ESSENTIAL INFORMATION
MODULE CODE MODULE TITLE ASSESSMENT TYPE
MMME4056 Integrated Systems
Analysis
Simulink and Report
COURSEWORK TITLE WEIGHT (INDICATIVE EFFORT)
MMME4056, ISA 2024, COURSEWORK 30% (Approx. 10-15
hrs)
SUBMISSION DATE SUBMISSION TIME SUBMISSION METHOD
15/11/2024 15:00 Moodle
FEEDBACK DETAILS
Feedback will be provided within 20 working days and will consist of an individual feedback
form. Please note the marks released on Moodle are raw. If you have made a late submission
and it is not covered by an EC or an accommodation then the deductions will be made when I
submit the marks to the board after the exams.
LEARNING OUTCOMES ASSESSED (IN BOLD)
1. Demonstrate an understanding of the concept of system behaviour and the design of
experiments for characterising system components. - AHEP4: 2, 6
2. Critically evaluate and analyse complex dynamic systems behaviour using an
appropriate numerical or analytical methodology - AHEP4: 1, 2, 3, 6
3. Evaluate the reliability of the separable system components, coupled system
components and systems as a whole - AHEP4: 6, 9
SUBMISSION REQUIREMENTS
• This exercise constitutes 30% of the total course mark and is marked out of 100.
Marks for individual sections are indicated for that section.
• Submit your coursework via MOODLE as a ZIP file. This ZIP-file should contain the
coursework report itself (as a pdf document) and all files that you used in the CW.
Please adopt the file-naming suggested in this coursework specification. More details
about ‘WHAT TO SUBMIT’ can be found in the ASSESSMENT DETAILS.
• It must be possible to open the SIMULINK models submitted using MATLAB release
R2023 or later. Models presented in different releases that cannot be opened will not
be marked.
• Your report should not exceed 20 pages including the cover page, references, and
appendixes.
• Your Coursework should have a front page which will have your name and student
number.
• Text elements should be typed. Ideally in Arial 11 point.
• Drawings and figures must be made by computer. Drawings and figures may not be
copied from the internet. In ALL cases they should be appropriately titled and
captioned. The titles and captions should be clear and legible.
• You may not discuss the details of your answers with other students. Software checks
will be made to ensure no copying or plagiarism has occurred.
• Whenever you talk about someone else’s work (including journal papers, books,
conference papers, technical reports, theses/dissertations, websites, etc.) if necessary,
you must include a reference to the original source of this information. You should use
the IEEE referencing style for your report.
MMME4056... Integrated Systems Analysis
COURSEWORK
SYSTEM DESCRIPTION.
Figure 1 shows a floating wind turbine of spar-buoy type. These floating
supports for wind turbines achieve stability by having a centre of mass
below the centre of buoyancy (i.e. the centre of gravity of the displaced
water).
Spar-buoy floating arrangements are considered by some to be suitable for
very deep water. They are relatively compliant in “pitch”. That is to say,
when the wind blows and exerts a downwind thrust force on the rotor of
the wind turbine, the entire structure rocks backwards a little bit. As the
structure is moving backwards relative to the oncoming wind, the relative
wind speed reduces and so a coupling arises between the thrust force, F(t),
acting on the turbine and the angle of tilt, (t), of the platform. This
coursework is based on modelling the dynamics of such a floating wind
turbine platform and applying the methods taught within MMME4056.
The downwind thrust on a wind turbine rotor is not a simple function of
the wind speed, v(t). Every modern wind turbine has a particular fixed
rated wind speed vrated. For wind speeds lower than the rated wind speed
(v(t) < vrated), the turbine controller tries to extract the maximum available
power from the air and this results in a downwind thrust that is
proportional to the square of the wind speed, 𝐹(w**5;) = 𝑎 × w**7;(w**5;)
2
. By
contrast, for wind speeds higher than the rated wind speed (v(t) > vrated),
the turbine is not able to absorb all of the power available and the
controller must deliberately spill some power by pitching the blades
suitably. This results in a different downwind force relationship …
𝐹(w**5;) = 𝑎 × w**7;w**3;𝑎w**5;Ү**;𝑑
3⁄w**7;(w**5;). Figure 2 below shows a typical relationship
between wind speed and the downwind thrust force acting on a wind turbine.
q
Fig. 1: A Spar-buoy floating
wind turbine support
F
H
Fig. 2: Downwind thrust vs. (relative) wind speed.
vrated
Vcut-out
Wind speed, v →
Downwind thrust, F
→
OVERALL REQUIREMENTS
The requirement of this coursework is to understand this floating wind turbine as a simple dynamic system, to
simulate its behaviour as wind-speed changes using SIMULINK and to analyse its behaviour at two different
equilibrium states using methods taught in the course.
