ESSENTIAL INFORMATIONMODULE CODE
MODULE TITLE SSESSMENT TYPE
MMME4056Integrated SystemsAnalysisSimulink and Report
COURSEWORK TITLE
WEIGHT (INDICATIVE EFFORT) MMME4056, ISA 2024, COURSEWORK30% (Approx. 10-15hrs)
FEEDBACK DETAILS
Feedback will be provided within 20 working days and will consist of an individual feedbackform. Please note the marks released on Moodle are raw. If you have made a late submissionand it is not covered by an EC or an accommodation then the deductions will be made when Isubmit the marks to the board after the exams.LEARNING OUTCOMES ASSESSED (IN BOLD)
- Demonstrate an understanding of the concept of system behaviour and the design of
experiments for characterising system components. - AHEP4: 2, 6
- Critically evaluate and analyse complex dynamic systems behaviour using an
appropriate numerical or analytical methodology - AHEP4: 1, 2, 3, 6
- 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 becopied from the internet. In ALL cases they should be appropriately titled andcaptioned. The titles and captions should be clear and legible.
- You may not discuss the details of your answers with other students. Software checkswill 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 usethe 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 floatingsupports for wind turbines achieve stability by having a centre of massbelow the centre of buoyancy (i.e. the centre of gravity of the displacedwater).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 ofthe wind turbine, the entire structure rocks backwards a little bit. As thestructure is moving backwards relative to the oncoming wind, the relativewind 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. Thiscoursework is based on modelling the dynamics of such a floating windturbine platform and applying the methods taught within代寫MMME4056 Integrated System sAnalysis Simulink 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 fixedrated wind speed vrated. For wind speeds lower than the rated wind speed(v(t) < vrated),theturbine controller tries to extract the maximum availablepower from the air and this results in a downwind thrust that isproportional to the square of the wind speed, 𝐹(𝑡) = 𝑎 × 𝑣(𝑡) 2 . Bycontrast, 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 thecontroller must deliberately spill some power by pitching the bladessuitably. This results in a different downwind force relationship …𝐹(𝑡) = 𝑎 × 𝑣𝑟𝑎𝑡𝑒𝑑 3⁄𝑣(𝑡). Figure 2 below shows a typical relationshipbetween 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 REQUIREMENTSThe requirement of this coursework is to understand this floating wind turbine as a simple dynamic system, to
mulate its behaviour as wind-speed changes using SIMULINK and to analyse its behaviour at two differentequilibrium states using methods taught in the course.
The submission should be based on what is explicitly asked for in this coursework specification. The primarymaterial being marked is a report – although you are asked to submit your SIMULINK models also. It must bepossible to open the SIMULINK models submitted using the version of MATLAB presently installed onUniversity 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 bymodifying each line of code carrying the comment % Modify this line In some cases, the modification simply involves you inserting the appropriatenumerical 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 canobtain 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 vs. time. You mightchoose 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 greenarrowhead in the top toolbar of the editor or else by just typing >>start_hereat 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 aWORD or PDF document) and all files that you used inthe CW.IMPORTANT: Please make clear on the first page of the report which student you are by identifying whichStudent ID# (SID# in the spreadsheet) applies to you (a number less than 401). If, for some reason, you do not findyour 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, 𝑞9.5} and {𝐹14,𝜙14, 𝑞14}.
- 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-spaceepresentation for one condition (you need not repeat this explanation) and how you used the state-spacerepresentation to determine how q(t) varies with respect to time, t. Also a graph representing q(t) vs. t fromeach 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 atv(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 indicatesdifferentiation with respect to time. The angle 𝜙 ismeasured in radians.
1) Define: 𝑤(𝑡) ≔ 𝑣(𝑡) − 𝐻 × 𝑐𝑜𝑠(𝜙) × 𝜙(𝑡)
(2) If𝑤(𝑡) > 𝑣𝑐𝑢𝑡𝑜𝑢𝑡, 𝐹(𝑡) = (𝑎 × 𝑣𝑟𝑎𝑡𝑒𝑑 3⁄𝑣𝑐𝑢𝑡𝑜𝑢𝑡) ∗ exp (−5(𝑤(𝑡) − 𝑣𝑐𝑢𝑡𝑜𝑢𝑡))Otherwise if 𝑤(𝑡) ≥ 𝑣𝑟𝑎𝑡𝑒𝑑, 𝐹(𝑡) = 𝑎 × 𝑣𝑟𝑎𝑡𝑒𝑑 3⁄𝑤(𝑡)Otherwise 𝑤(𝑡) < 𝑣𝑟𝑎𝑡𝑒𝑑 and 𝐹(𝑡) = 𝑎 × 𝑤(𝑡)2× 𝑠𝑖𝑔𝑛(𝑤(𝑡))
3) 𝐽 × 𝜙(𝑡) + 𝑐 × 𝜙(𝑡) + 𝑘 × 𝜙(𝑡) = 𝐹(𝑡) × 𝐻 × 𝑐𝑜𝑠2 (𝜙)(4) 𝑞 = 𝐻 × 𝑠𝑖𝑛(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”) ineach un-shaded box of the table below to identify the nature of each quantity that appears in the equations.Quantity An Input ?er there is any other state variable not mentioned in the table above. State also whether there is anyother 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 thatfunction 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 windspeeds 9.5m/s and 14m/s. For each of these speeds, reportthe following steady values,𝐹9HINT: There is no “closed-form” solution here so you will have to apply an iterative approach of some sort. Amanual iteration process is fine. You do not have to write any code to implement an iterative solution automaticallyor 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 sinusoidallyaccording to 𝑣(𝑡) = 9.5 + 0.2𝑐𝑜𝑠(0.2𝑡). 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 conditionsdiscovered 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 theseeigenvalues tell you. Modify the SIMULINK model from Task 4 so that the input wind speed is now a steady14m/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 whatyou found fromhe eigenvalues of matrix A.
[15 marks]