to scientic practice
and reasoning.
2Available through https://www.stevenstrogatz.com/ or directly at the following link.
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3 Task 3: Data Analysis
A common digital PI-controller is given by the equations,
e(k) = r(k) − y(k)
u(k) = u(k − 1) + Kc
1 +
Ts
Ti
e(k) − e(k − 1)
(2)
where k is the sampling index, Ts is the sampling period, r(k) is the setpoint, y(k) is the (measured)
process value, e(k) is the control error and u(k) is the controller output. The parameter Kc is called the
gain and Ti
is called integration time. These are typically tuned in order to achieve a desired performance
of the closed-loop system.
Measurements from a heater and a heat exchanger, schematically depicted in Fig. 1, are provided in the
comma-separated values le HeatControl.txt. The process has three control signals, denoted uc for the
pump on the cold side, uh for the pump on the hot side, and up for the power to the heater. Depicted
external disturbances are Tci and Tsurr, i.e., the temperature of the ow on the cold side in to the heat
exchanger and the surrounding temperature. The main process values to be controlled are the ow on
the cold side, V ̇
c, the temperature entering on the hot side, Thi, and the temperature exiting on the cold
side, Tco.
Figure 1: Schematic view of the heating process. Blue is used to illustrate the cold side of the heat
exchanger and depicted are also the control signal to the pump on the cold side, uc, the incoming
temperature on the cold side, Tci, the ow on the cold side V ̇
c and the temperature exiting the
cold side, Tco. Red is used to illustrate the hot side of the heat exchanger and heater. Depicted
in red are also the control signal to the pump on the hot side, uh, the incoming temperature
on the hot side, Thi, the ow on the hot side V ̇
h, the temperature exiting the hot side, Tho, the
control signal to the heater up and the power to the heater P.
In the le HeatControl.txt, the rst three columns are uc, uh and up followed by V ̇
c, Tco and Thi, all
sampled with 1 Hz. The measurements are illustrated in Figs. 24.
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Figure 2: Upper panel illustrates the ow on the cold side, V ̇
c, for a period of 2000 seconds. Lower panel
illustrates the corresponding control signal to the pump on the cold side, uc. Automatic control
is turned on a little before 400 seconds. Data can be found in the le HeatControl.txt.
Figure 3: Upper panel illustrates the temperatures on the cold side Tco in red and Tci in blue for the same
2000 seconds as in Fig. 2. Lower panel illustrates the corresponding control signal to the pump
on the hot side, uh. Automatic control is turned on a little before 400 seconds. Data can be
found in the le HeatControl.txt.
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