The submission should be based on what is explicitly asked for in this coursework specification. The primary
material being marked is a report – although you are asked to submit your SIMULINK models also. It must be
possible to open the SIMULINK models submitted using the version of MATLAB presently installed on
University computers. Models prepared in more modern releases will not be marked.
There are no additional marks for long reports!
FILES PROVIDED TO YOU – AND WHAT THEY DO.
CW_Spec.docx : This file. It contains the coursework specification.
f_diesel.m : A MATLAB function not directly related to this coursework but supplied to help illustrate
how a SIMULINK model can call a MATLAB function.
f_thrust.m : An MATLAB function that is not complete. You should complete this function by
modifying each line of code carrying the comment % Modify this line
In some cases, the modification simply involves you inserting the appropriate
numerical values. In the remaining cases, you should insert the correct formula.
sim_diesel.slx : A SIMULINK model calling the function f_diesel.m.
As well as showing how to call an Interpreted MATLAB Function in SIMULINK,
this also shows how to transfer data into the MATLAB workspace so that you can
obtain plots using MATLAB directly.
stud_data.xls : An EXCEL spreadsheet containing one unique row of data for each student.
Each row contains (in this order) … {vrated, a, J, k, c, H, p, q…}
start_here.m : A MATLAB script. This opens up a SIMULINK model of the diesel engine only,
(<sim_diesel.slx>) and then runs the model and plots both and &#***3; vs. time. You might
choose to copy and then modify this so as to use it as a way to open and run your own
SIMULINK model. You can run <start_here.m> either by clicking the big green
arrowhead in the top toolbar of the editor or else by just typing >>start_here
at the MATLAB command prompt).
WHAT TO SUBMIT
Submit your coursework via MOODLE as a ZIP file. This ZIP-file should contain the coursework report itself (as a
WORD or PDF document) and all files that you used in the CW.
IMPORTANT: Please make clear on the first page of the report which student you are by identifying which
Student ID# (SID# in the spreadsheet) applies to you (a number less than 401). If, for some reason, you do not find
your name in the spreadsheet, please contact the academic in charge of this coursework to get one. For the
purposes of your report, please refer to this number as the “SID_No”. (Student Identification number) on your
report clearly.
Marks will be deducted if you do not show this information clearly on page 1.
The coursework report should comprise:
• A response to Task 1 (the Table and, at most, 2 further sentences)
• A response to Task 2 (the corrected function, <f_thrust.m>, and four numerical answers)
• A response to Task 3 (maximum 2 pages). This should include an explanation of how you
applied an algebraic or iterative approach to finding the two equilibrium conditions and a
description of each equilibrium condition comprising {𝐹9.5,𝜙9.5, w**2;9.5} and {𝐹14,𝜙14, w**2;14}.
• A response to Task 4 which should comprise
- a legible view of the SIMULINK model (on a single page)
- an explanation in text of how you have applied the initial conditions
- the plot of q(t) vs. t.
• A response to Task 5 (1 page) comprising the SIMULINK Model and a plot of q(t) vs. t.
• A response to Task 6 (<2 pages) containing an explanation of how you determined the state-space
representation for one condition (you need not repeat this explanation) and how you used the state-space
representation to determine how q(t) varies with respect to time, t. Also a graph representing q(t) vs. t from
each of the two calculations (Task 5 and Task 6).
• A response to Task 7 (<2 pages) containing the eigenvalues of the A matrix for the equilibrium condition at
v(t) 14 and an interpretation of these. Also the graph of q(t) vs. t from the new SIMULINK model and a
commentary on any connection between the eigenvalues and this graph.
EQUATIONS DEFINING THE SYSTEM
The following equations define the behaviour of this system. In these equations, a dot above a quantity indicates
differentiation with respect to time. The angle 𝜙 is measured in radians.
(1) Define: w**8;(w**5;) ≔ w**7;(w**5;) − 𝐻 × 𝑐w**0;w**4;(𝜙) × 𝜙(w**5;)
(2) If w**8;(w**5;) > w**7;𝑐w**6;w**5;w**0;w**6;w**5;, 𝐹(w**5;) = (𝑎 × w**7;w**3;𝑎w**5;Ү**;𝑑
3⁄w**7;𝑐w**6;w**5;w**0;w**6;w**5;) ∗ exp (−5(w**8;(w**5;) − w**7;𝑐w**6;w**5;w**0;w**6;w**5;))
Otherwise if w**8;(w**5;) ≥ w**7;w**3;𝑎w**5;Ү**;𝑑, 𝐹(w**5;) = 𝑎 × w**7;w**3;𝑎w**5;Ү**;𝑑
3⁄w**8;(w**5;)
Otherwise w**8;(w**5;) < w**7;w**3;𝑎w**5;Ү**;𝑑 and 𝐹(w**5;) = 𝑎 × w**8;(w**5;)
2 × w**4;𝑖𝑔𝑛(w**8;(w**5;))
(3) 𝐽 × 𝜙(w**5;) + 𝑐 × 𝜙(w**5;) + 𝑘 × 𝜙(w**5;) = 𝐹(w**5;) × 𝐻 × 𝑐w**0;w**4;2
(𝜙)
(4) w**2; = 𝐻 × w**4;𝑖𝑛(𝜙)
THE COURSEWORK REQUIREMENT – 7 TASKS.
Task 1. Based on the equations supplied above, insert “Y” (for “yes”), “N” (for “no”) or “M” (for “maybe”) in
each un-shaded box of the table below to identify the nature of each quantity that appears in the equations.
Quantity An Input ? A State
Variable ?
A Rate
Variable ?
An Output ? An Intermediate
(Derived) Variable ?
A Parameter?
State whether there is any other state variable not mentioned in the table above. State also whether there is any
other rate variable not mentioned in the table above.
[10 marks]
Task 2. Correct the necessary lines of code present in the supplied function, <f_thrust.m> and present that
function in your report. Then call that function directly from the MATLAB for four different wind speeds:
{ 3m/s, 9.5m/s, 14m/s, 28m/s }. Report the results.
HINT: To get the answer for 9.5m/s, type … f_thrust( 9.5) at the MATLAB command prompt.
[10 marks]
Task 3. Without using SIMULINK, determine an equilibrium condition for the dynamic system at the wind
speeds 9.5m/s and 14m/s. For each of these speeds, report the following steady values,
𝐹9.5 = , 𝐹14 =
𝜙9.5 = , 𝜙14 =
w**2;9.5 = , w**2;14 =
HINT: There is no “closed-form” solution here so you will have to apply an iterative approach of some sort. A
manual iteration process is fine. You do not have to write any code to implement an iterative solution automatically
or to use any built-in iterative methods within MATLAB.
[15 marks]
Task 4. Now create a SIMULINK model of the system and run this model over a period of 500s with a constant
wind-speed of 9.5m/s taking the initial conditions to be (0) = 0.15 rad and 𝜙(0) = 0. Plot q(t) vs. t .
[25 marks]
Task 5. Modify the SIMULINK model from Task 4 so that the wind speed is now varying sinusoidally
according to w**7;(w**5;) = 9.5 + 0.2𝑐w**0;w**4;(0.2w**5;). Change the initial conditions so that (0) = determined from Task 3.
Plot q(t) vs. t over 500s.
[10 marks]
Task 6. Create state-space representations of the system for each of the two different equilibrium conditions
discovered in Task 3. In each case, treat v(t) as the only input and q(t) as the only output and report the matrices,
{A, B, C, D} for both cases separately. For the case of v(t) 9.5 m/s, use these matrices to develop an alternative
prediction for q(t) vs. t from Task 5. Create a plot containing two curves on the same graph representing q(t) vs. t.
One of those curves should use the data from Task 5 and the second curve should use the data from Task 6.
[15 marks]
Task 7. Calculate the eigenvalues of the matrix A for the case v(t) 14 m/s and interpret what these
eigenvalues tell you. Modify the SIMULINK model from Task 4 so that the input wind speed is now a steady
14m/s. Set the initial conditions to be (0) = ( + ) and run this model for 500s. Once again, plot q(t) vs. t.
Comment on any connections between what you see from the SIMULINK model output and what you found from
the eigenvalues of matrix A.
[15 marks]
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